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Augustine believed that in a real presence of Christ in the Eucharist, saying that Christ's statement, "This is my body" referred to the bread he carried in his hands, and that Christians must have faith the bread and wine are in fact the body and blood of Christ, despite what they see with their eyes. For instance, he stated that "He [Jesus] walked here in the same flesh, and gave us the same flesh to be eaten unto salvation. But no one eats that flesh unless first he adores it; and thus it is discovered how such a footstool of the Lord's feet is adored; and not only do we not sin by adoring, we do sin by not adoring." Presbyterian professor and author John Riggs argued that Augustine held that Christ is really present in the elements of the Eucharist, but not in a bodily manner, because his body remains in Heaven. Augustine, in his work "On Christian Doctrine", referred to the Eucharist as a "figure" and a "sign". Against the Pelagians, Augustine strongly stressed the importance of infant baptism. About the question whether baptism is an absolute necessity for salvation, however, Augustine appears to have refined his beliefs during his lifetime, causing some confusion among later theologians about his position. He said in one of his sermons that only the baptized are saved. This belief was shared by many early Christians. However, a passage from his "City of God", concerning the Apocalypse, may indicate Augustine did believe in an exception for children born to Christian parents.
Philosophy. Astrology. Augustine's contemporaries often believed astrology to be an exact and genuine science. Its practitioners were regarded as true men of learning and called "mathematici". Astrology played a prominent part in Manichaean doctrine, and Augustine himself was attracted by their books in his youth, being particularly fascinated by those who claimed to foretell the future. Later, as a bishop, he warned that one should avoid astrologers who combine science and horoscopes. (Augustine's term "mathematici", meaning "astrologers", is sometimes mistranslated as "mathematicians".) According to Augustine, they were not genuine students of Hipparchus or Eratosthenes but "common swindlers". Epistemology. Epistemological concerns shaped Augustine's intellectual development. His early dialogues "Contra academicos" (386) and "De Magistro" (389), both written shortly after his conversion to Christianity, reflect his engagement with sceptical arguments and show the development of his doctrine of divine illumination. The doctrine of illumination claims God plays an active and regular part in human perception and understanding by illuminating the mind so human beings can recognize intelligible realities God presents (as opposed to God designing the human mind to be reliable consistently, as in, for example, Descartes's idea of clear and distinct perceptions). According to Augustine, illumination is obtainable to all rational minds and is different from other forms of sense perception. It is meant to be an explanation of the conditions required for the mind to have a connection with intelligible entities.
Augustine also posed the problem of other minds throughout different works, most famously perhaps in "On the Trinity" (VIII.6.9), and developed what has come to be a standard solution: the argument from analogy to other minds. In contrast to Plato and other earlier philosophers, Augustine recognized the centrality of testimony to human knowledge and argued that what others tell us can provide knowledge even if we do not have independent reasons to believe their testimonial reports. Just war. Augustine asserted Christians should be pacifists as a personal, philosophical stance. However, peacefulness in the face of a grave wrong that could only be stopped by violence would be a sin. Defence of one's self or others could be a necessity, especially when authorized by a legitimate authority. While not breaking down the conditions necessary for war to be just, Augustine coined the phrase in his work "The City of God". In essence, the pursuit of peace must include the option of fighting for its long-term preservation. Such a war could not be pre-emptive, but defensive, to restore peace. Thomas Aquinas, centuries later, used the authority of Augustine's arguments in an attempt to define the conditions under which a war could be just.
Free will. Included in Augustine's earlier theodicy is the claim God created humans and angels as rational beings possessing free will. Free will was not intended for sin, meaning it is not equally predisposed to both good and evil. A will defiled by sin is not considered as "free" as it once was because it is bound by material things, which could be lost or be difficult to part with, resulting in unhappiness. Sin impairs free will, while grace restores it. Only a will that was once free can be subjected to sin's corruption. After 412, Augustine changed his theology, teaching that humanity had no free will to believe in Christ but only a free will to sin: "I in fact strove on behalf of the free choice of the human 'will,' but God's grace conquered" ("Retract". 2.1). The early Christians opposed the deterministic views (e.g., fate) of Stoics, Gnostics, and Manichaeans prevalent in the first four centuries. Christians championed the concept of a relational God who interacts with humans rather than a Stoic or Gnostic God who unilaterally foreordained every event (yet Stoics still claimed to teach free will). Patristics scholar Ken Wilson argues that every early Christian author with extant writings who wrote on the topic prior to Augustine of Hippo (412) advanced human free choice rather than a deterministic God. According to Wilson, Augustine taught traditional free choice until 412, when he reverted to his earlier Manichaean and Stoic deterministic training when battling the Pelagians. Only a few Christians accepted Augustine's view of free will until the Protestant Reformation when both Luther and Calvin embraced Augustine's deterministic teachings wholeheartedly.
The Catholic Church considers Augustine's teaching to be consistent with free will. He often said that anyone can be saved if they wish. While God knows who will and will not be saved, with no possibility for the latter to be saved in their lives, this knowledge represents God's perfect knowledge of how humans will freely choose their destinies. Sociology, morals and ethics. Natural law. Augustine was among the earliest to examine the legitimacy of the laws of man, and attempt to define the boundaries of what laws and rights occur naturally, instead of being arbitrarily imposed by mortals. All who have wisdom and conscience, he concludes, are able to use reason to recognize the "lex naturalis", natural law. Mortal law should not attempt to force people to do what is right or avoid what is wrong, but simply to remain just. Therefore "an unjust law is no law at all". People are not obligated to obey laws that are unjust, those that their conscience and reason tell them violate natural law and rights. Slavery. Augustine led many clergy under his authority at Hippo to free their slaves as a "pious and holy" act. He boldly wrote a letter urging the emperor to set up a new law against slave traders and was very much concerned about the sale of children. Christian emperors of his time for 25 years had permitted the sale of children, not because they approved of the practice, but as a way of preventing infanticide when parents were unable to care for a child. Augustine noted that the tenant farmers in particular were driven to hire out or to sell their children as a means of survival.
In his book, "The City of God", he presents the development of slavery as a product of sin and as contrary to God's divine plan. He wrote that God "did not intend that this rational creature, who was made in his image, should have dominion over anything but the irrational creation – not man over man, but man over the beasts". Thus he wrote that righteous men in primitive times were made shepherds of cattle, not kings over men. "The condition of slavery is the result of sin", he declared. In "The City of God", Augustine wrote he felt the existence of slavery was a punishment for the existence of sin, even if an individual enslaved person committed no sin meriting punishment. He wrote: "Slavery is, however, penal, and is appointed by that law which enjoins the preservation of the natural order and forbids its disturbance." Augustine believed slavery did more harm to the slave owner than the enslaved person himself: "the lowly position does as much good to the servant as the proud position does harm to the master." Augustine proposes as a solution to sin a type of cognitive reimagining of one's situation, where slaves "may themselves make their slavery in some sort free, by serving not in crafty fear, but in faithful love," until the end of the world eradicated slavery for good: "until all unrighteousness pass away, and all principality and every human power be brought to nothing, and God be all in all."
Jews. Against certain Christian movements, some of which rejected the use of Hebrew Scripture, Augustine countered that God had chosen the Jews as a special people, and he considered the scattering of Jewish people by the Roman Empire to be a fulfilment of prophecy. He rejected homicidal attitudes, quoting part of the same prophecy, namely "Slay them not, lest they should at last forget Thy law" (Psalm 59:11). Augustine, who believed Jewish people would be converted to Christianity at "the end of time", argued God had allowed them to survive their dispersion as a warning to Christians; as such, he argued, they should be permitted to dwell in Christian lands. The sentiment sometimes attributed to Augustine that Christians should let the Jews "survive but not thrive" (it is repeated by the author James Carroll in his book "Constantine's Sword", for example) is apocryphal and is not found in any of his writings. Sexuality and the sexes.
Before the Fall, Augustine believed sex was a passionless affair, "just like many a laborious work accomplished by the compliant operation of our other limbs, without any lascivious heat", that the seed "might be sown without any shameful lust, the genital members simply obeying the inclination of the will". After the Fall, by contrast, the penis cannot be controlled by mere will, subject instead to both unwanted impotence and involuntary erections: "Sometimes the urge arises unwanted; sometimes, on the other hand, it forsakes the eager lover, and desire grows cold in the body while burning in the mind... It arouses the mind, but it does not follow through what it has begun and arouse the body also" ("City of God" 14.16). Augustine censured those who try to prevent the creation of offspring when engaging in sexual relations, saying that though they may be nominally married they are not really, but are using that designation as a cloak for turpitude. When they allow their unwanted children to die of exposure, they unmask their sin. Sometimes they use drugs to produce sterility, or other means to try to destroy the fetus before they are born. Their marriage is not wedlock but debauchery.
Augustine believed Adam and Eve had both already chosen in their hearts to disobey God's command not to eat of the Tree of Knowledge before Eve took the fruit, ate it, and gave it to Adam. Accordingly, Augustine did not believe Adam was any less guilty of sin. Augustine praises women and their role in society and in the Church. In his "Tractates on the Gospel of John", Augustine, commenting on the Samaritan woman from John 4:1–42, uses the woman as a figure of the Church in agreement with the New Testament teaching that the Church is the bride of Christ. "Husbands, love your wives, as Christ loved the church and gave himself up for her." Augustine believed that "woman has been made for man" and that "in sex she is physically subject to him in the same way as our natural impulses need to be subjected to the reasoning power of the mind, in order that the actions to which they lead may be inspired by the principles of good conduct". Women were created as a "helper" to men for Augustine. Pedagogy. Augustine is considered an influential figure in the history of education. A work early in Augustine's writings is "De Magistro" (On the Teacher), which contains insights into education. His ideas changed as he found better directions or better ways of expressing his ideas. In the last years of his life, Augustine wrote his "Retractationes" ("Retractations"), reviewing his writings and improving specific texts. Henry Chadwick believes an accurate translation of "retractationes" may be "reconsiderations". Reconsiderations can be seen as an overarching theme of the way Augustine learned. Augustine's understanding of the search for understanding, meaning, and truth as a restless journey leaves room for doubt, development, and change.
Augustine was a strong advocate of critical thinking skills. Because written works were limited during this time, spoken communication of knowledge was very important. His emphasis on the importance of community as a means of learning distinguishes his pedagogy from some others. Augustine believed dialectic is the best means for learning and that this method should serve as a model for learning encounters between teachers and students. Augustine's dialogue writings model the need for lively interactive dialogue among learners. He recommended adapting educational practices to fit the students' educational backgrounds: If a student has been well educated in a wide variety of subjects, the teacher must be careful not to repeat what they have already learned, but to challenge the student with material they do not yet know thoroughly. With the student who has had no education, the teacher must be patient, willing to repeat things until the student understands, and sympathetic. Perhaps the most difficult student, however, is the one with an inferior education who believes he understands something when he does not. Augustine stressed the importance of showing this type of student the difference between "having words and having understanding" and of helping the student to remain humble with his acquisition of knowledge.
Under the influence of Bede, Alcuin, and Rabanus Maurus, "De catechizandis rudibus" came to exercise an important role in the education of clergy at the monastic schools, especially from the eighth century onwards. Augustine believed students should be given an opportunity to apply learned theories to practical experience. Yet another of Augustine's major contributions to education is his study on the styles of teaching. He claimed there are two basic styles a teacher uses when speaking to the students. The "mixed style" includes complex and sometimes showy language to help students see the beautiful artistry of the subject they are studying. The "grand style" is not quite as elegant as the mixed style, but is exciting and heartfelt, with the purpose of igniting the same passion in the students' hearts. Augustine balanced his teaching philosophy with the traditional Bible-based practice of strict discipline. Augustine knew Latin and Ancient Greek. He had a long correspondence with St Jerome regarding the textual differences existing between the Hebrew Bible and the Greek Septuagint, concluding that the original Greek manuscripts were closely similar to the other Hebrew ones, and also that even the differences in the two original versions of the Holy Scripture could enlight its spiritual meaning to have been unitarily inspired by God.
Coercion. Augustine of Hippo had to deal with issues of violence and coercion throughout his entire career due largely to the Donatist-Catholic conflict. He is one of the very few authors in Antiquity who ever truly theoretically examined the ideas of religious freedom and coercion. Augustine handled the infliction of punishment and the exercise of power over law-breakers by analyzing these issues in ways similar to modern debates on penal reform. His teaching on coercion has "embarrassed his modern defenders and vexed his modern detractors," because it is seen as making him appear "to generations of religious liberals as "le prince et patriarche de persecuteurs."" Yet Brown asserts that, at the same time, Augustine becomes "an eloquent advocate of the ideal of corrective punishment" and reformation of the wrongdoer. Russell says Augustine's theory of coercion "was not crafted from dogma, but in response to a unique historical situation" and is, therefore, context-dependent, while others see it as inconsistent with his other teachings.
The context. During the Great Persecution, "When Roman soldiers came calling, some of the [Catholic] officials handed over the sacred books, vessels, and other church goods rather than risk legal penalties" over a few objects. Maureen Tilley says this was a problem by 305, that became a schism by 311, because many of the North African Christians had a long established tradition of a "physicalist approach to religion." The sacred scriptures were not simply books to them, but were the Word of God in physical form, therefore they saw handing over the Bible, and handing over a person to be martyred, as "two sides of the same coin." Those who cooperated with the authorities became known as "traditores." The term originally meant "one who hands over a physical object", but it came to mean "traitor". According to Tilley, after the persecution ended, those who had apostatized wanted to return to their positions in the church. The North African Christians, (the rigorists who became known as Donatists), refused to accept them. Catholics were more tolerant and wanted to wipe the slate clean. For the next 75 years, both parties existed, often directly alongside each other, with a double line of bishops for the same cities. Competition for the loyalty of the people included multiple new churches and violence. No one is exactly sure when the Circumcellions and the Donatists allied, but for decades, they fomented protests and street violence, accosted travellers and attacked random Catholics without warning, often doing serious and unprovoked bodily harm such as beating people with clubs, cutting off their hands and feet, and gouging out eyes.
Augustine became coadjutor Bishop of Hippo in 395, and since he believed that conversion must be voluntary, his appeals to the Donatists were verbal. For several years, he used popular propaganda, debate, personal appeal, General Councils, appeals to the emperor and political pressure to bring the Donatists back into union with the Catholics, but all attempts failed. The harsh realities Augustine faced can be found in his Letter 28 written to bishop Novatus around 416. Donatists had attacked, cut out the tongue and cut off the hands of a Bishop Rogatus who had recently converted to Catholicism. An unnamed count of Africa had sent his agent with Rogatus, and he too had been attacked; the count was "inclined to pursue the matter." Russell says Augustine demonstrates a "hands-on" involvement with the details of his bishopric, but at one point in the letter, he confesses he does not know what to do. "All the issues that plague him are there: stubborn Donatists, Circumcellion violence, the vacillating role of secular officials, the imperative to persuade, and his own trepidations." The empire responded to the civil unrest with the law and its enforcement, and thereafter, Augustine changed his mind about using verbal arguments alone. Instead, he came to support the state's use of coercion. Augustine did not believe the empire's enforcement would "make the Donatists more virtuous" but he did believe it would make them "less vicious."
The theology. The primary 'proof-text' of what Augustine thought concerning coercion is from Letter 93, written in 408, as a reply to bishop Vincentius, of Cartenna (Mauretania, North Africa). This letter shows that both practical and biblical reasons led Augustine to defend the legitimacy of coercion. He confesses that he changed his mind because of "the ineffectiveness of dialogue and the proven efficacy of laws." He had been worried about false conversions if force was used, but "now," he says, "it seems imperial persecution is working." Many Donatists had converted. "Fear had made them reflect, and made them docile." Augustine continued to assert that coercion could not directly convert someone, but concluded it could make a person ready to be reasoned with. According to Mar Marcos, Augustine made use of several biblical examples to legitimize coercion, but the primary analogy in Letter 93 and in Letter 185, is the parable of the Great Feast in Luke 14.15–24 and its statement "compel them to come in." Russell says, Augustine uses the Latin term "cogo", instead of the "compello" of the Vulgate, since to Augustine, "cogo" meant to "gather together" or "collect" and was not simply "compel by physical force."
In 1970, Robert Markus argued that, for Augustine, a degree of external pressure being brought for the purpose of reform was compatible with the exercise of free will. Russell asserts that "Confessions 13" is crucial to understanding Augustine's thought on coercion; using Peter Brown's explanation of Augustine's view of salvation, he explains that Augustine's past, his own sufferings and "conversion through God's pressures," along with his biblical hermeneutics, is what led him to see the value in suffering for discerning truth. According to Russell, Augustine saw coercion as one among many conversion strategies for forming "a pathway to the inner person." In Augustine's view, there is such a thing as just and unjust persecution. Augustine explains that when the purpose of persecution is to lovingly correct and instruct, then it becomes discipline and is just. He said the church would discipline its people out of a loving desire to heal them, and that, "once compelled to come in, heretics would gradually give their voluntary assent to the truth of Christian orthodoxy." Frederick H. Russell describes this as "a pastoral strategy in which the church did the persecuting with the dutiful assistance of Roman authorities," adding that it is "a precariously balanced blend of external discipline and inward nurturance."
Augustine placed limits on the use of coercion, recommending fines, imprisonment, banishment, and moderate floggings, preferring beatings with rods which was a common practice in the ecclesial courts. He opposed severity, maiming, and the execution of heretics. While these limits were mostly ignored by Roman authorities, Michael Lamb says that in doing this, "Augustine appropriates republican principles from his Roman predecessors..." and maintains his commitment to liberty, legitimate authority, and the rule of law as a constraint on arbitrary power. He continues to advocate holding authority accountable to prevent domination but affirms the state's right to act. Herbert A. Deane, on the other hand, says there is a fundamental inconsistency between Augustine's political thought and "his final position of approval of the use of political and legal weapons to punish religious dissidence" and others have seconded this view. Brown asserts that Augustine's thinking on coercion is more of an attitude than a doctrine since it is "not in a state of rest," but is instead marked by "a painful and protracted attempt to embrace and resolve tensions."
According to Russell, it is possible to see how Augustine himself had evolved from his earlier "Confessions" to this teaching on coercion and the latter's strong patriarchal nature: "Intellectually, the burden has shifted imperceptibly from discovering the truth to disseminating the truth." The bishops had become the church's elite with their own rationale for acting as "stewards of the truth." Russell points out that Augustine's views are limited to time and place and his own community, but later, others took what he said and applied it outside those parameters in ways Augustine never imagined or intended. Works. Augustine was one of the most prolific Latin authors in terms of surviving works, and the list of his works consists of more than one hundred separate titles. They include apologetic works against the heresies of the Arians, Donatists, Manichaeans and Pelagians; texts on Christian doctrine, notably ("On Christian Doctrine"); exegetical works such as commentaries on Genesis, the Psalms and Paul's Letter to the Romans; many sermons and letters; and the "Retractationes", a review of his earlier works which he wrote near the end of his life.
Apart from those, Augustine is probably best known for his "Confessions", which is a personal account of his earlier life, and for "De civitate Dei" ("The City of God", consisting of 22 books), which he wrote to restore the confidence of his fellow Christians, which was badly shaken by the sack of Rome by the Visigoths in 410. His "On the Trinity", in which he developed what has become known as the 'psychological analogy' of the Trinity, is also considered to be among his masterpieces, and arguably of more doctrinal importance than the "Confessions" or the "City of God". He also wrote "On Free Choice of the Will" ("De libero arbitrio"), addressing why God gives humans free will that can be used for evil. Legacy. In both his philosophical and theological reasoning, Augustine was greatly influenced by Stoicism, Platonism and Neoplatonism, particularly by the work of Plotinus, author of the "Enneads", probably through the mediation of Porphyry and Victorinus (as Pierre Hadot has argued). Some Neoplatonic concepts are still visible in Augustine's early writings. His early and influential writing on the human will, a central topic in ethics, would become a focus for later philosophers such as Schopenhauer, Kierkegaard, and Nietzsche. He was also influenced by the works of Virgil (known for his teaching on language), and Cicero (known for his teaching on argument). Augustine, along with Ambrose, Jerome and pope Gregory the Great, is considered one of the four Great Latin Church Fathers.
In philosophy. Philosopher Bertrand Russell was impressed by Augustine's meditation on the nature of time in the "Confessions", comparing it favourably to Kant's version of the view that time is subjective. Catholic theologians generally subscribe to Augustine's belief that God exists outside of time in the "eternal present"; that time only exists within the created universe because only in space is time discernible through motion and change. His meditations on the nature of time are closely linked to his consideration of the human ability of memory. Frances Yates in her 1966 study "The Art of Memory" argues that a brief passage of the "Confessions", 10.8.12, in which Augustine writes of walking up a flight of stairs and entering the vast fields of memory clearly indicates that the ancient Romans were aware of how to use explicit spatial and architectural metaphors as a mnemonic technique for organizing large amounts of information. Augustine's philosophical method, especially demonstrated in his "Confessions", had a continuing influence on Continental philosophy throughout the 20th century. His descriptive approach to intentionality, memory, and language as these phenomena are experienced within consciousness and time anticipated and inspired the insights of modern phenomenology and hermeneutics. Edmund Husserl writes: "The analysis of time-consciousness is an age-old crux of descriptive psychology and theory of knowledge. The first thinker to be deeply sensitive to the immense difficulties to be found here was Augustine, who laboured almost to despair over this problem."
Martin Heidegger refers to Augustine's descriptive philosophy at several junctures in his influential work "Being and Time". Hannah Arendt began her philosophical writing with a dissertation on Augustine's concept of love, "Der Liebesbegriff bei Augustin" (1929): "The young Arendt attempted to show that the philosophical basis for "vita socialis" in Augustine can be understood as residing in neighbourly love, grounded in his understanding of the common origin of humanity." Jean Bethke Elshtain in "Augustine and the Limits of Politics" tried to associate Augustine with Arendt in their concept of evil: "Augustine did not see evil as glamorously demonic but rather as absence of good, something which paradoxically is really nothing. Arendt ... envisioned even the extreme evil which produced the Holocaust as merely banal [in "Eichmann in Jerusalem"]." Augustine's philosophical legacy continues to influence contemporary critical theory through the contributions and inheritors of these 20th-century figures. Seen from a historical perspective, there are three main perspectives on the political thought of Augustine: first, political Augustinianism; second, Augustinian political theology; and third, Augustinian political theory.
In theology. The historian Diarmaid MacCulloch has written: "Augustine's impact on Western Christian thought can hardly be overstated; only his beloved example, Paul of Tarsus, has been more influential, and Westerners have generally seen Paul through Augustine's eyes." Thomas Aquinas was influenced heavily by Augustine. On the topic of original sin, Aquinas proposed a more optimistic view of man than that of Augustine in that his conception leaves to the reason, will, and passions of fallen man their natural powers even after the Fall, without "supernatural gifts". While in his pre-Pelagian writings Augustine taught that Adam's guilt as transmitted to his descendants much enfeebles, though does not destroy, the freedom of their will, Protestant reformers Martin Luther and John Calvin affirmed that Original Sin completely destroyed liberty (see total depravity). According to Leo Ruickbie, Augustine's arguments against magic, differentiating it from a miracle, were crucial in the early Church's fight against paganism and became a central thesis in the later denunciation of witches and witchcraft. According to Professor Deepak Lal, Augustine's vision of the heavenly city has influenced the secular projects and traditions of the Enlightenment, Marxism, Freudianism and eco-fundamentalism. Post-Marxist philosophers Antonio Negri and Michael Hardt rely heavily on Augustine's thoughts, particularly "The City of God", in their book of political philosophy "Empire".
Augustine has influenced many modern-day theologians and authors such as John Piper. Hannah Arendt, an influential 20th-century political theorist, wrote her doctoral dissertation in philosophy on Augustine, and continued to rely on his thought throughout her career. Ludwig Wittgenstein extensively quotes Augustine in "Philosophical Investigations" for his approach to language, both admiringly, and as a sparring partner to develop his own ideas, including an extensive opening passage from the "Confessions". Contemporary linguists have argued that Augustine has significantly influenced the thought of Ferdinand de Saussure, who did not 'invent' the modern discipline of semiotics, but rather built upon Aristotelian and Neoplatonic knowledge from the Middle Ages, via an Augustinian connection: "as for the constitution of Saussurian semiotic theory, the importance of the Augustinian thought contribution (correlated to the Stoic one) has also been recognized. Saussure did not do anything but reform an ancient theory in Europe, according to the modern conceptual exigencies."
Pope Francis suggests that Augustine's reflections on the relationship between the "beloved disciple" and Jesus (John 13:23: "reclining next to him") contributed to the development of devotion to the Sacred Heart in the following centuries. In his autobiographical book "Milestones", Pope Benedict XVI notes that Augustine was one of the deepest influences in his thought. Oratorio, music. Marc-Antoine Charpentier, Motet "Pour St Augustin mourant", H.419, for 2 voices and continuo (1687), and "Pour St Augustin", H.307, for 2 voices and continuo (1670s). Much of Augustine's conversion is dramatized in the oratorio "La conversione di Sant'Agostino" (1750) composed by Johann Adolph Hasse. The libretto for this oratorio, written by Duchess Maria Antonia of Bavaria, draws upon the influence of Metastasio (the finished libretto having been edited by him) and is based on an earlier five-act play "Idea perfectae conversionis dive Augustinus" written by the Jesuit priest Franz Neumayr. In the libretto Augustine's mother Monica is presented as a prominent character that is worried that Augustine might not convert to Christianity. As Dr. Andrea Palent says: Throughout the oratorio Augustine shows his willingness to turn to God, but the burden of the act of conversion weighs heavily on him. This is displayed by Hasse through extended recitative passages.
In popular art. In his poem "Confessional", Frank Bidart compares the relationship between Augustine and his mother, Saint Monica, to the relationship between the poem's speaker and his mother. In the 2010 TV miniseries "", Augustine is played by Matteo Urzia (aged 15), Alessandro Preziosi (aged 25) and Franco Nero (aged 76). In 1967, American singer-songwriter Bob Dylan released a song entitled "I Dreamed I Saw St. Augustine" as part of his album "John Wesley Harding". The song has been covered by several artists including Joan Baez, Vic Chesnutt, Eric Clapton, John Doe, Thea Gilmore, Adam Selzer and Dirty Projectors. In 2016, the band The Chairman Dances released "Augustine", a response song to Bob Dylan’s "I Dreamed I Saw St. Augustine". In it, Augustine says he's not sure why Dylan dreams about him. English pop/rock musician, singer and songwriter Sting wrote a song related to Saint Augustine entitled "Saint Augustine in Hell" which was part of his fourth solo studio album "Ten Summoner's Tales" released in March 1993.
Acting Acting is an activity in which a story is told by means of its enactment by an actor who adopts a character—in theatre, television, film, radio, or any other medium that makes use of the mimetic mode. Acting involves a broad range of skills, including a well-developed imagination, emotional facility, physical expressivity, vocal projection, clarity of speech, and the ability to interpret drama. Acting also demands an ability to employ dialects, accents, improvisation, observation and emulation, mime, and stage combat. Many actors train at length in specialist programs or colleges to develop these skills. The vast majority of professional actors have gone through extensive training. Actors and actresses will often have many instructors and teachers for a full range of training involving singing, scene-work, audition techniques, and acting for camera. Most early sources in the West that examine the art of acting (, "hypokrisis") discuss it as part of rhetoric. History. One of the first known actors was an ancient Greek called Thespis of Icaria in Athens. Writing two centuries after the event, Aristotle in his "Poetics" () suggests that Thespis stepped out of the dithyrambic chorus and addressed it as a separate character. Before Thespis, the chorus narrated (for example, "Dionysus did this, Dionysus said"). When Thespis stepped out from the chorus, he spoke as if he were the character (for example, "I am Dionysus, I did this"). To distinguish between these different modes of storytelling—enactment and narration—Aristotle uses the terms "mimesis" (via enactment) and "diegesis" (via narration). From the Greek actor Thespis' name derives the word "thespian".
Training. Conservatories and drama schools typically offer two- to four-year training on all aspects of acting. Universities mostly offer three- to four-year programs, in which a student is often able to choose to focus on acting, whilst continuing to learn about other aspects of theatre. Schools vary in their approach, but in North America the most popular method taught derives from the 'system' of Konstantin Stanislavski, which was developed and popularised in America as method acting by Lee Strasberg, Stella Adler, Sanford Meisner, and others. Other approaches may include a more physically based orientation, such as that promoted by theatre practitioners as diverse as Anne Bogart, Jacques Lecoq, Jerzy Grotowski, or Vsevolod Meyerhold. Classes may also include psychotechnique, mask work, physical theatre, improvisation, and acting for camera. Regardless of a school's approach, students should expect intensive training in textual interpretation, voice, and movement. Applications to drama programmes and conservatories usually involve extensive auditions. Anybody over the age of 18 can usually apply. Training may also start at a very young age. Acting classes and professional schools targeted at under-18s are widespread. These classes introduce young actors to different aspects of acting and theatre, including scene study.
Increased training and exposure to public speaking allows people to maintain a calmer and more relaxed physiology. Measuring a public speaker's heart rate is perhaps one of the easiest ways to assess changes in stress, as heart rate increases with anxiety. As actors increase their performances, heart rate and other signs of stress may decrease. This is very important in training actors, as adaptive strategies gained from increased exposure to public speaking can regulate implicit and explicit anxiety. By attending an institution that specializes in acting, the increased opportunity to act will lead to a more relaxed physiology and a decrease in stress and its effects on the body. These effects can range from hormonal to cognitive health that can impact quality of life and performance. Improvisation. Some classical forms of acting involve a substantial element of improvised performance. Most notable is its use by the troupes of the "commedia dell'arte", a form of masked comedy that originated in Italy. Improvisation as an approach to acting formed an important part of the Russian theatre practitioner Konstantin Stanislavski's 'system' of actor training, which he developed from the 1910s onwards. Late in 1910, the playwright Maxim Gorky invited Stanislavski to join him in Capri, where they discussed training and Stanislavski's emerging "grammar" of acting. Inspired by a popular theatre performance in Naples that utilised the techniques of the "commedia dell'arte", Gorky suggested that they form a company, modelled on the medieval strolling players, in which a playwright and group of young actors would devise new plays together by means of improvisation. Stanislavski would develop this use of improvisation in his work with his First Studio of the Moscow Art Theatre. Stanislavski's use was extended further in the approaches to acting developed by his students, Michael Chekhov and Maria Knebel.
In the United Kingdom, the use of improvisation was pioneered by Joan Littlewood from the 1930s onwards and, later, by Keith Johnstone and Clive Barker. In the United States, it was promoted by Viola Spolin, after working with Neva Boyd at a Hull House in Chicago, Illinois (Spolin was Boyd's student from 1924 to 1927). Like the British practitioners, Spolin felt that playing games was a useful means of training actors and helped to improve an actor's performance. With improvisation, she argued, people may find expressive freedom, since they do not know how an improvised situation will turn out. Improvisation demands an open mind in order to maintain spontaneity, rather than pre-planning a response. A character is created by the actor, often without reference to a dramatic text, and a drama is developed out of the spontaneous interactions with other actors. This approach to creating new drama has been developed most substantially by the British filmmaker Mike Leigh, in films such as "Secrets & Lies" (1996), "Vera Drake" (2004), "Another Year" (2010), and "Mr. Turner" (2014).
Improvisation is also used to cover up if an actor or actress makes a mistake. Physiological effects. Acting in front of an audience many times can cause "stage fright", a form of stress in which someone becomes anxious in front of an audience. This is common among actors, especially new actors, and can cause symptoms such as increased heart rate, increased blood pressure, and sweating. In a 2017 study on American university students, actors of various experience levels all showed similarly elevated heart rates throughout their performances; this agrees with previous studies on professional and amateur actors' heart rates. While all actors experienced stress, causing elevated heart rate, the more experienced actors displayed less heart rate variability than the less experienced actors in the same play. The more experienced actors experienced less stress while performing, and therefore had a smaller degree of variability than the less experienced, more stressed actors. The more experienced an actor is, the more stable their heart rate will be while performing, but will still experience elevated heart rates.
Semiotics. The semiotics of acting involves a study of the ways in which aspects of a performance come to operate for its audience as signs. This process largely involves the production of meaning, whereby elements of an actor's performance acquire significance, both within the broader context of the dramatic action and in the relations each establishes with the real world. Following the ideas proposed by the Surrealist theorist Antonin Artaud, however, it may also be possible to understand communication with an audience that occurs 'beneath' significance and meaning (which the semiotician Félix Guattari described as a process involving the transmission of "a-signifying signs"). In his "The Theatre and its Double" (1938), Artaud compared this interaction to the way in which a snake charmer communicates with a snake, a process which he identified as "mimesis"—the same term that Aristotle in his "Poetics" () used to describe the mode in which drama communicates its story, by virtue of its embodiment by the actor enacting it, as distinct from "diegesis", or the way in which a narrator may describe it. These "vibrations" passing from the actor to the audience may not necessarily precipitate into significant elements as such (that is, consciously perceived "meanings"), but rather may operate by means of the circulation of "affects".
The approach to acting adopted by other theatre practitioners involve varying degrees of concern with the semiotics of acting. Konstantin Stanislavski, for example, addresses the ways in which an actor, building on what he calls the "experiencing" of a role, should also shape and adjust a performance in order to support the overall significance of the drama—a process that he calls establishing the "perspective of the role". The semiotics of acting plays a far more central role in Bertolt Brecht's epic theatre, in which an actor is concerned to bring out clearly the socio historical significance of behaviour and action by means of specific performance choices—a process that he describes as establishing the "not/but" element in a performed physical ""gestus" within context of the play's overall "Fabel"". Eugenio Barba argues that actors ought not to concern themselves with the significance of their performance behaviour; this aspect is the responsibility, he claims, of the director, who weaves the signifying elements of an actor's performance into the director's dramaturgical "montage".
The theatre semiotician Patrice Pavis, alluding to the contrast between Stanislavski's 'system' and Brecht's demonstrating performer—and, beyond that, to Denis Diderot's foundational essay on the art of acting, "Paradox of the Actor" (–78)—argues that: Elements of a semiotics of acting include the actor's gestures, facial expressions, intonation and other vocal qualities, rhythm, and the ways in which these aspects of an individual performance relate to the drama and the theatrical event (or film, television programme, or radio broadcast, each of which involves different semiotic systems) considered as a whole. A semiotics of acting recognises that all forms of acting involve conventions and codes by means of which performance behaviour acquires significance—including those approaches, such as Stanislvaski's or the closely related method acting developed in the United States, that offer themselves as "a natural kind of acting that can do without conventions and be received as self-evident and universal." Pavis goes on to argue that:
The conventions that govern acting in general are related to structured forms of play, which involve, in each specific experience, "rules of the game." This aspect was first explored by Johan Huizinga (in "Homo Ludens", 1938) and Roger Caillois (in "Man, Play and Games", 1958). Caillois, for example, distinguishes four aspects of play relevant to acting: "mimesis" (simulation), "agon" (conflict or competition), "alea" (chance), and "ilinx" (vertigo, or "vertiginous psychological situations" involving the spectator's identification or catharsis). This connection with play as an activity was first proposed by Aristotle in his "Poetics", in which he defines the desire to imitate in play as an essential part of being human and our first means of learning as children: This connection with play also informed the words used in English (as was the analogous case in many other European languages) for drama: the word "play" or "game" (translating the Anglo-Saxon "plèga" or Latin "ludus") was the standard term used until William Shakespeare's time for a dramatic entertainment—just as its creator was a "play-maker" rather than a "dramatist", the person acting was known as a "player", and, when in the Elizabethan era specific buildings for acting were built, they were known as "play-houses" rather than "theatres."
Resumes and auditions. Actors and actresses need to make a resume when applying for roles. The acting resume is very different from a normal resume; it is generally shorter, with lists instead of paragraphs, and it should have a head shot on the back. Sometimes, a resume also contains a short 30-second to 1-minute reel displaying the actor's abilities, so that the casting director can see previous performances, if any. An actor's resume should list projects they have acted in before, such as plays, movies, or shows, as well as special skills and their contact information. Auditioning is the act of performing either a monologue or sides (lines for one character) as sent by the casting director. Auditioning entails showing the actor's skills to present themselves as a different person; it may be as brief as two minutes. For theater auditions it can be longer than two minutes, or they may perform more than one monologue, as each casting director can have different requirements for actors. Actors should go to auditions dressed for the part, to make it easier for the casting director to visualize them as the character. For television or film they will have to undergo more than one audition. Oftentimes actors are called into another audition at the last minute, and are sent the sides either that morning or the night before. Auditioning can be a stressful part of acting, especially if one has not been trained to audition.
Rehearsal. Rehearsal is a process in which actors prepare and practice a performance together with directors and technical staff. Some actors continue to rehearse a scene throughout the run of a show in order to keep the scene fresh in their minds and exciting for the audience. Audience. A critical audience with evaluative spectators is known to induce stress on actors during performance. While public performances cause extremely high stress levels in actors (more so amateur ones), the stress actually improves the performance, supporting the idea of "positive stress in challenging situations." Heart rate. Depending on what an actor is doing, their heart rate will vary. This is the body's way of responding to stress. Prior to a show, one will see an increase in heart rate due to anxiety. While performing an actor has an increased sense of exposure which will increase performance anxiety and the associated physiological arousal, such as heart rate. Heart rates increases more during shows compared to rehearsals because of the increased pressure, which is because a performance has a potentially greater impact on an actor's career. After the show a decrease in the heart rate due to the conclusion of the stress inducing activity can be seen. Often the heart rate will return to normal after the show or performance is done; however, during the applause after the performance there is a rapid spike in heart rate. This can be seen not only in actors but also with public speaking and musicians.
Stress. There is a correlation between heart-rate and stress when actors' are performing in front of an audience. Actors claim that having an audience has no change in their stress level, but as soon as they come on stage their heart-rate rises quickly before they speak their first lines. A 2017 study measuring actors' heart-rate during performance showed that individual heart-rates rose right before the performance began. Length of monologues, experience levels, and actions done on stage were important factors in the study. Heart-rate drops significantly at the end of a monologue, big action scene, or performance. Acting has been shown to be an effective tool for reducing stress created by social anxiety.
Delian League The Delian League was a confederacy of Greek city-states, numbering between 150 and 330, founded in 478 BC under the leadership (hegemony) of Athens, whose purpose was to continue fighting the Persian Empire after the Greek victory in the Battle of Plataea at the end of the Second Persian invasion of Greece. The League functioned as a dual –offensive and defensive– alliance ("symmachia") of autonomous states, similar to its rival association, the Peloponnesian League. The League's modern name derives from its official meeting place, the island of Delos, where congresses were held within the sanctuary of the Temple of Apollo; contemporary authors referred to the organization simply as "the Athenians and their Allies". While Sparta excelled as Greece's greatest power on land, Athens turned to the seas becoming the dominant naval power of the Greek world. Following Sparta's withdrawal from the conflict with Persia, Athens took the lead of the Hellenic alliance accompanied by several states around the Aegean and the Anatolian coast. The Delian League was formed as an anti-Persian defensive association of equal city-states seeking protection under Athens, as the latter wished to extend its support towards the Ionian Greek colonies of Anatolia. By the mid-fifth century BC, the alliance had developed into a naval imperial power, called the Athenian Empire, where Athens established complete dominion and the allies became increasingly less autonomous. The alliance held an assembly of representatives in order to shape its policy, while the members swore an oath of loyalty to the coalition. The Delian League successfully accomplished its principal strategic goal by decisively expelling the remaining Persian forces from the Aegean. As a result, Persia would cease to pose a major threat to Greece for the following fifty years.
From its inception, Athens became the League's biggest source of military power, while more and more allies preferred to pay the dues in cash. Athens began to use the League's funds for its own purposes, like the reinforcement of its naval supremacy, which led to conflicts between the city and its less powerful allies, at times culminating in rebellions, like that of Thasos in 465 BC. The League's treasury initially stood in Delos until, in a symbolic gesture, Pericles moved it to Athens in 454 BC. By 431 BC, the threat that the League presented to Spartan hegemony combined with Athens's heavy-handed control of the Delian League prompted the outbreak of the Peloponnesian War; the League was dissolved upon the war's conclusion in 404 BC under the direction of Lysander, the Spartan commander. Witnessing Sparta's growing hegemony in the first half of the 4th century BC, Athens went on to partly revive the alliance, this time called the Second Athenian League, reestablishing its naval dominance in the eastern Mediterranean.
Background. The Greco-Persian Wars had their roots in the conquest of the Greek cities of Asia Minor, and particularly Ionia, by the Achaemenid Persian Empire of Cyrus the Great shortly after 550 BC. The Persians found the Ionians difficult to rule, eventually settling for sponsoring a tyrant in each Ionian city. While Greek states had in the past often been ruled by tyrants, this form of government was on the decline. By 500 BC, Ionia appears to have been ripe for rebellion against these Persian clients. The simmering tension finally broke into open revolt due to the actions of the tyrant of Miletus, Aristagoras. Attempting to save himself after a disastrous Persian-sponsored expedition in 499 BC, Aristagoras chose to declare Miletus a democracy. This triggered similar revolutions across Ionia, extending to Doris and Aeolis, beginning the Ionian Revolt. The Greek states of Athens and Eretria allowed themselves to be drawn into this conflict by Aristagoras, and during their only campaigning season (498 BC) they contributed to the capture and burning of the Persian regional capital of Sardis. After this, the Ionian revolt carried on (without further outside aid) for a further five years, until it was finally completely crushed by the Persians. However, in a decision of great historic significance, the Persian king Darius the Great decided that, despite having subdued the revolt, there remained the unfinished business of exacting punishment on Athens and Eretria for supporting the revolt. The Ionian revolt had severely threatened the stability of Darius's empire, and the states of mainland Greece would continue to threaten that stability unless dealt with. Darius thus began to contemplate the complete conquest of Greece, beginning with the destruction of Athens and Eretria.
In the next two decades, there would be two Persian invasions of Greece, occasioning, thanks to Greek historians, some of the most famous battles in history. During the first invasion, Thrace, Macedon and the Aegean Islands were added to the Persian Empire, and Eretria was duly destroyed. However, the invasion ended in 490 BC with the decisive Athenian victory at the Battle of Marathon. After this invasion, Darius died, and responsibility for the war passed to his son Xerxes I. Xerxes then personally led a second Persian invasion of Greece in 480 BC, taking an enormous (although oft-exaggerated) army and navy to Greece. Those Greeks who chose to resist (the 'Allies') were defeated in the twin simultaneous battles of Thermopylae on land and Artemisium at sea. All of Greece except the Peloponnesus thus having fallen into Persian hands, the Persians then seeking to destroy the Allied navy once and for all, suffered a decisive defeat at the Battle of Salamis. The following year, 479 BC, the Allies assembled the largest Greek army yet seen and defeated the Persian invasion force at the Battle of Plataea, ending the invasion and the threat to Greece.
The Allied fleet defeated the remnants of the Persian fleet in the Battle of Mycale near the island of Samos—on the same day as Plataea, according to tradition. This action marks the end of the Persian invasion, and the beginning of the next phase in the Greco-Persian wars, the Greek counterattack. After Mycale, the Greek cities of Asia Minor again revolted, with the Persians now powerless to stop them. The Allied fleet then sailed to the Thracian Chersonese, still held by the Persians, and besieged and captured the town of Sestos. The following year, 478 BC, the Allies sent a force to capture the city of Byzantion (modern day Istanbul). The siege was successful, but the behaviour of the Spartan general Pausanias alienated many of the Allies, and resulted in Pausanias's recall. Formation. After Byzantion, Sparta was eager to end its involvement in the war. The Spartans greatly feared the rise of the Athenians as a challenge to their power. Additionally, the Spartans were of the view that, with the liberation of mainland Greece, and the Greek cities of Asia Minor, the war's purpose had already been achieved. There was also perhaps a feeling that establishing long-term security for the Asian Greeks would prove impossible. In the aftermath of Mycale, the Spartan king Leotychidas had proposed transplanting all the Greeks from Asia Minor to Europe as the only method of permanently freeing them from Persian dominion.
Xanthippus, the Athenian commander at Mycale, had furiously rejected this; the Ionian cities had been Athenian colonies, and the Athenians, if no one else, would protect the Ionians. This marked the point at which the leadership of the Greek alliance effectively passed to the Athenians. With the Spartan withdrawal after Byzantion, the leadership of the Athenians became explicit. The loose alliance of city states which had fought against Xerxes's invasion had been dominated by Sparta and the Peloponnesian league. With the withdrawal of these states, a congress was called on the holy island of Delos to institute a new alliance to continue the fight against the Persians; hence the modern designation "Delian League". According to Thucydides, the official aim of the League was to "avenge the wrongs they suffered by ravaging the territory of the king." In reality, this goal was divided into three main efforts—to prepare for future invasion, to seek revenge against Persia, and to organize a means of dividing spoils of war. The members were given a choice of either offering armed forces or paying a tax to the joint treasury; most states chose the tax. League members swore to have the same friends and enemies, and dropped ingots of iron into the sea to symbolize the permanence of their alliance. The Athenian politician Aristides would spend the rest of his life occupied in the affairs of the alliance, dying (according to Plutarch) a few years later in Pontus, whilst determining what the tax of new members was to be.
Members. The Delian League, also known as the Athenian Empire, was a collection of Greek city-states largely based around the Aegean Sea which operated under the hegemony of Athens. This alliance initially served the purpose of coordinating a united Greek front against a perceived looming Persian threat against the Ionian city-states which bordered it. The members of the Delian League were made to swear an oath of loyalty to the league and contributed mostly monetarily but in some instances donated ships or other forces. It was also the case that many democratic members of the League owed their freedom from oligarchic or tyrannical rule to Athens. Because of this, Athens gained an overwhelming advantage in the voting system conducted by relying on the support of democratic city-states Athens had helped into being. By 454 Athens moved the treasury of the Delian League from the Island of Delos to the Parthenon in Athens. Benefitting greatly from the influx of cash coming out of the 150-330 members, Athens used the money to reinforce its own naval supremacy and used the remaining funds to embellish the city with art and architecture. In order to maintain the new synoecism, Athens began using its greatly expanded military to enforce membership in the League. City-states who wished to leave the alliance were punished by Athens with force such as Mytilene and Melos. No longer considered her allies, Athens eventually began to refer to the members of the Delian League as "all the cities Athens rules." Athens also extended its authority over members of the League through judicial decisions. Synoecism under the Athenian Empire was enforced by resolving matters of and between states in Athens by courts composed of Athenian citizens and enforcing those decisions through the Athenian military.
Composition and expansion. In the first ten years of the league's existence, Cimon/Kimon forced Karystos in Euboea to join the league, conquered the island of Skyros and sent Athenian colonists there. Over time, especially with the suppression of rebellions, Athens exercised hegemony over the rest of the league. Thucydides describes how Athens's control over the League grew: Of all the causes of defection, that connected with arrears of tribute and vessels, and with failure of service, was the chief; for the Athenians were very severe and exacting, and made themselves offensive by applying the screw of necessity to men who were not used to and in fact not disposed for any continuous labor. In some other respects the Athenians were not the old popular rulers they had been at first; and if they had more than their fair share of service, it was correspondingly easy for them to reduce any that tried to leave the confederacy. The Athenians also arranged for the other members of the league to pay its share of the expense in money instead of in ships and men, and for this the subject city-states had themselves to blame, their wish to get out of giving service making most leave their homes. Thus while Athens was increasing her navy with the funds they contributed, a revolt always found itself without enough resources or experienced leaders for war.
Rebellion. Naxos. The first member of the league to attempt to secede was the island of Naxos in c. 471 BC. After being defeated, Naxos is believed (based on similar, later revolts) to have been forced to tear down its walls along with losing its fleet and vote in the League. Thasos. In 465 BC, Athens founded the colony of Amphipolis on the Strymon river. Thasos, a member of the League, saw her interests in the mines of Mt. Pangaion threatened and defected from the League to Persia. She called to Sparta for assistance but was denied, as Sparta was facing the largest helot revolt in its history. After more than two years of siege, Thasos surrendered to the Athenian leader Aristides and was forced back into the league. As a result, the fortification walls of Thasos were torn down, and they had to pay yearly tribute and fines. Additionally, their land, naval ships, and the mines of Thasos were confiscated by Athens. The siege of Thasos marks the transformation of the Delian league from an alliance into, in the words of Thucydides, a hegemony.
Policies of the League. In 461 BC, Cimon was ostracized and was succeeded in his influence by democrats such as Ephialtes and Pericles. This signaled a complete change in Athenian foreign policy, neglecting the alliance with the Spartans and instead allying with her enemies, Argos and Thessaly. Megara deserted the Spartan-led Peloponnesian League and allied herself with Athens, allowing construction of a double line of walls across the Isthmus of Corinth and protecting Athens from attack from that quarter. Roughly a decade earlier, due to encouragement from influential speaker Themistocles, the Athenians had also constructed the Long Walls connecting their city to the Piraeus, its port, making it effectively invulnerable to attack by land. In 454 BC, the Athenian general Pericles moved the Delian League's treasury from Delos to Athens, allegedly to keep it safe from Persia. However, Plutarch indicates that many of Pericles's rivals viewed the transfer to Athens as usurping monetary resources to fund elaborate building projects. Athens also switched from accepting ships, men and weapons as dues from league members, to only accepting money.
The new treasury established in Athens was used for many purposes, not all relating to the defence of members of the league. It was from tribute paid to the league that Pericles set to building the Parthenon on the Acropolis, replacing an older temple, as well as many other non-defense related expenditures. The Delian League was turning from an alliance into an empire. Wars against Persia. War with the Persians continued. In 460 BC, Egypt revolted under local leaders the Hellenes called Inaros and Amyrtaeus, who requested aid from Athens. Pericles led 250 ships, intended to attack Cyprus, to their aid because it would further damage Persia. After four years, however, the Egyptian rebellion was defeated by the Achaemenid general Megabyzus, who captured the greater part of the Athenian forces. In fact, according to Isocrates, the Athenians and their allies lost some 20,000 men in the expedition, while modern estimates place the figure at 50,000 men and 250 ships including reinforcements. The remainder escaped to Cyrene and thence returned home.
This was the Athenians' main (public) reason for moving the treasury of the League from Delos to Athens, further consolidating their control over the League. The Persians followed up their victory by sending a fleet to re-establish their control over Cyprus, and 200 ships were sent out to counter them under Cimon, who returned from ostracism in 451 BC. He died during the blockade of Citium, though the fleet won a double victory by land and sea over the Persians off Salamis, Cyprus. This battle was the last major one fought against the Persians. Many writers report that a peace treaty, known as the Peace of Callias, was formalized in 450 BC, but some writers believe that the treaty was a myth created later to inflate the stature of Athens. However, an understanding was definitely reached, enabling the Athenians to focus their attention on events in Greece proper. Wars in Greece. Soon, war with the Peloponnesians broke out. In 458 BC, the Athenians blockaded the island of Aegina, and simultaneously defended Megara from the Corinthians by sending out an army composed of those too young or old for regular military service. The following year, Sparta sent an army into Boeotia, reviving the power of Thebes in order to help hold the Athenians in check. Their return was blocked, and they resolved to march on Athens, where the Long Walls were not yet completed, winning a victory at the Battle of Tanagra. All this accomplished, however, was to allow them to return home via the Megarid. Two months later, the Athenians under Myronides invaded Boeotia, and winning the Battle of Oenophyta gained control of the whole country except Thebes.
Reverses followed peace with Persia in 449 BC. The Battle of Coronea, in 447 BC, led to the abandonment of Boeotia. Euboea and Megara revolted, and while the former was restored to its status as a tributary ally, the latter was a permanent loss. The Delian and Peloponnesian Leagues signed a peace treaty, which was set to endure for thirty years. It only lasted until 431 BC, when the Peloponnesian War broke out. Those who revolted unsuccessfully during the war saw the example made of the Mytilenians, the principal people on Lesbos. After an unsuccessful revolt, the Athenians ordered the death of the entire male population. After some thought, they rescinded this order, and only put to death the leading 1000 ringleaders of the revolt, and redistributed the land of the entire island to Athenian shareholders, who were sent out to reside on Lesbos. This type of treatment was not reserved solely for those who revolted. Thucydides documents the example of Melos, a small island, neutral in the war, though founded by Spartans. The Melians were offered a choice to join the Athenians, or be conquered. Choosing to resist, their town was besieged and conquered; the males were put to death and the women sold into slavery (see Melian dialogue).
Athenian Empire (454–404 BC). By 454 BC, the Delian League could be fairly characterised as an Athenian Empire; a key event of 454 BC was the moving of the treasury of the Delian League from Delos to Athens. This is often seen as a key marker of the transition from alliance to empire, but while it is significant, it is important to view the period as a whole when considering the development of Athenian imperialism, and not to focus on a single event as being the main contributor to it. At the start of the Peloponnesian War, only Chios and Lesbos were left to contribute ships, and these states were by now far too weak to secede without support. Lesbos tried to revolt first, and failed completely. Chios, the most powerful of the original members of the Delian League save Athens, was the last to revolt, and in the aftermath of the Syracusan Expedition enjoyed success for several years, inspiring all of Ionia to revolt. Athens was nonetheless eventually able to suppress these revolts. To further strengthen Athens's grip on its empire, Pericles in 450 BC began a policy of establishing "kleruchiai"—quasi-colonies that remained tied to Athens and which served as garrisons to maintain control of the League's vast territory. Furthermore, Pericles employed a number of offices to maintain Athens' empire: "proxenoi", who fostered good relations between Athens and League members; "episkopoi" and "archontes", who oversaw the collection of tribute; and "hellenotamiai", who received the tribute on Athens' behalf.
Athens's empire was not very stable and after 27 years of war, the Spartans, aided by the Persians and Athenian internal strife, were able to defeat it. However, it did not remain defeated for long. The Second Athenian League, a maritime self-defense league, was founded in 377 BC and was led by Athens. The Athenians would never recover the full extent of their power, and their enemies were now far stronger and more varied.
August Horch August Horch (12 October 1868 – 3 February 1951) was a German engineer and automobile pioneer, the founder of the manufacturing giant that eventually became Audi. Beginnings. Horch was born in Winningen, Rhenish Prussia. His initial trade was as a blacksmith, and then was educated at (Mittweida Technical College). After receiving a degree in engineering, he worked in shipbuilding. Horch worked for Karl Benz from 1896, before founding "A. Horch & Co." in November 1899, in Ehrenfeld, Cologne, Germany. Manufacturing. The first Horch automobile was built in 1901. The company moved to Reichenbach in 1902 and Zwickau in 1904. Horch left the company in 1909 after a dispute, and set up in competition in Zwickau. His new firm was initially called "Horch Automobil-Werke GmbH", but following a legal dispute over the "Horch" name, he decided to make another automobile company. (The court decided that "Horch" was a registered trademark on behalf of August's former partners and August was not entitled to use it any more). Consequently, Horch named his new company "Audi Automobilwerke GmbH" in 1910, "Audi" being the Latinization of Horch.
Post Audi. Horch left Audi in 1920 and went to Berlin and took various jobs. He published his autobiography, "I Built Cars ()" in 1937. He also served on the board of Auto Union, the successor to Audi Automobilwerke GmbH he had founded. Horch remained an honorary executive at Auto Union during and after its reincorporation in Ingolstadt, Bavaria in the late 1940s until his death in 1951, ultimately not living to see the later resurrection of his Audi brand a decade later under the ownership of Volkswagen. He was an honorary citizen of Zwickau and had a street named for his Audi cars in both Zwickau and his birthplace Winningen. He was made an honorary professor at Braunschweig University of Technology. There is an "August Horchstrasse" (August Horch Street) at Audi's main manufacturing plant in Ingolstadt.
Avionics Avionics (a portmanteau of "aviation" and "electronics") are the electronic systems used on aircraft. Avionic systems include communications, navigation, the display and management of multiple systems, and the hundreds of systems that are fitted to aircraft to perform individual functions. These can be as simple as a searchlight for a police helicopter or as complicated as the tactical system for an airborne early warning platform. History. The term "avionics" was coined in 1949 by Philip J. Klass, senior editor at "Aviation Week & Space Technology" magazine as a portmanteau of "aviation electronics". Radio communication was first used in aircraft just prior to World War I. The first airborne radios were in zeppelins, but the military sparked development of light radio sets that could be carried by heavier-than-air craft, so that aerial reconnaissance biplanes could report their observations immediately in case they were shot down. The first experimental radio transmission from an airplane was conducted by the U.S. Navy in August 1910. The first aircraft radios transmitted by radiotelegraphy. They required a two-seat aircraft with a second crewman who operated a telegraph key to spell out messages in Morse code. During World War I, AM voice two way radio sets were made possible in 1917 (see TM (triode)) by the development of the triode vacuum tube, which were simple enough that the pilot in a single seat aircraft could use it while flying.
Radar, the central technology used today in aircraft navigation and air traffic control, was developed by several nations, mainly in secret, as an air defense system in the 1930s during the runup to World War II. Many modern avionics have their origins in World War II wartime developments. For example, autopilot systems that are commonplace today began as specialized systems to help bomber planes fly steadily enough to hit precision targets from high altitudes. Britain's 1940 decision to share its radar technology with its U.S. ally, particularly the magnetron vacuum tube, in the famous Tizard Mission, significantly shortened the war. Modern avionics is a substantial portion of military aircraft spending. Aircraft like the F-15E and the now retired F-14 have roughly 20 percent of their budget spent on avionics. Most modern helicopters now have budget splits of 60/40 in favour of avionics. The civilian market has also seen a growth in cost of avionics. Flight control systems (fly-by-wire) and new navigation needs brought on by tighter airspaces, have pushed up development costs. The major change has been the recent boom in consumer flying. As more people begin to use planes as their primary method of transportation, more elaborate methods of controlling aircraft safely in these high restrictive airspaces have been invented.
Modern avionics. Avionics plays a heavy role in modernization initiatives like the Federal Aviation Administration's (FAA) Next Generation Air Transportation System project in the United States and the Single European Sky ATM Research (SESAR) initiative in Europe. The Joint Planning and Development Office put forth a roadmap for avionics in six areas: Market. The Aircraft Electronics Association reports $1.73 billion avionics sales for the first three quarters of 2017 in business and general aviation, a 4.1% yearly improvement: 73.5% came from North America, forward-fit represented 42.3% while 57.7% were retrofits as the U.S. deadline of January 1, 2020 for mandatory ADS-B out approach. Aircraft avionics. The cockpit or, in larger aircraft, under the cockpit of an aircraft or in a movable nosecone, is a typical location for avionic bay equipment, including control, monitoring, communication, navigation, weather, and anti-collision systems. The majority of aircraft power their avionics using 14- or 28‑volt DC electrical systems; however, larger, more sophisticated aircraft (such as airliners or military combat aircraft) have AC systems operating at 115 volts 400 Hz, AC. There are several major vendors of flight avionics, including The Boeing Company, Panasonic Avionics Corporation, Honeywell (which now owns Bendix/King), Universal Avionics Systems Corporation, Rockwell Collins (now Collins Aerospace), Thales Group, GE Aviation Systems, Garmin, Raytheon, Parker Hannifin, UTC Aerospace Systems (now Collins Aerospace), Selex ES (now Leonardo), Shadin Avionics, and Avidyne Corporation.
International standards for avionics equipment are prepared by the Airlines Electronic Engineering Committee (AEEC) and published by ARINC. Avionics Installation. Avionics installation is a critical aspect of modern aviation, ensuring that aircraft are equipped with the necessary electronic systems for safe and efficient operation. These systems encompass a wide range of functions, including communication, navigation, monitoring, flight control, and weather detection. Avionics installations are performed on all types of aircraft, from small general aviation planes to large commercial jets and military aircraft. Installation Process. The installation of avionics requires a combination of technical expertise, precision, and adherence to stringent regulatory standards. The process typically involves: Regulatory Standards. Avionics installation is governed by strict regulatory frameworks to ensure the safety and reliability of aircraft systems. In the United States, the Federal Aviation Administration (FAA) sets the standards for avionics installations. These include guidelines for:
Advancements in Avionics Technology. The field of avionics has seen rapid technological advancements in recent years, leading to more integrated and automated systems. Key trends include: Communications. Communications connect the flight deck to the ground and the flight deck to the passengers. On‑board communications are provided by public-address systems and aircraft intercoms. The VHF aviation communication system works on the airband of 118.000 MHz to 136.975 MHz. Each channel is spaced from the adjacent ones by 8.33 kHz in Europe, 25 kHz elsewhere. VHF is also used for line of sight communication such as aircraft-to-aircraft and aircraft-to-ATC. Amplitude modulation (AM) is used, and the conversation is performed in simplex mode. Aircraft communication can also take place using HF (especially for trans-oceanic flights) or satellite communication. Navigation. Air navigation is the determination of position and direction on or above the surface of the Earth. Avionics can use satellite navigation systems (such as GPS and WAAS), inertial navigation system (INS), ground-based radio navigation systems (such as VOR or LORAN), or any combination thereof. Some navigation systems such as GPS calculate the position automatically and display it to the flight crew on moving map displays. Older ground-based Navigation systems such as VOR or LORAN requires a pilot or navigator to plot the intersection of signals on a paper map to determine an aircraft's location; modern systems calculate the position automatically and display it to the flight crew on moving map displays.
Monitoring. The first hints of glass cockpits emerged in the 1970s when flight-worthy cathode-ray tube (CRT) screens began to replace electromechanical displays, gauges and instruments. A "glass" cockpit refers to the use of computer monitors instead of gauges and other analog displays. Aircraft were getting progressively more displays, dials and information dashboards that eventually competed for space and pilot attention. In the 1970s, the average aircraft had more than 100 cockpit instruments and controls. Glass cockpits started to come into being with the Gulfstream G‑IV private jet in 1985. One of the key challenges in glass cockpits is to balance how much control is automated and how much the pilot should do manually. Generally they try to automate flight operations while keeping the pilot constantly informed. Aircraft flight-control system. Aircraft have means of automatically controlling flight. Autopilot was first invented by Lawrence Sperry during World War I to fly bomber planes steady enough to hit accurate targets from 25,000 feet. When it was first adopted by the U.S. military, a Honeywell engineer sat in the back seat with bolt cutters to disconnect the autopilot in case of emergency. Nowadays most commercial planes are equipped with aircraft flight control systems in order to reduce pilot error and workload at landing or takeoff.
The first simple commercial auto-pilots were used to control heading and altitude and had limited authority on things like thrust and flight control surfaces. In helicopters, auto-stabilization was used in a similar way. The first systems were electromechanical. The advent of fly-by-wire and electro-actuated flight surfaces (rather than the traditional hydraulic) has increased safety. As with displays and instruments, critical devices that were electro-mechanical had a finite life. With safety critical systems, the software is very strictly tested. Fuel Systems. Fuel Quantity Indication System (FQIS) monitors the amount of fuel aboard. Using various sensors, such as capacitance tubes, temperature sensors, densitometers & level sensors, the FQIS computer calculates the mass of fuel remaining on board. Fuel Control and Monitoring System (FCMS) reports fuel remaining on board in a similar manner, but, by controlling pumps & valves, also manages fuel transfers around various tanks. Collision-avoidance systems.
To supplement air traffic control, most large transport aircraft and many smaller ones use a traffic alert and collision avoidance system (TCAS), which can detect the location of nearby aircraft, and provide instructions for avoiding a midair collision. Smaller aircraft may use simpler traffic alerting systems such as TPAS, which are passive (they do not actively interrogate the transponders of other aircraft) and do not provide advisories for conflict resolution. To help avoid controlled flight into terrain (CFIT), aircraft use systems such as ground-proximity warning systems (GPWS), which use radar altimeters as a key element. One of the major weaknesses of GPWS is the lack of "look-ahead" information, because it only provides altitude above terrain "look-down". In order to overcome this weakness, modern aircraft use a terrain awareness warning system (TAWS). Flight recorders. Commercial aircraft cockpit data recorders, commonly known as "black boxes", store flight information and audio from the cockpit. They are often recovered from an aircraft after a crash to determine control settings and other parameters during the incident.
Weather systems. Weather systems such as weather radar (typically Arinc 708 on commercial aircraft) and lightning detectors are important for aircraft flying at night or in instrument meteorological conditions, where it is not possible for pilots to see the weather ahead. Heavy precipitation (as sensed by radar) or severe turbulence (as sensed by lightning activity) are both indications of strong convective activity and severe turbulence, and weather systems allow pilots to deviate around these areas. Lightning detectors like the Stormscope or Strikefinder have become inexpensive enough that they are practical for light aircraft. In addition to radar and lightning detection, observations and extended radar pictures (such as NEXRAD) are now available through satellite data connections, allowing pilots to see weather conditions far beyond the range of their own in-flight systems. Modern displays allow weather information to be integrated with moving maps, terrain, and traffic onto a single screen, greatly simplifying navigation.
Modern weather systems also include wind shear and turbulence detection and terrain and traffic warning systems. In‑plane weather avionics are especially popular in Africa, India, and other countries where air-travel is a growing market, but ground support is not as well developed. Aircraft management systems. There has been a progression towards centralized control of the multiple complex systems fitted to aircraft, including engine monitoring and management. Health and usage monitoring systems (HUMS) are integrated with aircraft management computers to give maintainers early warnings of parts that will need replacement. The integrated modular avionics concept proposes an integrated architecture with application software portable across an assembly of common hardware modules. It has been used in fourth generation jet fighters and the latest generation of airliners. Mission or tactical avionics. Military aircraft have been designed either to deliver a weapon or to be the eyes and ears of other weapon systems. The vast array of sensors available to the military is used for whatever tactical means required. As with aircraft management, the bigger sensor platforms (like the E‑3D, JSTARS, ASTOR, Nimrod MRA4, Merlin HM Mk 1) have mission-management computers.
Police and EMS aircraft also carry sophisticated tactical sensors. Military communications. While aircraft communications provide the backbone for safe flight, the tactical systems are designed to withstand the rigors of the battle field. UHF, VHF Tactical (30–88 MHz) and SatCom systems combined with ECCM methods, and cryptography secure the communications. Data links such as Link 11, 16, 22 and BOWMAN, JTRS and even TETRA provide the means of transmitting data (such as images, targeting information etc.). Radar. Airborne radar was one of the first tactical sensors. The benefit of altitude providing range has meant a significant focus on airborne radar technologies. Radars include airborne early warning (AEW), anti-submarine warfare (ASW), and even weather radar (Arinc 708) and ground tracking/proximity radar. The military uses radar in fast jets to help pilots fly at low levels. While the civil market has had weather radar for a while, there are strict rules about using it to navigate the aircraft. Sonar. Dipping sonar fitted to a range of military helicopters allows the helicopter to protect shipping assets from submarines or surface threats. Maritime support aircraft can drop active and passive sonar devices (sonobuoys) and these are also used to determine the location of enemy submarines.
Electro-optics. Electro-optic systems include devices such as the head-up display (HUD), forward looking infrared (FLIR), infrared search and track and other passive infrared devices (Passive infrared sensor). These are all used to provide imagery and information to the flight crew. This imagery is used for everything from search and rescue to navigational aids and target acquisition. ESM/DAS. Electronic support measures and defensive aids systems are used extensively to gather information about threats or possible threats. They can be used to launch devices (in some cases automatically) to counter direct threats against the aircraft. They are also used to determine the state of a threat and identify it. Aircraft networks. The avionics systems in military, commercial and advanced models of civilian aircraft are interconnected using an avionics databus. Common avionics databus protocols, with their primary application, include:
Ares Ares (; , "Árēs" ) is the Greek god of war and courage. He is one of the Twelve Olympians, and the son of Zeus and Hera. The Greeks were ambivalent towards him. He embodies the physical valor necessary for success in war but can also personify sheer brutality and bloodlust, in contrast to his sister Athena, whose martial functions include military strategy and generalship. An association with Ares endows places, objects, and other deities with a savage, dangerous, or militarized quality. Although Ares' name shows his origins as Mycenaean, his reputation for savagery was thought by some to reflect his likely origins as a Thracian deity. Some cities in Greece and several in Asia Minor held annual festivals to bind and detain him as their protector. In parts of Asia Minor, he was an oracular deity. Still further away from Greece, the Scythians were said to ritually kill one in a hundred prisoners of war as an offering to their equivalent of Ares. The later belief that ancient Spartans had offered human sacrifice to Ares may owe more to mythical prehistory, misunderstandings, and reputation than to reality.
Although there are many literary allusions to Ares' love affairs and children, he has a limited role in Greek mythology. When he does appear, he is often humiliated. In the Trojan War, Aphrodite, protector of Troy, persuades Ares to take the Trojans' side. The Trojans lose, while Ares' sister Athena helps the Greeks to victory. Most famously, when the craftsman-god Hephaestus discovers his wife Aphrodite is having an affair with Ares, he traps the lovers in a net and exposes them to the ridicule of the other gods. Ares' nearest counterpart in Roman religion is Mars, who was given a more important and dignified place in ancient Roman religion as ancestral protector of the Roman people and state. During the Hellenization of Latin literature, the myths of Ares were reinterpreted by Roman writers under the name of Mars, and in later Western art and literature, the mythology of the two figures became virtually indistinguishable. Names. The etymology of the name "Ares" is traditionally connected with the Greek word ("arē"), the Ionic form of the Doric ("ara"), "bane, ruin, curse, imprecation". Walter Burkert notes that "Ares is apparently an ancient abstract noun meaning throng of battle, war." R. S. P. Beekes has suggested a Pre-Greek origin of the name. The earliest attested form of the name is the Mycenaean Greek , "a-re", written in the Linear B syllabic script.
The adjectival epithet, "Areios" ("warlike") was frequently appended to the names of other gods when they took on a warrior aspect or became involved in warfare: "Zeus Areios", "Athena Areia", even Aphrodite Areia ("Aphrodite within Ares" or "feminine Ares"), who was warlike, fully armoured and armed, partnered with Athena in Sparta, and represented at Kythira's temple to Aphrodite Urania. In the "Iliad", the word "ares" is used as a common noun synonymous with "battle." In the Classical period, Ares is given the epithet Enyalios, which seems to appear on the Mycenaean KN V 52 tablet as , "e-nu-wa-ri-jo". Enyalios was sometimes identified with Ares and sometimes differentiated from him as another war god with separate cult, even in the same town; Burkert describes them as "doubles almost". Cult. In mainland Greece and the Peloponnese, only a few places are known to have had a formal temple and cult of Ares. Pausanias (2nd century AD) notes an altar to Ares at Olympia, and the moving of a Temple of Ares to the Athenian agora during the reign of Augustus, essentially rededicating it (2 AD) as a Roman temple to the Augustan Mars Ultor. The Areopagus ("mount of Ares"), a natural rock outcrop in Athens, some distance from the Acropolis, was supposedly where Ares was tried and acquitted by the gods for his revenge-killing of Poseidon's son, Halirrhothius, who had raped Ares' daughter Alcippe. Its name was used for the court that met there, mostly to investigate and try potential cases of treason.
Numismatist M. Jessop Price states that Ares "typified the traditional Spartan character", but had no important cult in Sparta; and he never occurs on Spartan coins. Pausanias gives two examples of his cult, both of them conjointly with or "within" a warlike Aphrodite, on the Spartan acropolis. Gonzalez observes, in his 2005 survey of Ares' cults in Asia Minor, that cults to Ares on the Greek mainland may have been more common than some sources assert. Wars between Greek states were endemic; war and warriors provided Ares's tribute, and fed his insatiable appetite for battle. Ares' attributes are instruments of war: a helmet, shield, and sword or spear. Libanius "makes the apple sacred to Ares", but "offers no further comment", nor connections to any aetiological myth. Apples are one of Aphrodites' sacred or symbolic fruits. Littlewood follows Artemidorus claim that to dream of sour apples presages conflict, and lists Ares alongside Eris and the mythological "Apples of Discord". Chained statues. Gods were immortal but could be bound and restrained, both in mythic narrative and in cult practice. There was an archaic Spartan statue of Ares in chains in the temple of Enyalios (sometimes regarded as the son of Ares, sometimes as Ares himself), which Pausanias claimed meant that the spirit of war and victory was to be kept in the city. The Spartans are known to have ritually bound the images of other deities, including Aphrodite and Artemis (cf Ares and Aphrodite bound by Hephaestus), and in other places there were chained statues of Artemis and Dionysos.
Statues of Ares in chains are described in the instructions given by an oracle of the late Hellenistic era to various cities of Pamphylia (in Anatolia) including Syedra, Lycia and Cilicia, places almost perpetually under threat from pirates. Each was told to set up a statue of "bloody, man-slaying Ares" and provide it with an annual festival in which it was ritually bound with iron fetters ("by Dike and Hermes") as if a supplicant for justice, put on trial and offered sacrifice. The oracle promises that "thus will he become a peaceful deity for you, once he has driven the enemy horde far from your country, and he will give rise to prosperity much prayed for." This Ares "karpodotes" ("giver of Fruits") is well attested in Lycia and Pisidia. Sacrifices. Like most Greek deities, Ares was given animal sacrifice; in Sparta, after battle, he was given an ox for a victory by stratagem, or a rooster for victory through onslaught. The usual recipient of sacrifice before battle was Athena. Reports of historic human sacrifice to Ares in an obscure rite known as the "Hekatomphonia" represent a very long-standing error, repeated through several centuries and well into the modern era. The "hekatomphonia" was an animal sacrifice to Zeus; it could be offered by any warrior who had personally slain one hundred of the enemy. Pausanias reports that in Sparta, each company of youths sacrificed a puppy to Enyalios before engaging in a hand-to-hand "fight without rules" at the Phoebaeum. The chthonic night-time sacrifice of a dog to Enyalios became assimilated to the cult of Ares. Porphyry claims, without detail, that Apollodorus of Athens (circa second century BC) says the Spartans made human sacrifices to Ares, but this may be a reference to mythic pre-history.
Thrace and Scythia. A Thracian god identified by Herodotus ( – ) as Ares, through "interpretatio Graeca", was one of three otherwise unnamed deities that Thracian commoners were said to worship. Herodotus recognises and names the other two as "Dionysus" and "Artemis", and claims that the Thracian aristocracy exclusively worshiped "Hermes". In Herodotus' "Histories", the Scythians worship an indigenous form of Greek Ares, who is otherwise unnamed, but ranked beneath Tabiti (whom Herodotus claims as a form of Hestia), Api and Papaios in Scythia's divine hierarchy. His cult object was an iron sword. The "Scythian Ares" was offered blood-sacrifices (or ritual killings) of cattle, horses and "one in every hundred human war-captives", whose blood was used to douse the sword. Statues, and complex platform-altars made of heaped brushwood were devoted to him. This sword-cult, or one very similar, is said to have persisted among the Alans. Some have posited that the "Sword of Mars" in later European history alludes to the Huns having adopted Ares.
Asia Minor. In some parts of Asia Minor, Ares was a prominent oracular deity, something not found in any Hellennic cult to Ares or Roman cult to Mars. Ares was linked in some regions or polities with a local god or cultic hero, and recognised as a higher, more prestigious deity than in mainland Greece. His cults in southern Asia Minor are attested from the 5th century BC and well into the later Roman Imperial era, at 29 different sites, and on over 70 local coin issues. He is sometimes represented on coinage of the region by the "Helmet of Ares" or carrying a spear and a shield, or as a fully armed warrior, sometimes accompanied by a female deity. In what is now western Turkey, the Hellenistic city of Metropolis built a monumental temple to Ares as the city's protector, not before the 3rd century BC. It is now lost, but the names of some of its priests and priestesses survive, along with the temple's likely depictions on coins of the province. Crete. A sanctuary of Aphrodite was established at Sta Lenika, on Crete, between the cities of Lato and Olus, possibly during the Geometric period. It was rebuilt in the late 2nd century BC as a double-sanctuary to Ares and Aphrodite. Inscriptions record disputes over the ownership of the sanctuary. The names of Ares and Aphrodite appear as witness to sworn oaths, and there is a Victory thanks-offering to Aphrodite, whom Millington believes had capacity as a "warrior-protector acting in the realm of Ares". There were cultic links between the Sta Lenika sanctuary, Knossos and other Cretan states, and perhaps with Argos on the mainland. While the Greek literary and artistic record from both the Archaic and Classical eras connects Ares and Aphrodite as complementary companions and ideal though adulterous lovers, their cult pairing and Aphrodite as warrior-protector is localised to Crete.
Aksum. In Africa, Maḥrem, the principal god of the kings of Aksum prior to the 4th century AD, was invoked as Ares in Greek inscriptions. The anonymous king who commissioned the Monumentum Adulitanum in the late 2nd or early 3rd century refers to "my greatest god, Ares, who also begat me, through whom I brought under my sway [various peoples]". The monumental throne celebrating the king's conquests was itself dedicated to Ares. In the early 4th century, the last pagan king of Aksum, Ezana, referred to "the one who brought me forth, the invincible Ares". Characterisation. Ares was one of the Twelve Olympians in the archaic tradition represented by the "Iliad" and "Odyssey." In Greek literature, Ares often represents the physical or violent and untamed aspect of war and is the personification of sheer brutality and bloodlust ("overwhelming, insatiable in battle, destructive, and man-slaughtering", as Burkert puts it), in contrast to his sister, the armored Athena, whose functions as a goddess of intelligence include military strategy and generalship. An association with Ares endows places and objects with a savage, dangerous, or militarized quality; but when Ares does appear in myths, he typically faces humiliation.
In the Iliad, Zeus expresses a recurring Greek revulsion toward the god when Ares returns wounded and complaining from the battlefield at Troy: This ambivalence is expressed also in the Greeks' association of Ares with the Thracians, whom they regarded as a barbarous and warlike people. Thrace was considered to be Ares's birthplace and his refuge after the affair with Aphrodite was exposed to the general mockery of the other gods. A late-6th-century BC funerary inscription from Attica emphasizes the consequences of coming under Ares's sway: Mythology. Birth. He is one of the Twelve Olympians, and the son of Zeus and Hera. Argonautica. In the "Argonautica", the "Golden Fleece" hangs in a grove sacred to Ares, until its theft by Jason. The Birds of Ares ("Ornithes Areioi") drop feather darts in defense of the Amazons' shrine to Ares, as father of their queen, on a coastal island in the Black Sea. Founding of Thebes. Ares plays a central role in the founding myth of Thebes, as the progenitor of the water-dragon slain by Cadmus. The dragon's teeth were sown into the ground as if a crop and sprang up as the fully armored autochthonic Spartoi. Cadmus placed himself in the god's service for eight years to atone for killing the dragon. To further propitiate Ares, Cadmus married Harmonia, a daughter of Ares's union with Aphrodite. In this way, Cadmus harmonized all strife and founded the city of Thebes. In reality, Thebes came to dominate Boeotia's great and fertile plain, which in both history and myth was a battleground for competing polities. According to Plutarch, the plain was anciently described as "The dancing-floor of Ares".
Aphrodite. In Homer's "Odyssey", in the tale sung by the bard in the hall of Alcinous, the Sun-god Helios once spied Ares and Aphrodite having sex secretly in the hall of Hephaestus, her husband. Helios reported the incident to Hephaestus. Contriving to catch the illicit couple in the act, Hephaestus fashioned a finely-knitted and nearly invisible net with which to snare them. At the appropriate time, this net was sprung, and trapped Ares and Aphrodite locked in very private embrace. But Hephaestus was not satisfied with his revenge, so he invited the Olympian gods and goddesses to view the unfortunate pair. For the sake of modesty, the goddesses demurred, but the male gods went to witness the sight. Some commented on the beauty of Aphrodite, others remarked that they would eagerly trade places with Ares, but all who were present mocked the two. Once the couple was released, the embarrassed Ares returned to his homeland, Thrace, and Aphrodite went to Paphos. In a much later interpolated detail, Ares put the young soldier Alectryon, who was Ares companion in drinking and even love-making, by his door to warn them of Helios's arrival as Helios would tell Hephaestus of Aphrodite's infidelity if the two were discovered, but Alectryon fell asleep on guard duty. Helios discovered the two and alerted Hephaestus. The furious Ares turned the sleepy Alectryon into a rooster which now always announces the arrival of the sun in the morning, as a way of apologizing to Ares.
The Chorus of Aeschylus' "Suppliants" (written 463 BC) refers to Ares as Aphrodite's "mortal-destroying bedfellow". In the "Illiad", Ares helps the Trojans because of his affection for their divine protector, Aphrodite; she thus redirects his innate destructive savagery to her own purposes. Giants. In one archaic myth, related only in the "Iliad" by the goddess Dione to her daughter Aphrodite, two chthonic giants, the Aloadae, named Otus and Ephialtes, bound Ares in chains and imprisoned him in a bronze urn, where he remained for thirteen months, a lunar year. "And that would have been the end of Ares and his appetite for war, if the beautiful Eriboea, the young giants' stepmother, had not told Hermes what they had done," she related. In this, [Burkert] suspects "a festival of licence which is unleashed in the thirteenth month." Ares was held screaming and howling in the urn until Hermes rescued him, and Artemis tricked the Aloadae into slaying each other. In Nonnus's "Dionysiaca", in the war between Cronus and Zeus, Ares killed an unnamed giant son of Echidna who was allied with Cronus, and described as spitting "horrible poison" and having "snaky" feet.
In the 2nd century AD "Metamorphoses" of Antoninus Liberalis, when the monstrous Typhon attacked Olympus the gods transformed into animals and fled to Egypt; Ares changed into a fish, the Lepidotus (sacred to the Egyptian war-god Anhur). Liberalis's koine Greek text is a "completely inartistic" epitome of Nicander's now lost "Heteroeumena" (2nd century BC). "Iliad". In Homer's "Iliad", Ares has no fixed allegiance. He promises Athena and Hera that he will fight for the Achaeans but Aphrodite persuades him to side with the Trojans. During the war, Diomedes fights Hector and sees Ares fighting on the Trojans' side. Diomedes calls for his soldiers to withdraw. Zeus grants Athena permission to drive Ares from the battlefield. Encouraged by Hera and Athena, Diomedes thrusts with his spear at Ares. Athena drives the spear home, and all sides tremble at Ares's cries. Ares flees to Mount Olympus, forcing the Trojans to fall back. Ares overhears that his son Ascalaphus has been killed and wants to change sides again, rejoining the Achaeans for vengeance, disregarding Zeus's order that no Olympian should join the battle. Athena stops him. Later, when Zeus allows the gods to fight in the war again, Ares attacks Athena to avenge his previous injury. Athena overpowers him by striking him with a boulder.
Attendants. Deimos ("Terror" or "Dread") and Phobos ("Fear") are Ares' companions in war, and according to Hesiod, are also his children by Aphrodite. Eris, the goddess of discord, or Enyo, the goddess of war, bloodshed, and violence, was considered the sister and companion of the violent Ares. In at least one tradition, Enyalius, rather than another name for Ares, was his son by Enyo. Ares may also be accompanied by Kydoimos, the daemon of the din of battle; the Makhai ("Battles"); the "Hysminai" ("Acts of manslaughter"); Polemos, a minor spirit of war, or only an epithet of Ares, since it has no specific dominion; and Polemos's daughter, Alala, the goddess or personification of the Greek war-cry, whose name Ares uses as his own war-cry. Ares's sister Hebe ("Youth") also draws baths for him. According to Pausanias, local inhabitants of Therapne, Sparta, recognized Thero, "feral, savage," as a nurse of Ares. Offspring and affairs. Though Ares plays a relatively limited role in Greek mythology as represented in literary narratives, his numerous love affairs and abundant offspring are often alluded to.
The union of Ares and Aphrodite created the gods Eros, Anteros, Phobos, Deimos, and Harmonia. Other versions include Alcippe as one of his daughters. Cycnus (Κύκνος) of Macedonia was a son of Ares who tried to build a temple to his father with the skulls and bones of guests and travellers. Heracles fought him and, in one account, killed him. In another account, Ares fought his son's killer but Zeus parted the combatants with a thunderbolt. Ares had a romantic liaison with Eos, the goddess of the dawn. Aphrodite discovered them, and in anger she cursed Eos with insatiable lust for men. By a woman named Teirene he had a daughter named Thrassa, who in turn had a daughter named Polyphonte. Polyphonte was cursed by Aphrodite to love and mate with a bear, producing two sons, Agrius and Oreius, who were hubristic toward the gods and had a habit of eating their guests. Zeus sent Hermes to punish them, and he chose to chop off their hands and feet. Since Polyphonte was descended from him, Ares stopped Hermes, and the two brothers came into an agreement to turn Polyphonte's family into birds instead. Oreius became an eagle owl, Agrius a vulture, and Polyphonte a strix, possibly a small owl, certainly a portent of war; Polyphonte's servant prayed not to become a bird of evil omen and Ares and Hermes fulfilled her wish by choosing the woodpecker for her, a good omen for hunters.
List of offspring and their mothers. Sometimes poets and dramatists recounted ancient traditions, which varied, and sometimes they invented new details; later scholiasts might draw on either or simply guess. Thus while Phobos and Deimos were regularly described as offspring of Ares, others listed here such as Meleager, Sinope and Solymus were sometimes said to be children of Ares and sometimes given other fathers. The following is a list of Ares' offspring, by various mothers. Beside each offspring, the earliest source to record the parentage is given, along with the century to which the source dates. Mars. The nearest counterpart of Ares among the Roman gods is Mars, a son of Jupiter and Juno, pre-eminent among the Roman army's military gods but originally an agricultural deity. As a father of Romulus, Rome's legendary founder, Mars was given an important and dignified place in ancient Roman religion, as a guardian deity of the entire Roman state and its people. Under the influence of Greek culture, Mars was identified with Ares, but the character and dignity of the two deities differed fundamentally. Mars was represented as a means to secure peace, and he was a father "(pater)" of the Roman people. In one tradition, he fathered Romulus and Remus through his rape of Rhea Silvia. In another, his lover, the goddess Venus, gave birth to Aeneas, the Trojan prince and refugee who "founded" Rome several generations before Romulus.
In the Hellenization of Latin literature, the myths of Ares were reinterpreted by Roman writers under the name of Mars. Greek writers under Roman rule also recorded cult practices and beliefs pertaining to Mars under the name of Ares. Thus in the classical tradition of later Western art and literature, the mythology of the two figures later became virtually indistinguishable. Renaissance and later depictions. In Renaissance and Neoclassical works of art, Ares's symbols are a spear and helmet, his animal is a dog, and his bird is the vulture. In literary works of these eras, Ares is replaced by the Roman Mars, a romantic emblem of manly valor rather than the cruel and blood-thirsty god of Greek mythology.
Alexander Grothendieck Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century. Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the Fields Medal in 1966 for advances in algebraic geometry, homological algebra, and K-theory. He later became professor at the University of Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014.
Life. Family and childhood. Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro (also known as Alexander Tanaroff), had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother, Johanna "Hanka" Grothendieck, came from a Protestant German family in Hamburg and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's mother was married to the journalist Johannes Raddatz and initially, his birth name was recorded as "Alexander Raddatz." That marriage was dissolved in 1929 and Schapiro acknowledged his paternity, but never married Hanka Grothendieck. Grothendieck had a maternal sibling, his half sister Maidi. Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to Paris to evade Nazism. His mother followed soon thereafter. Grothendieck was left in the care of Wilhelm Heydorn, a Lutheran pastor and teacher in Hamburg. According to Winfried Scharlau, during this time, his parents took part in the Spanish Civil War as non-combatant auxiliaries. However, others state that Schapiro fought in the anarchist militia.
World War II. In May 1939, Grothendieck was put on a train in Hamburg for France. Shortly afterward his father was interned in Le Vernet. He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners." The first camp was the Rieucros Camp, where his mother contracted the tuberculosis that would eventually cause her death in 1957. While there, Grothendieck managed to attend the local school, at Mende. Once, he managed to escape from the camp, intending to assassinate Hitler. Later, his mother Hanka was transferred to the Gurs internment camp for the remainder of World War II. Grothendieck was permitted to live separated from his mother. In the village of Le Chambon-sur-Lignon, he was sheltered and hidden in local boarding houses or pensions, although he occasionally had to seek refuge in the woods during Nazi raids, surviving at times without food or water for several days. His father was arrested under the Vichy anti-Jewish legislation, and sent to the Drancy internment camp, and then handed over by the French Vichy government to the Germans to be sent to be murdered at the Auschwitz concentration camp in 1942.
In Le Chambon, Grothendieck attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children hidden in Le Chambon attended Collège Cévenol, and it was at this school that Grothendieck apparently first became fascinated with mathematics. In 1990, for risking their lives to rescue Jews, the entire village was recognized as "Righteous Among the Nations". Studies and contact with research mathematics. After the war, the young Grothendieck studied mathematics in France, initially at the University of Montpellier where at first he did not perform well, failing such classes as astronomy. Working on his own, he rediscovered the Lebesgue measure. After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948. Initially, Grothendieck attended Henri Cartan's Seminar at , but he lacked the necessary background to follow the high-powered seminar. On the advice of Cartan and André Weil, he moved to the University of Nancy where two leading experts were working on Grothendieck's area of interest, topological vector spaces: Jean Dieudonné and Laurent Schwartz. The latter had recently won a Fields Medal. Dieudonné and Schwartz showed the new student their latest paper "La dualité dans les espaces () et ()"; it ended with a list of 14 open questions, relevant for locally convex spaces. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months.
In Nancy, he wrote his dissertation under those two professors on functional analysis, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the University of São Paulo in Brazil, where he immigrated by means of a Nansen passport, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in São Paulo (apart from a lengthy visit in France from October 1953 to March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of Banach spaces). Grothendieck moved to Lawrence, Kansas at the beginning of 1955, and there he set his old subject aside in order to work in algebraic topology and homological algebra, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of abelian categories and the reformulation of sheaf cohomology based on them, leading to the very influential "Tôhoku paper".
In 1957 he was invited to visit Harvard University by Oscar Zariski, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States government—a refusal which, he was warned, threatened to land him in prison. The prospect of prison did not worry him, so long as he could have access to books. Comparing Grothendieck during his Nancy years to the -trained students at that time (Pierre Samuel, Roger Godement, René Thom, Jacques Dixmier, Jean Cerf, Yvonne Bruhat, Jean-Pierre Serre, and Bernard Malgrange), Leila Schneps said: His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between Grothendieck inequality and the Einstein–Podolsky–Rosen paradox in quantum physics. IHÉS years. In 1958, Grothendieck was installed at the Institut des hautes études scientifiques (IHÉS), a new privately funded research institute that, in effect, had been created for Jean Dieudonné and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there ("de facto" working groups drafting into foundational work some of the ablest French and other mathematicians of the younger generation). Grothendieck practically ceased publication of papers through the conventional, learned journal route. However, he was able to play a dominant role in mathematics for approximately a decade, gathering a strong school.
Officially during this time, he had as students Michel Demazure (who worked on SGA3, on group schemes), (relative schemes and classifying topos), Luc Illusie (cotangent complex), Michel Raynaud, Michèle Raynaud, Jean-Louis Verdier (co-founder of the derived category theory), and Pierre Deligne. Collaborators on the SGA projects also included Michael Artin (étale cohomology), Nick Katz (monodromy theory, and Lefschetz pencils). Jean Giraud worked out torsor theory extensions of nonabelian cohomology there as well. Many others such as David Mumford, Robin Hartshorne, Barry Mazur and C.P. Ramanujam were also involved. "Golden Age". Alexander Grothendieck's work during what is described as the "Golden Age" period at the IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory, and complex analysis. His first (pre-IHÉS) discovery in algebraic geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context he also introduced K-theory.
His first (pre-IHÉS) discovery in algebraic geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context he also introduced K-theory. Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his "Éléments de géométrie algébrique" ("EGA") and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it. He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it. As a framework for his coherent duality theory, he also introduced derived categories, which were further developed by Verdier.
The results of his work on these and other topics were published in the "EGA" and in less polished form in the notes of the "Séminaire de géométrie algébrique" ("SGA") that he directed at the IHÉS. Political activism. Grothendieck's political views were radical and pacifistic. He strongly opposed both United States intervention in Vietnam and Soviet military expansionism. To protest against the Vietnam War, he gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed. In 1966, he had declined to attend the International Congress of Mathematicians (ICM) in Moscow, where he was to receive the Fields Medal. He retired from scientific life around 1970 after he had found out that IHÉS was partly funded by the military. He returned to academia a few years later as a professor at the University of Montpellier.
In 1970, Grothendieck, with two other mathematicians, Claude Chevalley and Pierre Samuel, created a political group entitled "Survivre"—the name later changed to "Survivre et vivre". The group published a bulletin and was dedicated to antimilitary and ecological issues. It also developed strong criticism of the indiscriminate use of science and technology. Grothendieck devoted the next three years to this group and served as the main editor of its bulletin. Although Grothendieck continued with mathematical enquiries, his standard mathematical career mostly ended when he left the IHÉS. After leaving the IHÉS, Grothendieck became a temporary professor at Collège de France for two years. He then became a professor at the University of Montpellier, where he became increasingly estranged from the mathematical community. He formally retired in 1988, a few years after having accepted a research position at the CNRS. Manuscripts written in the 1980s. While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.
Produced during 1980 and 1981, "La Longue Marche à travers la théorie de Galois" ("The Long March Through Galois Theory") is a 1600-page handwritten manuscript containing many of the ideas that led to the "Esquisse d'un programme". It also includes a study of Teichmüller theory. In 1983, stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University, Grothendieck wrote a 600-page manuscript entitled "Pursuing Stacks". It began with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor (see External links below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, "Les Dérivateurs". Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in "Pursuing Stacks". Much of this work anticipated the subsequent development during the mid-1990s of the motivic homotopy theory of Fabien Morel and Vladimir Voevodsky.
In 1984, Grothendieck wrote the proposal "Esquisse d'un Programme" ("Sketch of a Programme") for a position at the Centre National de la Recherche Scientifique (CNRS). It describes new ideas for studying the moduli space of complex curves. Although Grothendieck never published his work in this area, the proposal inspired other mathematicians to work in the area by becoming the source of dessin d'enfant theory and anabelian geometry. Later, it was published in two-volumes and entitled "Geometric Galois Actions" (Cambridge University Press, 1997). During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on Bertini-type theorems ("EGA" V, published in Ulam Quarterly in 1992–1993 and later made available on the Grothendieck Circle web site in 2004).
In 1988, Grothendieck declined the Crafoord Prize with an open letter to the media. He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become commonplace and tolerated. The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. Grothendieck added however that his views were "in no way meant as a criticism of the Royal Academy's aims in the administration of its funds" and he added, "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy." "La Clef des Songes", a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that a deity exists. As part of the notes to this manuscript, Grothendieck described the life and the work of 18 "mutants", people whom he admired as visionaries far ahead of their time and heralding a new age. The only mathematician on his list was Bernhard Riemann. Influenced by the Catholic mystic Marthe Robin who was claimed to have survived on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988. His growing preoccupation with spiritual matters was also evident in a letter entitled "Lettre de la Bonne Nouvelle" sent to 250 friends in January 1990. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996.
The "Grothendieck Festschrift", published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988. More than 20,000 pages of Grothendieck's mathematical and other writings are held at the University of Montpellier and remain unpublished. They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal. Retirement into reclusion and death. In 1991, Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community. Very few people visited him afterward. Local villagers helped sustain him with a more varied diet after he tried to live on a staple of dandelion soup. At some point, Leila Schneps and located him, then carried on a brief correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". After his death, it was revealed that he lived alone in a house in Lasserre, Ariège, a small village at the foot of the Pyrenees.
In January 2010, Grothendieck wrote the letter entitled "Déclaration d'intention de non-publication" to Luc Illusie, claiming that all materials published in his absence had been published without his permission. He asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. He characterized a website devoted to his work as "an abomination". His dictate may have been reversed in 2010. In September 2014, almost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself. His neighbour refused to do so. On 13 November 2014, aged 86, Grothendieck died in the hospital of Saint-Lizier or Saint-Girons, Ariège. Citizenship. Grothendieck was born in Weimar Germany. In 1938, aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the fall of Nazi Germany in 1945 and he did not apply for French citizenship after the war. Thus, he became a stateless person for at least the majority of his working life and he traveled on a Nansen passport. Part of his reluctance to hold French nationality is attributed to not wishing to serve in the French military, particularly due to the Algerian War (1954–62). He eventually applied for French citizenship in the early 1980s, after he was well past the age that would have required him to do military service.
Family. Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in 1957 from tuberculosis that she contracted in camps for displaced persons. He had five children: a son with his landlady during his time in Nancy; three children, Johanna (1959), Alexander (1961), and Mathieu (1965) with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a commune in the early 1970s. Mathematical work. Grothendieck's early mathematical work was in functional analysis. Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz. His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of Lp spaces in studying linear maps between topological vector spaces. In a few years, he had become a leading authority on this area of functional analysis—to the extent that Dieudonné compares his impact in this field to that of Banach.
It is, however, in algebraic geometry and related fields where Grothendieck did his most important and influential work. From approximately 1955 he started to work on sheaf theory and homological algebra, producing the influential "Tôhoku paper" ("Sur quelques points d'algèbre homologique", published in the Tohoku Mathematical Journal in 1957) where he introduced abelian categories and applied their theory to show that sheaf cohomology may be defined as certain derived functors in this context. Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre and others, after sheaves had been defined by Jean Leray. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his "relative point of view" (pairs of varieties related by a morphism), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite-dimensional; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space.
In 1956, he applied the same thinking to the Riemann–Roch theorem, which recently had been generalized to any dimension by Hirzebruch. The Grothendieck–Riemann–Roch theorem was announced by Grothendieck at the initial Mathematische Arbeitstagung in Bonn, in 1957. It appeared in print in a paper written by Armand Borel with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in Claude Chevalley's seminar. He outlined his programme in his talk at the 1958 International Congress of Mathematicians. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed generic points, which led to the theory of schemes. Grothendieck also pioneered the systematic use of nilpotents. As 'functions' these can take only the value 0, but they carry infinitesimal information, in purely algebraic settings. His "theory of schemes" has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use birational geometry, techniques from number theory, Galois theory, commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way.

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