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Work. Weil made substantial contributions in a number of areas, the most important being his discovery of profound connections between algebraic geometry and number theory. This began in his doctoral work leading to the Mordell–Weil theorem (1928, and shortly applied in Siegel's theorem on integral points). Mordell's theorem had an "ad hoc" proof; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which would not be categorized as such for another two decades. Both aspects of Weil's work have steadily developed into substantial theories. Among his major accomplishments were the 1940s proof of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). The so-called Weil conjectures were hugely influential from around 1950; these statements were later proved by Bernard Dwork, Alexander Grothendieck, Michael Artin, and finally by Pierre Deligne, who completed the most difficult step in 1973.
Weil introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and gave a proof of the Riemann–Roch theorem with them (a version appeared in his "Basic Number Theory" in 1967). His 'matrix divisor' (vector bundle "avant la lettre") Riemann–Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. The Weil conjecture on Tamagawa numbers proved resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up another credited "Weil conjecture", around 1967, which later under pressure from Serge Lang (resp. of Jean-Pierre Serre) became known as the Taniyama–Shimura conjecture (resp. Taniyama–Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.
Other significant results were on Pontryagin duality and differential geometry. He introduced the concept of a uniform space in general topology, as a by-product of his collaboration with Nicolas Bourbaki (of which he was a Founding Father). His work on sheaf theory hardly appears in his published papers, but correspondence with Henri Cartan in the late 1940s, and reprinted in his collected papers, proved most influential. He also chose the symbol ∅, derived from the letter Ø in the Norwegian alphabet (which he alone among the Bourbaki group was familiar with), to represent the empty set. Weil also made a well-known contribution in Riemannian geometry in his very first paper in 1926, when he showed that the classical isoperimetric inequality holds on non-positively curved surfaces. This established the 2-dimensional case of what later became known as the Cartan–Hadamard conjecture. He discovered that the so-called Weil representation, previously introduced in quantum mechanics by Irving Segal and David Shale, gave a contemporary framework for understanding the classical theory of quadratic forms. This was also a beginning of a substantial development by others, connecting representation theory and theta functions.
Weil was a member of both the National Academy of Sciences and the American Philosophical Society. As expositor. Weil's ideas made an important contribution to the writings and seminars of Bourbaki, before and after World War II. He also wrote several books on the history of number theory. Beliefs. Hindu thought had great influence on Weil. He was an agnostic, and he respected religions. Legacy. Asteroid 289085 Andreweil, discovered by astronomers at the Saint-Sulpice Observatory in 2004, was named in his memory. The official was published by the Minor Planet Center on 14 February 2014 (). Books. Mathematical works: Collected papers: Autobiography: Memoir by his daughter:
Achaeans (Homer) The Achaeans or Akhaians (; , "the Achaeans" or "of Achaea") is one of the names in Homer which is used to refer to the Greeks collectively. The term "Achaean" is believed to be related to the Hittite term Ahhiyawa and the Egyptian term Ekwesh which appear in texts from the Late Bronze Age and are believed to refer to the Mycenaean civilization or some part of it. In the historical period, the term fell into disuse as a general term for Greek people, and was generally reserved for inhabitants of the region of Achaea, a region in the north-central part of the Peloponnese. The city-states of this region later formed a confederation known as the Achaean League, which was influential during the 3rd and 2nd centuries BC. Etymology. According to Margalit Finkelberg the name Ἀχαιοί (earlier Ἀχαιϝοί) is possibly derived, via an intermediate form Ἀχαϝyοί, from a hypothetical older Greek form reflected in the Hittite form "Aḫḫiyawā"; the latter is attested in the Hittite archives, e.g. in the Tawagalawa letter. However, Robert S. P. Beekes doubted its validity and suggested a Pre-Greek "Akaywa-".
Homeric versus later use. In Homer, the term Achaeans is one of the primary terms used to refer to the Greeks as a whole. It is used 598 times in the "Iliad", often accompanied by the epithet "long-haired". Other common names used in Homer are Danaans (; "Danaoi"; used 138 times in the "Iliad") and Argives (; ; used 182 times in the "Iliad") while Panhellenes ( "Panhellenes," "All of the Greeks") and Hellenes (; "Hellenes") both appear only once; All of the aforementioned terms were used synonymously to denote a common Greek identity. In some English translations of the "Iliad", the Achaeans are simply called the Greeks throughout. Later, by the Archaic and Classical periods, the term "Achaeans" referred to inhabitants of the much smaller region of Achaea. Herodotus identified the Achaeans of the northern Peloponnese as descendants of the earlier, Homeric Achaeans. According to Pausanias, writing in the 2nd century AD, the term "Achaean" was originally given to those Greeks inhabiting the Argolis and Laconia.
Pausanias and Herodotus both recount the legend that the Achaeans were forced from their homelands by the Dorians, during the legendary Dorian invasion of the Peloponnese. They then moved into the region later called Achaea. A scholarly consensus has not yet been reached on the origin of the historic Achaeans relative to the Homeric Achaeans and is still hotly debated. Former emphasis on presumed race, such as John A. Scott's article about the blond locks of the Achaeans as compared to the dark locks of "Mediterranean" Poseidon, on the basis of hints in Homer, has been rejected by some. The contrasting belief that "Achaeans", as understood through Homer, is "a name without a country", an "ethnos" created in the Epic tradition, has modern supporters among those who conclude that "Achaeans" were redefined in the 5th century BC, as contemporary speakers of Aeolic Greek. Karl Beloch suggested there was no Dorian invasion, but rather that the Peloponnesian Dorians were the Achaeans. Eduard Meyer, disagreeing with Beloch, instead put forth the suggestion that the real-life Achaeans were mainland pre-Dorian Greeks. His conclusion is based on his research on the similarity between the languages of the Achaeans and pre-historic Arcadians. William Prentice disagreed with both, noting archeological evidence suggests the Achaeans instead migrated from "southern Asia Minor to Greece, probably settling first in lower Thessaly" probably prior to 2000 BC.
Hittite documents. Some Hittite texts mention a nation to the west called Ahhiyawa ( "Aḫḫiyawa"). In the earliest reference to this land, a letter outlining the treaty violations of the Hittite vassal Madduwatta, it is called "Ahhiya". Another important example is the "Tawagalawa Letter" written by an unnamed Hittite king (most probably Hattusili III) of the empire period (14th–13th century BC) to the king of "Ahhiyawa", treating him as an equal and implying Miletus ("Millawanda") was under his control. It also refers to an earlier ""Wilusa" episode" involving hostility on the part of "Ahhiyawa". Ahhiya(wa) has been identified with the Achaeans of the Trojan War and the city of Wilusa with the legendary city of Troy (note the similarity with early Greek "Wilion", later "Ilion", the name of the acropolis of Troy). Emil Forrer, a Swiss Hittitologist who worked on the Boghazköy tablets in Berlin, said the Achaeans of pre-Homeric Greece were directly associated with the term "Land of Ahhiyawa" mentioned in the Hittite texts. His conclusions at the time were challenged by other Hittitologists (i.e. Johannes Friedrich in 1927 and Albrecht Götze in 1930), as well as by Ferdinand Sommer, who published his ("The Ahhiyawa Documents") in 1932. The exact relationship of the term "Ahhiyawa" to the Achaeans beyond a similarity in pronunciation was hotly debated by scholars, even following the discovery that Mycenaean Linear B is an early form of Greek; the earlier debate was summed up in 1984 by Hans G. Güterbock of the Oriental Institute. More recent research based on new readings and interpretations of the Hittite texts, as well as of the material evidence for Mycenaean contacts with the Anatolian mainland, came to the conclusion that "Ahhiyawa" referred to the Mycenaean world, or at least to a part of it.
Scholarship up to 2011 was reviewed by Gary M. Beckman et al. In this review, the increasing acceptance of the Ahhiyawa-Mycenaeans hypothesis was noted. As to the exact location of Ahhiyawa: In fact, the authors state that "there is now little doubt that Ahhiyawa was a reference by the Hittites to some or all of the Bronze Age Mycenaean world", and that Forrer was "largely correct after all". Egyptian sources. It has been proposed that "Ekwesh" of the Egyptian records may relate to "Achaea" (compared to Hittite "Ahhiyawa"), whereas "Denyen" and "Tanaju" may relate to Classical Greek "Danaoi". The earliest textual reference to the Mycenaean world is in the Annals of Thutmosis III (–1425 BC), which refers to messengers from the king of the Tanaju, , offering greeting gifts to the Egyptian king, in order to initiate diplomatic relations, when the latter campaigned in Syria. Tanaju is also listed in an inscription at the Mortuary Temple of Amenhotep III. The latter ruled Egypt in –1344 BC. Moreover, a list of the cities and regions of the Tanaju is also mentioned in this inscription; among the cities listed are Mycenae, Nauplion, Kythera, Messenia and the Thebaid (region of Thebes).
During the 5th year of Pharaoh Merneptah, a confederation of Libyan and northern peoples is supposed to have attacked the western delta. Included amongst the ethnic names of the repulsed invaders is the Ekwesh or Eqwesh, whom some have seen as Achaeans, although Egyptian texts specifically mention these Ekwesh to be circumcised. Homer mentions an Achaean attack upon the delta, and Menelaus speaks of the same in Book IV of the "Odyssey" to Telemachus when he recounts his own return home from the Trojan War. Some ancient Greek authors also say that Helen had spent the time of the Trojan War in Egypt, and not at Troy, and that after Troy the Greeks went there to recover her. Greek mythology. In Greek mythology, the perceived cultural divisions among the Hellenes were represented as legendary lines of descent that identified kinship groups, with each line being derived from an eponymous ancestor. Each of the Greek "ethne" were said to be named in honor of their respective ancestors: Achaeus of the Achaeans, Danaus of the Danaans, Cadmus of the Cadmeans (the Thebans), Hellen of the Hellenes (not to be confused with Helen of Troy), Aeolus of the Aeolians, Ion of the Ionians, and Dorus of the Dorians.
Cadmus from Phoenicia, Danaus from Egypt, and Pelops from Anatolia each gained a foothold in mainland Greece and were assimilated and Hellenized. Hellen, Graikos, Magnes, and Macedon were sons of Deucalion and Pyrrha, the only people who survived the Great Flood; the "ethne" were said to have originally been named "Graikoi" after the elder son but later renamed "Hellenes" after Hellen who was proved to be the strongest. Sons of Hellen and the nymph Orseis were Dorus, Xuthos, and Aeolus. Sons of Xuthos and Kreousa, daughter of Erechthea, were Ion and Achaeus. According to Hyginus, 22 Achaeans killed 362 Trojans during their ten years at Troy.
Atle Selberg Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950 and an honorary Abel Prize in 2002. Early years. Selberg was born in Langesund, Norway, the son of teacher Anna Kristina Selberg and mathematician Ole Michael Ludvigsen Selberg. Two of his three brothers, Sigmund and Henrik, were also mathematicians. His other brother, Arne, was a professor of engineering. While he was still at school he was influenced by the work of Srinivasa Ramanujan and he found an exact analytical formula for the partition function as suggested by the works of Ramanujan; however, this result was first published by Hans Rademacher. He studied at the University of Oslo and completed his doctorate in 1943. World War II. During World War II, Selberg worked in isolation due to the German occupation of Norway. After the war, his accomplishments became known, including a proof that a positive proportion of the zeros of the Riemann zeta function lie on the line formula_1.
During the war, he fought against the German invasion of Norway, and was imprisoned several times. Post-war in Norway. After the war, he turned to sieve theory, a previously neglected topic which Selberg's work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a method well adapted in particular to providing auxiliary upper bounds, and which contributed to Chen's theorem, among other important results. In 1948 Selberg submitted two papers in "Annals of Mathematics" in which he proved by elementary means the theorems for primes in arithmetic progression and the density of primes. This challenged the widely held view of his time that certain theorems are only obtainable with the advanced methods of complex analysis. Both results were based on his work on the asymptotic formula where for primes formula_4. He established this result by elementary means in March 1948, and by July of that year, Selberg and Paul Erdős each obtained elementary proofs of the prime number theorem, both using the asymptotic formula above as a starting point. Circumstances leading up to the proofs, as well as publication disagreements, led to a bitter dispute between the two mathematicians.
For his fundamental accomplishments during the 1940s, Selberg received the 1950 Fields Medal. Institute for Advanced Study. Selberg moved to the United States and worked as an associate professor at Syracuse University and later settled at the Institute for Advanced Study in Princeton, New Jersey in the 1950s, where he remained until his death. During the 1950s he worked on introducing spectral theory into number theory, culminating in his development of the Selberg trace formula, the most famous and influential of his results. In its simplest form, this establishes a duality between the lengths of closed geodesics on a compact Riemann surface and the eigenvalues of the Laplacian, which is analogous to the duality between the prime numbers and the zeros of the zeta function. He generally worked alone. His only coauthor was Sarvadaman Chowla. Selberg was awarded the 1986 Wolf Prize in Mathematics. He was also awarded an honorary Abel Prize in 2002, its founding year, before the awarding of the regular prizes began.
Selberg received many distinctions for his work, in addition to the Fields Medal, the Wolf Prize and the Gunnerus Medal. He was elected to the Norwegian Academy of Science and Letters, the Royal Danish Academy of Sciences and Letters and the American Academy of Arts and Sciences. In 1972, he was awarded an honorary degree, doctor philos. honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology. His first wife, Hedvig, died in 1995. With her, Selberg had two children: Ingrid Selberg (married to playwright Mustapha Matura) and Lars Selberg. In 2003 Atle Selberg married Betty Frances ("Mickey") Compton (born in 1929). He died at home in Princeton, New Jersey on 6 August 2007 of heart failure. Upon his death he was survived by his widow, daughter, son, and four grandchildren. Selected publications. Selberg's collected works were published in two volumes. The first volume contains 41 articles, and the second volume contains three additional articles, in addition to Selberg's lectures on sieves.
Aeschylus Aeschylus (, ; ; /524 – /455 BC) was an ancient Greek tragedian often described as the father of tragedy. Academic knowledge of the genre begins with his work, and understanding of earlier Greek tragedy is largely based on inferences made from reading his surviving plays. According to Aristotle, he expanded the number of characters in the theatre and allowed conflict among them. Formerly, characters interacted only with the chorus. Only seven of Aeschylus's estimated 70 to 90 plays have survived in complete form. There is a long-standing debate regarding the authorship of one of them, "Prometheus Bound", with some scholars arguing that it may be the work of his son Euphorion. Fragments from other plays have survived in quotations, and more continue to be discovered on Egyptian papyri. These fragments often give further insights into Aeschylus' work. He was likely the first dramatist to present plays as a trilogy. His "Oresteia" is the only extant ancient example. At least one of his plays was influenced by the Persians' second invasion of Greece (480–479 BC). This work, "The Persians", is one of very few classical Greek tragedies concerned with contemporary events, and the only one extant. The significance of the war with Persia was so great to Aeschylus and the Greeks that his epitaph commemorates his participation in the Greek victory at Marathon while making no mention of his success as a playwright.
Life. Aeschylus was born around 525 BC in Eleusis, a small town about northwest of Athens, in the fertile valleys of western Attica. Some scholars argue that the date of Aeschylus's birth may be based on counting back 40 years from his first victory in the Great Dionysia. His family was wealthy and well established. His father, Euphorion, was said to be a member of the Eupatridae, the ancient nobility of Attica, but this might be a fiction invented by the ancients to account for the grandeur of Aeschylus' plays. As a youth, Aeschylus worked at a vineyard until, according to the 2nd-century AD geographer Pausanias, the god Dionysus visited him in his sleep and commanded him to turn his attention to the nascent art of tragedy. As soon as he woke, he began to write a tragedy, and his first performance took place in 499 BC, when he was 26 years old. He won his first victory at the Dionysia in 484 BC. In 510 BC, when Aeschylus was 15 years old, Cleomenes I expelled the sons of Peisistratus from Athens, and Cleisthenes came to power. Cleisthenes' reforms included a system of registration that emphasized the importance of the deme over family tradition. In the last decade of the 6th century, Aeschylus and his family were living in the deme of Eleusis.
The Persian Wars played a large role in Aeschylus' life and career. In 490 BC, he and his brother Cynegeirus fought to defend Athens against the invading army of Darius I of Persia at the Battle of Marathon. The Athenians emerged triumphant, and the victory was celebrated across the city-states of Greece. Cynegeirus was killed while trying to prevent a Persian ship retreating from the shore, for which his countrymen extolled him as a hero. In 480 BC, Aeschylus was called into military service again, together with his younger brother Ameinias, against Xerxes I's invading forces at the Battle of Salamis. Aeschylus also fought at the Battle of Plataea in 479 BC. Ion of Chios was a witness for Aeschylus' war record and his contribution in Salamis. Salamis holds a prominent place in "The Persians", his oldest surviving play, which was performed in 472 BC and won first prize at the Dionysia. Aeschylus was one of many Greeks who were initiated into the Eleusinian Mysteries, an ancient cult of Demeter based in his home town of Eleusis. According to Aristotle, Aeschylus was accused of asebeia (impiety) for revealing some of the cult's secrets on stage.
Other sources claim that an angry mob tried to kill Aeschylus on the spot but he fled the scene. Heracleides of Pontus asserts that the audience tried to stone Aeschylus. Aeschylus took refuge at the altar in the orchestra of the Theater of Dionysus. He pleaded ignorance at his trial. He was acquitted, with the jury sympathetic to the military service of him and his brothers during the Persian Wars. According to the 2nd-century AD author Aelian, Aeschylus' younger brother Ameinias helped to acquit Aeschylus by showing the jury the stump of the hand he had lost at Salamis, where he was voted bravest warrior. The truth is that the award for bravery at Salamis went not to Aeschylus' brother but to Ameinias of Pallene. Aeschylus travelled to Sicily once or twice in the 470s BC, having been invited by Hiero I, tyrant of Syracuse, a major Greek city on the eastern side of the island. He produced "The Women of Aetna" during one of these trips (in honor of the city founded by Hieron), and restaged his "Persians". By 473 BC, after the death of Phrynichus, one of his chief rivals, Aeschylus was the yearly favorite in the Dionysia, winning first prize in nearly every competition. In 472 BC, Aeschylus staged the production that included the "Persians", with Pericles serving as "choregos".
Personal life. Aeschylus married and had two sons, Euphorion and Euaeon, both of whom became tragic poets. Euphorion won first prize in 431 BC in competition against both Sophocles and Euripides. A nephew of Aeschylus, Philocles (his sister's son), was also a tragic poet, and won first prize in the competition against Sophocles' "Oedipus Rex". Aeschylus had at least two brothers, Cynegeirus and Ameinias. Death. In 458 BC, Aeschylus returned to Sicily for the last time, visiting the city of Gela, where he died in 456 or 455 BC. Valerius Maximus wrote that he was killed outside the city by a tortoise dropped by an eagle which had mistaken his head for a rock suitable for shattering the shell, and killed him. Pliny, in his "Naturalis Historiæ", adds that Aeschylus had been staying outdoors to avoid a prophecy that he would be killed by a falling object, but this story may be a legend and due to a misunderstanding of the iconography on Aeschylus' tomb. Aeschylus' work was so respected by the Athenians that after his death his tragedies were the only ones allowed to be restaged in subsequent competitions. His sons Euphorion and Euæon and his nephew Philocles also became playwrights.
The inscription on Aeschylus' gravestone makes no mention of his theatrical renown, commemorating only his military achievements: Works. The seeds of Greek drama were sown in religious festivals for the gods, chiefly Dionysus, the god of wine. During Aeschylus' lifetime, dramatic competitions became part of the City Dionysia, held in spring. The festival opened with a procession which was followed by a competition of boys singing dithyrambs, and all culminated in a pair of dramatic competitions. The first competition Aeschylus would have participated in involved three playwrights each presenting three tragedies and one satyr play. A second competition involving five comedic playwrights followed, and the winners of both competitions were chosen by a panel of judges. Aeschylus entered many of these competitions, and various ancient sources attribute between seventy and ninety plays to him. Only seven tragedies attributed to him have survived intact: "The Persians", "Seven Against Thebes", "The Suppliants", the trilogy known as "The Oresteia" (the three tragedies "Agamemnon", "The Libation Bearers" and "The Eumenides"), and "Prometheus Bound" (whose authorship is disputed). With the exception of this last play – the success of which is uncertain – all of Aeschylus's extant tragedies are known to have won first prize at the City Dionysia.
The Alexandrian "Life of Aeschylus" claims that he won the first prize at the City Dionysia thirteen times. This compares favorably with Sophocles' reported eighteen victories (with a substantially larger catalogue, an estimated 120 plays), and dwarfs the five victories of Euripides, who is thought to have written roughly 90 plays. Trilogies. One hallmark of Aeschylean dramaturgy appears to have been his tendency to write connected trilogies in which each play serves as a chapter in a continuous dramatic narrative. The "Oresteia" is the only extant example of this type of connected trilogy, but there is evidence that Aeschylus often wrote such trilogies. The satyr plays that followed his tragic trilogies also drew from myth. The satyr play Proteus, which followed the "Oresteia", treated the story of Menelaus' detour in Egypt on his way home from the Trojan War. It is assumed, based on the evidence provided by a catalogue of Aeschylean play titles, scholia, and play fragments recorded by later authors, that three other extant plays of his were components of connected trilogies: "Seven Against Thebes" was the final play in an Oedipus trilogy, and "The Suppliants" and "Prometheus Bound" were each the first play in a Danaid trilogy and Prometheus trilogy, respectively. Scholars have also suggested several completely lost trilogies, based on known play titles. A number of these treated myths about the Trojan War. One, collectively called the "Achilleis", comprised "Myrmidons", "Nereids" and "Phrygians" (alternately, "The Ransoming of Hector").
Another trilogy apparently recounted the entrance of the Trojan ally Memnon into the war, and his death at the hands of Achilles ("Memnon" and "The Weighing of Souls" being two components of the trilogy). "The Award of the Arms", "The Phrygian Women", and "The Salaminian Women" suggest a trilogy about the madness and subsequent suicide of the Greek hero Ajax. Aeschylus seems to have written about Odysseus' return to Ithaca after the war (including his killing of his wife Penelope's suitors and its consequences) in a trilogy consisting of "The Soul-raisers", "Penelope", and "The Bone-gatherers". Other suggested trilogies touched on the myth of Jason and the Argonauts ("Argô", "Lemnian Women", "Hypsipylê"), the life of Perseus ("The Net-draggers", "Polydektês", "Phorkides"), the birth and exploits of Dionysus ("Semele", "Bacchae", "Pentheus"), and the aftermath of the war portrayed in "Seven Against Thebes" ("Eleusinians", "Argives" (or "Argive Women"), "Sons of the Seven"). Surviving plays. "The Persians" (472 BC).
"The Persians" ("Persai") is the earliest of Aeschylus' extant plays. It was performed in 472 BC. It was based on Aeschylus' own experiences, specifically the Battle of Salamis. It is unique among surviving Greek tragedies in that it describes a recent historical event. "The Persians" focuses on the popular Greek theme of hubris and blames Persia's loss on the pride of its king. It opens with the arrival of a messenger in Susa, the Persian capital, bearing news of the catastrophic Persian defeat at Salamis, to Atossa, the mother of the Persian King Xerxes. Atossa then travels to the tomb of Darius, her husband, where his ghost appears, to explain the cause of the defeat. It is, he says, the result of Xerxes' hubris in building a bridge across the Hellespont, an action which angered the gods. Xerxes appears at the end of the play, not realizing the cause of his defeat, and the play closes to lamentations by Xerxes and the chorus. "Seven Against Thebes" (467 BC). "Seven against Thebes" ("Hepta epi Thebas") was performed in 467 BC. It has the contrasting theme of the interference of the gods in human affairs. Another theme, with which Aeschylus' would continually involve himself, makes its first known appearance in this play, namely that the polis was a key development of human civilization.
The play tells the story of Eteocles and Polynices, the sons of the shamed king of Thebes, Oedipus. Eteocles and Polynices agree to share and alternate the throne of the city. After the first year, Eteocles refuses to step down. Polynices therefore undertakes war. The pair kill each other in single combat, and the original ending of the play consisted of lamentations for the dead brothers. But a new ending was added to the play some fifty years later: Antigone and Ismene mourn their dead brothers, a messenger enters announcing an edict prohibiting the burial of Polynices, and Antigone declares her intention to defy this edict. The play was the third in a connected Oedipus trilogy. The first two plays were "Laius" and "Oedipus". The concluding satyr play was "The Sphinx". "The Suppliants" (463 BC). Aeschylus continued his emphasis on the polis with "The Suppliants" ("Hiketides") in 463 BC. The play gives tribute to the democratic undercurrents which were running through Athens and preceding the establishment of a democratic government in 461. The Danaids (50 daughters of Danaus, founder of Argos) flee a forced marriage to their cousins in Egypt. They turn to King Pelasgus of Argos for protection, but Pelasgus refuses until the people of Argos weigh in on the decision (a distinctly democratic move on the part of the king). The people decide that the Danaids deserve protection and are allowed within the walls of Argos despite Egyptian protests.
A Danaid trilogy had long been assumed because of "The Suppliants"' cliffhanger ending. This was confirmed by the 1952 publication of Oxyrhynchus Papyrus 2256 fr. 3. The constituent plays are generally agreed to be "The Suppliants", "The Egyptians" and "The Danaids". A plausible reconstruction of the trilogy's last two-thirds runs thus: In "The Egyptians", the Argive-Egyptian war threatened in the first play has transpired. King Pelasgus was killed during the war, and Danaus rules Argos. Danaus negotiates a settlement with Aegyptus, a condition of which requires his 50 daughters to marry the 50 sons of Aegyptus. Danaus secretly informs his daughters of an oracle which predicts that one of his sons-in-law would kill him. He orders the Danaids to murder their husbands therefore on their wedding night. His daughters agree. "The Danaids" would open the day after the wedding. It is revealed that 49 of the 50 Danaids killed their husbands. Hypermnestra did not kill her husband, Lynceus, and helped him escape. Danaus is angered by his daughter's disobedience and orders her imprisonment and possibly execution. In the trilogy's climax and dénouement, Lynceus reveals himself to Danaus and kills him, thus fulfilling the oracle. He and Hypermnestra will establish a ruling dynasty in Argos. The other 49 Danaids are absolved of their murders, and married off to unspecified Argive men. The satyr play following this trilogy was titled "Amymone", after one of the Danaids.
"The Oresteia" (458 BC). Besides a few missing lines, the "Oresteia" of 458 BC is the only complete trilogy of Greek plays by any playwright still extant (of "Proteus", the satyr play which followed, only fragments are known). "Agamemnon" and "The Libation Bearers" ("Choephoroi") and "The Eumenides" together tell the violent story of the family of Agamemnon, king of Argos. "Agamemnon". Aeschylus begins in Greece, describing the return of King Agamemnon from his victory in the Trojan War, from the perspective of the townspeople (the Chorus) and his wife, Clytemnestra. Dark foreshadowings build to the death of the king at the hands of his wife, who was angry that their daughter Iphigenia was killed so that the gods would restore the winds and allow the Greek fleet to sail to Troy. Clytemnestra was also unhappy that Agamemnon kept the Trojan prophetess Cassandra as his concubine. Cassandra foretells the murder of Agamemnon and of herself to the assembled townsfolk, who are horrified. She then enters the palace knowing that she cannot avoid her fate. The ending of the play includes a prediction of the return of Orestes, son of Agamemnon, who will seek to avenge his father.
"The Libation Bearers". "The Libation Bearers" opens with Orestes' arrival at Agamemnon's tomb, from exile in Phocis. Electra meets Orestes there. They plan revenge against Clytemnestra and her lover, Aegisthus. Clytemnestra's account of a nightmare in which she gives birth to a snake is recounted by the chorus. This leads her to order her daughter, Electra, to pour libations on Agamemnon's tomb (with the assistance of libation bearers) in hope of making amends. Orestes enters the palace pretending to bear news of his own death. Clytemnestra calls in Aegisthus to learn the news. Orestes kills them both. Orestes is then beset by the Furies, who avenge the murders of kin in Greek mythology. "The Eumenides". The third play addresses the question of Orestes' guilt. The Furies drive Orestes from Argos and into the wilderness. He makes his way to the temple of Apollo and begs Apollo to drive the Furies away. Apollo had encouraged Orestes to kill Clytemnestra, so he bears some of the guilt for the murder. Apollo sends Orestes to the temple of Athena with Hermes as a guide.
The Furies track him down, and Athena steps in and declares that a trial is necessary. Apollo argues Orestes' case, and after the judges (including Athena) deliver a tie vote, Athena announces that Orestes is acquitted. She renames the Furies "The Eumenides" (The Good-spirited, or Kindly Ones), and extols the importance of reason in the development of laws. As in "The Suppliants", the ideals of a democratic Athens are praised. "Prometheus Bound" (date disputed). "Prometheus Bound" is attributed to Aeschylus by ancient authorities. Since the late 19th century, however, scholars have increasingly doubted this ascription, largely on stylistic grounds. Its production date is also in dispute, with theories ranging from the 480s BC to as late as the 410s. The play consists mostly of static dialogue. The Titan Prometheus is bound to a rock throughout, which is his punishment from the Olympian Zeus for providing fire to humans. The god Hephaestus and the Titan Oceanus and the chorus of Oceanids all express sympathy for Prometheus' plight. Prometheus is met by Io, a fellow victim of Zeus' cruelty. He prophesies her future travels, revealing that one of her descendants will free Prometheus. The play closes with Zeus sending Prometheus into the abyss because Prometheus will not tell him of a potential marriage which could prove Zeus' downfall.
"Prometheus Bound" seems to have been the first play in a trilogy, the "Prometheia". In the second play, "Prometheus Unbound", Heracles frees Prometheus from his chains and kills the eagle that had been sent daily to eat Prometheus' perpetually regenerating liver, then believed the source of feeling. We learn that Zeus has released the other Titans which he imprisoned at the conclusion of the Titanomachy, perhaps foreshadowing his eventual reconciliation with Prometheus. In the trilogy's conclusion, "Prometheus the Fire-Bringer", it seems that the Titan finally warns Zeus not to sleep with the sea nymph Thetis, for she is fated to beget a son greater than the father. Not wishing to be overthrown, Zeus marries Thetis off to the mortal Peleus. The product of that union is Achilles, Greek hero of the Trojan War. After reconciling with Prometheus, Zeus probably inaugurates a festival in his honor at Athens. Lost plays. Of Aeschylus' other plays, only titles and assorted fragments are known. There are enough fragments (along with comments made by later authors and scholiasts) to produce rough synopses for some plays.
"Myrmidons". This play was based on books 9 and 16 of the "Iliad". Achilles sits in silent indignation over his humiliation at Agamemnon's hands for most of the play. Envoys from the Greek army attempt to reconcile Achilles to Agamemnon, but he yields only to Patroclus, who then battles the Trojans in Achilles' armour. The bravery and death of Patroclus are reported in a messenger's speech, which is followed by mourning. "Nereids". This play was based on books 18 and 19 and 22 of the "Iliad". It follows the Daughters of Nereus, the sea god, who lament Patroclus' death. A messenger tells how Achilles (perhaps reconciled to Agamemnon and the Greeks) slew Hector. "Phrygians", or "Hector's Ransom". After a brief discussion with Hermes, Achilles sits in silent mourning over Patroclus. Hermes then brings in King Priam of Troy, who wins over Achilles and ransoms his son's body in a spectacular coup de théâtre. A scale is brought on stage and Hector's body is placed in one scale and gold in the other. The dynamic dancing of the chorus of Trojans when they enter with Priam is reported by Aristophanes.
"Niobe". The children of Niobe, the heroine, have been slain by Apollo and Artemis because Niobe had gloated that she had more children than their mother, Leto. Niobe sits in silent mourning on stage during most of the play. In the "Republic", Plato quotes the line "God plants a fault in mortals when he wills to destroy a house utterly." These are the remaining 71 plays ascribed to Aeschylus which are known: Influence. Influence on Greek drama and culture. The theatre was just beginning to evolve when Aeschylus started writing for it. Earlier playwrights such as Thespis had already expanded the cast to include an actor who was able to interact with the chorus. Aeschylus added a second actor, allowing for greater dramatic variety, while the chorus played a less important role. He is sometimes credited with introducing "skenographia", or scene-decoration, though Aristotle gives this distinction to Sophocles. Aeschylus is also said to have made the costumes more elaborate and dramatic, and made his actors wear platform boots ("cothurni") to make them more visible to the audience. According to a later account of Aeschylus' life, the chorus of Furies in the first performance of the "Eumenides" were so frightening when they entered that children fainted, patriarchs urinated, pregnant women went into labour.
Aeschylus wrote his plays in verse. No violence is performed onstage. The plays have a remoteness from daily life in Athens, relating stories about the gods, or being set, like "The Persians", far away. Aeschylus' work has a strong moral and religious emphasis. The "Oresteia" trilogy concentrated on humans' position in the cosmos relative to the gods and divine law and divine punishment. Aeschylus' popularity is evident in the praise that the comic playwright Aristophanes gives him in "The Frogs", produced some 50 years after Aeschylus' death. Aeschylus appears as a character in the play and claims, at line 1022, that his "Seven against Thebes" "made everyone watching it to love being warlike". He claims, at lines 1026–7, that with "The Persians" he "taught the Athenians to desire always to defeat their enemies." Aeschylus goes on to say, at lines 1039ff., that his plays inspired the Athenians to be brave and virtuous. Influence outside Greek culture. Aeschylus' works were influential beyond his own time. Hugh Lloyd-Jones draws attention to Richard Wagner's reverence of Aeschylus. Michael Ewans argues in his "Wagner and Aeschylus. The Ring and the Oresteia" (London: Faber. 1982) that the influence was so great as to merit a direct character by character comparison between Wagner's "Ring" and Aeschylus's "Oresteia". But a critic of that book, while not denying that Wagner read and respected Aeschylus, has described the arguments as unreasonable and forced.
J.T. Sheppard argues in the second half of his "Aeschylus and Sophocles: Their Work and Influence" that Aeschylus and Sophocles have played a major part in the formation of dramatic literature from the Renaissance to the present, specifically in French and Elizabethan drama. He also claims that their influence went beyond just drama and applies to literature in general, citing Milton and the Romantics. Eugene O'Neill's "Mourning Becomes Electra" (1931), a trilogy of three plays set in America after the Civil War, is modeled after the "Oresteia". Before writing his acclaimed trilogy, O'Neill had been developing a play about Aeschylus, and he noted that Aeschylus "so changed the system of the tragic stage that he has more claim than anyone else to be regarded as the founder (Father) of Tragedy." The quotation from Aeschylus was later inscribed on a memorial at the gravesite of Robert Kennedy following his own assassination.
Amber Road The Amber Road was an ancient trade route for the transfer of amber from coastal areas of the North Sea and the Baltic Sea to the Mediterranean Sea. Prehistoric trade routes between Northern and Southern Europe were defined by the amber trade. As an important commodity, sometimes dubbed "the gold of the north", amber was transported from the North Sea and Baltic Sea coasts overland by way of the Vistula and Dnieper rivers to Italy, Greece, the Black Sea, Syria and Egypt over a period of thousands of years. Antiquity. The oldest trade in amber started from Sicily. The Sicilian amber trade was directed to Greece, North Africa and Spain. Sicilian amber was also discovered in Mycenae by the archaeologist Heinrich Schliemann, and it appeared in sites in southern Spain and Portugal. Its distribution is similar to that of ivory, so it is possible that amber from Sicily reached the Iberian Peninsula through contacts with North Africa. After a decline in the consumption and trade of amber at the beginning of the Bronze Age, around 2000 BC, the influence of Baltic amber gradually took the place of Sicilian amber throughout the Iberian Peninsula from around 1000 BC. The new evidence comes from various archaeological and geological locations on the Iberian Peninsula.
From at least the 16th century BC, amber was moved from Northern Europe to the Mediterranean area. The breast ornament of the Egyptian Pharaoh Tutankhamen ( BC) contains large Baltic amber beads. Schliemann found Baltic amber beads at Mycenae, as shown by spectroscopic investigation. The quantity of amber in the Royal Hypogeum of Qatna, in Syria, is unparalleled among known second millennium BC sites in the Levant and the Ancient Near East. Amber was sent from the North Sea to the Temple of Apollo at Delphi as an offering. From the Black Sea, trade could continue to Asia along the Silk Road, another ancient trade route. In Roman times, a main route ran south from the Baltic coast (modern Lithuania), the entire north–south length of modern-day Poland (likely through the Iron Age settlement of Biskupin), through the land of the Boii (modern Czech Republic and Slovakia) to the head of the Adriatic Sea (Aquileia by the modern Gulf of Venice). Other commodities were exported to the Romans along with amber, such as animal fur and skin, honey, and wax, in exchange for Roman glass, brass, gold, and non-ferrous metals such as tin and copper imported into the early Baltic region. As this road was a lucrative trade route connecting the Baltic Sea to the Mediterranean Sea, Roman military fortifications were constructed along the route to protect merchants and traders from Germanic raids.
The Old Prussian towns of Kaup and Truso on the Baltic were the starting points of the route to the south. In Scandinavia the amber road probably gave rise to the thriving Nordic Bronze Age culture, bringing influences from the Mediterranean Sea to the northernmost countries of Europe. Kaliningrad Oblast is occasionally referred to in Russian as 'the amber region' (). Known roads by country. Estonia. Old coastal Amber road route goes along E67 highway from Reiu in Häädemeeste Parish of Pärnumaa South, where it continues as 331 local road between Rannametsa and Ikla villages. Poland. The shortest (and possibly oldest) road avoids alpine areas and led from the Baltic coastline (nowadays Lithuania and Poland), through Biskupin, Milicz, Wrocław, the Kłodzko Valley (less often through the Moravian Gate), crossed the Danube near Carnuntum in the Noricum province, headed southwest past Poetovio, Celeia, Emona, Nauportus, and reached Patavium and Aquileia at the Adriatic coast. One of the oldest directions of the last stage of the Amber Road to the south of the Danube, noted in the myth about the Argonauts, used the rivers Sava and Kupa, ending with a short continental road from Nauportus to Tarsatica in Rijeka on the coast of the Adriatic.
Germany. Several roads connected the North Sea and Baltic Sea, especially the city of Hamburg to the Brenner Pass, proceeding southwards to Brindisi (nowadays Italy) and Ambracia (nowadays Greece). Switzerland. The Swiss region indicates a number of alpine roads, concentrating around the capital city Bern and probably originating from the banks of the Rhône and Rhine. Netherlands. A small section, including Baarn, Barneveld, Amersfoort and Amerongen, connected the North Sea with the Lower Rhine. Belgium. A small section led southwards from Antwerp and Bruges to the towns Braine-l'Alleud and Braine-le-Comte, both originally named "Brennia-Brenna". The route continued by following the Meuse towards Bern in Switzerland. Southern France and Spain. Routes connected amber finding locations at Ambares (near Bordeaux), leading to Béarn and the Pyrenees. Routes connecting the amber finding locations in northern Spain and in the Pyrenees were a trading route to the Mediterranean Sea. Mongolia. Sources of archaeological finds suggest that routes may also have connected Mongolia to eastern Europe during the Kitan/Liao Period.
Modern usage. There is a tourist route stretching along the Baltic coast from Kaliningrad to Latvia called "Amber Road". "Amber Road" sites are: In Poland, the north–south motorway A1 is officially named Amber Highway. EV9 The Amber Route is a long-distance cycling route between Gdańsk, Poland and Pula, Croatia which follows the course of the Amber Road. The modern Baltic–Adriatic Corridor connects the two seas along routes that roughly follow the Amber Road.
Crandall University Crandall University is a Baptist Christian liberal arts university located in Moncton, New Brunswick, Canada. It is affiliated with the Canadian Baptists of Atlantic Canada (Canadian Baptist Ministries). History. Crandall University was founded in 1949 under the name United Baptist Bible Training School (UBBTS), and served as both a secondary school and a Bible school by the Canadian Baptists of Atlantic Canada. Over two decades, the focus of the school gradually shifted toward post-secondary programs. In 1968, UBBTS became a Bible and junior Christian liberal arts college, and in 1970 the name was changed to Atlantic Baptist College (ABC). A sustained campaign to expand the school's faculty and improve the level of education resulted in ABC being able to grant full Bachelor of Arts degrees in 1983. Its campus at this time was located along the Salisbury Road, west of Moncton's central business district. The institution moved to a new campus built on the Gorge Road, north of the central business district, in 1996. The name was changed to Atlantic Baptist University (ABU), a reflection of expanded student enrolment and academic accreditation. In 2003, the ABU sports teams adopted the name "The Blue Tide". The institution was the first, and thus far only, English-language university in Moncton. The "Atlantic Baptist University Act" was passed by the Legislative Assembly of New Brunswick in 2008.
On August 21, 2009, it was announced that the institution had changed its name to Crandall University in honour of Rev. Joseph Crandall, a pioneering Baptist minister in the maritime region. In conjunction with the university name change, Crandall Athletics took on a new identity as "The Crandall Chargers." Academics. , Crandall offers 16 undergraduate programs, 3 graduate programs, and a variety of certificate programs. Through its partnership with Acadia Divinity College, students can also enrol in the Bachelor of Theology program concurrent with a Crandall degree. Crandall has a 13:1 student-to-faculty ratio. Controversy. In 2012, Crandall University came under public scrutiny for receiving municipal funds while refusing to hire non-celibate LGBTQ people. That policy, although regarded as scriptural and consistent with its denominational tradition, was characterized by the press as anti-gay. That same year, the Crandall Student Association publicly broke with the university's administration over the policy, with the student president at the time telling the CBC, "The Christian faith does say do not judge others. And the Christian faith is all about love. So I feel that this policy – to me – doesn't seem like it's following those specific guidelines." In 2013, a year after the controversy erupted, the university opted to not apply for $150,000 in public funding that it had received annually. The university president also issued an apology, stating: "We wish to apologize for anything that Crandall University might possibly have communicated in the past that may have seemed unloving or disrespectful in any way toward any individual or groups."
Affiliations. Crandall is an affiliate member of the Association of the Registrars of the Universities and Colleges of Canada (ARUCC); a full member of the ARUCC regional association, the Atlantic Association of Registrars and Admissions Officers (AARAO); an active member of Christian Higher Education Canada (CHEC); and an active member of the New Brunswick Association of Private Colleges and Universities. However, Crandall faculty are not members of the Canadian Association of University Teachers (CAUT). In their report, the CAUT found that "while the university has a statement on academic freedom, it is significantly inconsistent with that of the CAUT and the majority of universities across the western world, and assurances that free enquiry is still possible within its constraints are unconvincing." They therefore recommended that Crandall University "be placed on the list of institutions 'found to have imposed a requirement of a commitment to a particular ideology or statement of faith as a condition of employment.'"
The university is affiliated with the Canadian Baptists of Atlantic Canada (Canadian Baptist Ministries). It is a member of the Council for Christian Colleges and Universities. Library and archives. Crandall University houses the Baptist Heritage Center whose 300 artifacts preserve the material history of Atlantic Baptists, the Convention of Atlantic Baptist Churches, and its predecessor organizations. The collection and archives includes objects used in worship services, furniture, musical instruments, church building architecture pictures and printed material. Athletics. Crandall University is represented in the Atlantic Collegiate Athletic Association (ACAA) by 8 varsity teams. The Chargers teams include men's and women's soccer, basketball, volleyball, and cross country. The Chargers also offer a boxing club program that competes internationally. The Chargers have won seven ACAA championship banners:
Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Knight Commander of the Order of the British Empire in 2000. In 2018, Wiles was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow. Wiles was born in Cambridge to theologian Maurice Frank Wiles and Patricia Wiles. While spending much of his childhood in Nigeria, Wiles developed an interest in mathematics and in Fermat's Last Theorem in particular. After moving to Oxford and graduating from there in 1974, he worked on unifying Galois representations, elliptic curves and modular forms, starting with Barry Mazur's generalizations of Iwasawa theory. In the early 1980s, Wiles spent a few years at the University of Cambridge before moving to Princeton University, where he worked on expanding out and applying Hilbert modular forms. In 1986, upon reading Ken Ribet's seminal work on Fermat's Last Theorem, Wiles set out to prove the modularity theorem for semistable elliptic curves, which implied Fermat's Last Theorem. By 1993, he had been able to convince a knowledgeable colleague that he had a proof of Fermat's Last Theorem, though a flaw was subsequently discovered. After an insight on 19 September 1994, Wiles and his student Richard Taylor were able to circumvent the flaw, and published the results in 1995, to widespread acclaim.
In proving Fermat's Last Theorem, Wiles developed new tools for mathematicians to begin unifying disparate ideas and theorems. His former student Taylor along with three other mathematicians were able to prove the full modularity theorem by 2000, using Wiles' work. Upon receiving the Abel Prize in 2016, Wiles reflected on his legacy, expressing his belief that he did not just prove Fermat's Last Theorem, but pushed the whole of mathematics as a field towards the Langlands program of unifying number theory. Education and early life. Wiles was born on 11 April 1953 in Cambridge, England, the son of Maurice Frank Wiles (1923–2005) and Patricia Wiles (née Mowll). From 1952 to 1955, his father worked as the chaplain at Ridley Hall, Cambridge, and later became the Regius Professor of Divinity at the University of Oxford. Wiles began his formal schooling in Nigeria, while living there as a very young boy with his parents. However, according to letters written by his parents, for at least the first several months after he was supposed to be attending classes, he refused to go. From that fact, Wiles himself concluded that in his earliest years, he was not enthusiastic about spending time in academic institutions. In an interview with Nadia Hasnaoui in 2021, he said he trusted the letters, yet he could not remember a time when he did not enjoy solving mathematical problems.
Wiles attended King's College School, Cambridge, and The Leys School, Cambridge. Wiles told WGBH-TV in 1999 that he came across Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped at his local library where he found a book "The Last Problem", by Eric Temple Bell, about the theorem. Fascinated by the existence of a theorem that was so easy to state that he, a ten-year-old, could understand it, but that no one had proven, he decided to be the first person to prove it. However, he soon realised that his knowledge was too limited, so he abandoned his childhood dream until it was brought back to his attention at the age of 33 by Ken Ribet's 1986 proof of the epsilon conjecture, which Gerhard Frey had previously linked to Fermat's equation. Early career. In 1974, Wiles earned his bachelor's degree in mathematics at Merton College, Oxford. Wiles's graduate research was guided by John Coates, beginning in the summer of 1975. Together they worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalised this result to totally real fields.
In 1980, Wiles earned a PhD while at Clare College, Cambridge. After a stay at the Institute for Advanced Study in Princeton, New Jersey, in 1981, Wiles became a Professor of Mathematics at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the . In 1989, Wiles was elected to the Royal Society. At that point according to his election certificate, he had been working "on the construction of ℓ-adic representations attached to Hilbert modular forms, and has applied these to prove the 'main conjecture' for cyclotomic extensions of totally real fields". Proof of Fermat's Last Theorem. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford, and then he returned to Princeton. From 1994 to 2009, Wiles was a Eugene Higgins Professor at Princeton. Starting in mid-1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, it became clear that Fermat's Last Theorem (the statement that no three positive integers , , and satisfy the equation for any integer value of greater than ) could be proven as a corollary of a limited form of the modularity theorem (unproven at the time and then known as the "Taniyama–Shimura–Weil conjecture"). The modularity theorem involved elliptic curves, which was also Wiles's own specialist area, and stated that all such curves have a modular form associated with them. These curves can be thought of as mathematical objects resembling solutions for a torus' surface, and if Fermat's Last Theorem were false and solutions existed, "a peculiar curve would result". A proof of the theorem therefore would involve showing that such a curve would not exist.
The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps impossible to prove. For example, Wiles's ex-supervisor John Coates stated that it seemed "impossible to actually prove", and Ken Ribet considered himself "one of the vast majority of people who believed [it] was completely inaccessible", adding that "Andrew Wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove [it]." Despite this, Wiles, with his from-childhood fascination with Fermat's Last Theorem, decided to undertake the challenge of proving the conjecture, at least to the extent needed for Frey's curve. He dedicated all of his research time to this problem for over six years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife. Wiles' research involved creating a proof by contradiction of Fermat's Last Theorem, which Ribet in his 1986 work had found to have an elliptic curve and thus an associated modular form if true. Starting by assuming that the theorem was incorrect, Wiles then contradicted the Taniyama–Shimura–Weil conjecture as formulated under that assumption, with Ribet's theorem (which stated that if were a prime number, no such elliptic curve could have a modular form, so no odd prime counterexample to Fermat's equation could exist). Wiles also proved that the conjecture applied to the special case known as the semistable elliptic curves to which Fermat's equation was tied. In other words, Wiles had found that the Taniyama–Shimura–Weil conjecture was true in the case of Fermat's equation, and Ribet's finding (that the conjecture holding for semistable elliptic curves could mean Fermat's Last Theorem is true) prevailed, thus proving Fermat's Last Theorem.
In June 1993, he presented his proof to the public for the first time at a conference in Cambridge. Gina Kolata of "The New York Times" summed up the presentation as follows: In August 1993, it was discovered that the proof contained a flaw in several areas, related to properties of the Selmer group and use of a tool called an Euler system. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing—rather than closing—this area came to him on 19 September 1994, when he was on the verge of giving up. The circumvention used Galois representations to replace elliptic curves, reduced the problem to a class number formula and solved it, among other matters, all using Victor Kolyvagin's ideas as a basis for fixing Matthias Flach's approach with Iwasawa theory. Together with his former student Richard Taylor, Wiles published a second paper which contained the circumvention and thus completed the proof. Both papers were published in May 1995 in a dedicated issue of the "Annals of Mathematics."
Later career. In 2011, Wiles rejoined the University of Oxford as Royal Society Research Professor. In May 2018, Wiles was appointed Regius Professor of Mathematics at Oxford, the first in the university's history. Legacy. Wiles' work has been used in many fields of mathematics. Notably, in 1999, three of his former students, Richard Taylor, Brian Conrad, and Fred Diamond, working with Christophe Breuil, built upon Wiles' proof to prove the full modularity theorem. Wiles's doctoral students have also included Manjul Bhargava (2014 winner of the Fields Medal), Ehud de Shalit, Ritabrata Munshi (winner of the SSB Prize and ICTP Ramanujan Prize), Karl Rubin (son of Vera Rubin), Christopher Skinner, and Vinayak Vatsal (2007 winner of the Coxeter–James Prize). In 2016, upon receiving the Abel Prize, Wiles said about his proof of Fermat's Last Theorem, "The methods that solved it opened up a new way of attacking one of the big webs of conjectures of contemporary mathematics called the Langlands Program, which as a grand vision tries to unify different branches of mathematics. It’s given us a new way to look at that".
Awards and honours. Wiles's proof of Fermat's Last Theorem has stood up to the scrutiny of the world's other mathematical experts. Wiles was interviewed for an episode of the BBC documentary series "Horizon" about Fermat's Last Theorem. This was broadcast as an episode of the PBS science television series "Nova" with the title "The Proof". His work and life are also described in great detail in Simon Singh's popular book "Fermat's Last Theorem". In 1988, Wiles was awarded the Junior Whitehead Prize of the London Mathematical Society (1988). In 1989, he was elected a Fellow of the Royal Society (FRS) In 1994, Wiles was elected member of the American Academy of Arts and Sciences. Upon completing his proof of Fermat's Last Theorem in 1995, he was awarded the Schock Prize, Fermat Prize, and Wolf Prize in Mathematics that year. Wiles was elected a Foreign Associate of the National Academy of Sciences and won an NAS Award in Mathematics from the National Academy of Sciences, the Royal Medal, and the Ostrowski Prize in 1996. He won the American Mathematical Society's Cole Prize, a MacArthur Fellowship, and the Wolfskehl Prize in 1997, and was elected member of the American Philosophical Society that year.
In 1998, Wiles was awarded a silver plaque from the International Mathematical Union recognising his achievements, in place of the Fields Medal, which is restricted to those under the age of 40 (Wiles was 41 when he proved the theorem in 1994). That same year, he was awarded the King Faisal Prize along with the Clay Research Award in 1999, the year the asteroid 9999 Wiles was named after him. In 2000, he was awarded Knight Commander of the Order of the British Empire (2000) In 2004 Wiles won the Premio Pitagora. In 2005, he won the Shaw Prize. The building at the University of Oxford housing the Mathematical Institute was named after Wiles in 2016. Later that year he won the Abel Prize. In 2017, Wiles won the Copley Medal. In 2019, he won the De Morgan Medal.
Ambient Ambient or ambiance or ambience may refer to:
Anne Brontë Anne Brontë (, ; 17 January 1820 – 28 May 1849) was an English novelist and poet, the youngest member of the Brontë literary family. Anne Brontë was the daughter of Maria ( Branwell) and Patrick Brontë, a poor Irish clergyman in the Church of England. Anne lived most of her life with her family at the parish of Haworth on the Yorkshire Dales. Otherwise, she attended a boarding school in Mirfield between 1836 and 1837, and between 1839 and 1845 lived elsewhere working as a governess. In 1846, she published a book of poems with her sisters and later two novels, initially under the pen name Acton Bell. Her first novel, "Agnes Grey", was published in 1847 at the same time as "Wuthering Heights" by her sister Emily Brontë. Anne's second novel, "The Tenant of Wildfell Hall", was published in 1848. "The Tenant of Wildfell Hall" is often considered one of the first feminist novels. Anne died at 29, most likely of pulmonary tuberculosis. After her death, her sister Charlotte edited "Agnes Grey" to fix issues with its first edition, but prevented republication of "The Tenant of Wildfell Hall". As a result, Anne is not as well known as her sisters. Nonetheless, both of her novels are considered classics of English literature.
Family background. Anne's father was Patrick Brontë. Patrick Brontë was born in a two-room cottage in Emdale, Loughbrickland, County Down, Ireland. He was the oldest of ten children born to Hugh Brunty and Eleanor McCrory, poor Irish peasant farmers. The family surname, "mac Aedh Ó Proinntigh", was Anglicised as Prunty or Brunty. Struggling against poverty, Patrick learned to read and write, and from 1798 taught others. In 1802, at 25, he won a place to study theology at St. John's College, Cambridge. Here he changed his name, Brunty, to the more distinguished sounding Brontë. In 1807, he was ordained in the priesthood in the Church of England. He served as a curate in Essex and then in Wellington, Shropshire. In 1810, he published his first poem, "Winter Evening Thoughts", in a local newspaper. In 1811, he published a collection of moral verse, "Cottage Poems". Also in 1811, he became vicar of St. Peter's Church in Hartshead, Yorkshire. In 1812, he was appointed an examiner in Classics at Woodhouse Grove School, near Bradford. This was a Wesleyan academy where, at 35, he met his future wife, the headmaster's niece, Maria Branwell.
Maria Branwell, Anne's mother, was the daughter of Anne Carne, the daughter of a silversmith, and Thomas Branwell, a successful and property-owning grocer and tea merchant in Penzance. Maria was the eleventh of twelve children and enjoyed the benefits of a prosperous family in a small town. After the death of her parents, Maria went to help her aunt with housekeeping functions at the school. Maria was intelligent and well read, and her strong Methodist faith attracted Patrick Brontë, whose own leanings were similar. Within three months, on 29 December 1812, though from considerably different backgrounds, Patrick Brontë and Maria Branwell were married. Their first child, Maria (1814–1825), was born after they moved to Hartshead. In 1815, Patrick was appointed curate of the chapel in Market Street Thornton, near Bradford. A second daughter, Elizabeth (1815–1825), was born shortly after. Four more children followed: Charlotte (1816–1855), Patrick Branwell (1817–1848), Emily (1818–1848), and Anne (1820–1849). Early life.
Anne was the youngest of the Brontë children. She was born on 17 January 1820 at the parsonage in Market Street, Thornton (now known as the Brontë Birthplace), on the outskirts of Bradford. Her father, Patrick, was curate there. Anne was baptised there on 25 March 1820. Later Patrick was appointed to the perpetual curacy in Haworth, a small town away. In April 1820 the family moved into the five-roomed Haworth Parsonage. When Anne was barely a year old her mother, Maria, became ill, probably with uterine cancer. Maria Branwell died on 15 September 1821. Patrick tried to remarry, without success. Maria's sister, Elizabeth Branwell, had moved to the parsonage initially for Maria, but spent the rest of her life there raising Maria's children from a sense of duty. She was stern and expected respect, not love. There was little affection between her and the older children. According to tradition Anne was her favourite. In Elizabeth Gaskell's biography of Charlotte, Patrick remembered Anne as precocious. Patrick said that when Anne was four years old he had asked her what a child most wanted and that she had said: "age and experience".
In summer 1824 Patrick sent daughters Maria, Elizabeth, Charlotte, and Emily to Crofton Hall in Crofton, West Yorkshire, and subsequently to the Clergy Daughter's School at Cowan Bridge in Lancashire. Maria and Elizabeth Brontë died of tuberculosis on 6 May and 15 June 1825 respectively, and Charlotte and Emily were brought home. The unexpected deaths distressed the family so much that Patrick could not face sending them away again. They were educated at home for the next five years, largely by Elizabeth Branwell and Patrick. The children made little attempt to mix with others outside the parsonage and relied on each other for company. The bleak moors surrounding Haworth became their playground. Anne shared a room with her aunt, Elizabeth. They were close, and she may have influenced Anne's personality and religious beliefs. Education. Anne's studies at home included music and drawing. The Keighley church organist gave piano lessons to Anne and Emily and Branwell, and John Bradley of Keighley gave them art lessons. Each drew with some skill. Their aunt tried to teach the girls how to run a household, but they inclined more to literature. They read much from their father's well-stocked library. Their reading included the Bible, Homer, Virgil, Shakespeare, Milton, Byron, Scott, articles from "Blackwood's Edinburgh Magazine" and "Fraser's Magazine" and "The Edinburgh Review", and books of history and geography and biography.
Their reading fed their imaginations, and their creativity soared after their father gave Branwell a set of toy soldiers in June 1826. They gave names to the soldiers, or the "Twelves", and developed their characters. This led to the creation of an imaginary world: the African kingdom of "Angria", which was illustrated with maps and watercolour renderings. The children devised plots about the inhabitants of Angria and its capital city, "Glass Town", later called Verreopolis or Verdopolis. Their fantastical worlds and kingdoms gradually acquired characteristics from their historical world, drawing from its sovereigns, armies, heroes, outlaws, fugitives, inns, schools, and publishers. The characters and lands created by the children were given newspapers and magazines and chronicles written in tiny books with writing so small that it was difficult to read without a magnifying glass. These creations and writings were an apprenticeship for their later literary talents. Juvenilia. Around 1831, when Anne was eleven, she and Emily broke away from Charlotte and Branwell to create and develop their own fantasy world, "Gondal". Anne and Emily were particularly close, especially after Charlotte left for Roe Head School in January 1831. Charlotte's friend Ellen Nussey visited Haworth in 1833 and reported that Emily and Anne were "like twins" and "inseparable companions". She described Anne so:
Anne took lessons from Charlotte after Charlotte had returned from Roe Head. Charlotte returned to Roe Head as a teacher on 29 July 1835, accompanied by Emily as a pupil. Emily's tuition was largely financed by Charlotte's teaching. Emily was unable to adapt to life at school and was physically ill from homesickness within a few months. She was withdrawn from school by October and replaced by Anne. Anne was 15 and it was her first time away from home. She made few friends at Roe Head. She was quiet and hardworking and determined to stay to acquire the education which she would need to support herself. She stayed for two years and returned home only during Christmas and summer holidays. She won a good-conduct medal in December 1836. Charlotte's letters almost never mention Anne while Anne was at Roe Head, which might imply that they were not close, but Charlotte was at least concerned about Anne's health. By December 1837 Anne had become seriously ill with gastritis and embroiled in religious crisis. A Moravian minister was called to see her several times during her illness, suggesting her distress was caused, in part, by conflict with the local Anglican clergy. Charlotte wrote to their father and he brought Anne home.
Employment at Blake Hall. A year after leaving the school, and aged 19, Anne was seeking a teaching position. She was the daughter of a poor clergyman and needed to earn money. Her father had no private income and the parsonage would revert to the church on his death. Teaching or working as a governess were among few options for a poor and educated woman. In April 1839 Anne started work as a governess for the Ingham family at Blake Hall, near Mirfield. The children in her charge were spoiled and disobedient. Anne had great difficulty controlling them and little success in educating them. She was not allowed to punish them, and when she complained about their behaviour she received no support and was criticised for being incapable. The Inghams were dissatisfied with their children's progress and dismissed Anne. She returned home in 1839 at Christmas. At home also were Charlotte and Emily, who had left their positions, and Branwell. Anne's time at Blake Hall was so traumatic that she reproduced it in almost perfect detail in her novel "Agnes Grey".
William Weightman. Anne returned to Haworth and met William Weightman, her father's new curate who had started work in the parish in August 1839. Weightman was 25 and had obtained a two-year licentiate in theology from the University of Durham. He was welcome at the parsonage. Anne's acquaintance with him parallels her writing a number of poems, which may suggest she fell in love with him although there is disagreement over this possibility. Little evidence exists beyond a small anecdote of Charlotte's to Ellen Nussey in January 1842. In "Agnes Grey", Agnes' interest in the curate refreshes her interest in poetry. Outside fiction, William Weightman aroused much curiosity. It seems that he was good-looking and engaging, and that his easy humour and kindness towards the sisters made an impression. It is such a character that she portrays in Edward Weston, and that her heroine Agnes Grey finds deeply appealing. Weightman died of cholera in the same year. Anne expressed her grief for his death in her poem "I will not mourn thee, lovely one", in which she called him "our darling".
Governess. From 1840 to 1845 Anne worked at Thorp Green Hall, a comfortable country house near York. Here she was governess to the children of the Reverend Edmund Robinson and his wife, Lydia. The house appeared as Horton Lodge in "Agnes Grey". Anne had four pupils: Lydia (15), Elizabeth (13), Mary (12), and Edmund (8). She initially had problems similar to those at Blake Hall. Anne missed her home and family. In a diary paper in 1841, she wrote that she did not like her situation and wished to leave it. Her quiet and gentle disposition did not help. But Anne was determined and made a success of her position, becoming well-liked by her employers. Her charges, the Robinson girls, became lifelong friends. Anne spent only five or six weeks a year with her family, during holidays at Christmas and in June. The rest of her time was spent with the Robinsons. She accompanied the Robinsons on annual holidays to Scarborough. Between 1840 and 1844 Anne spent around five weeks each summer at the coastal town and loved it. A number of locations in Scarborough were used for her novels. She had opportunities to collect semi-precious stones, considering an interest in geology, at least in her novels, or from personal experience, as something suitable for men and women to be considered as equals.
Anne and her sisters considered setting up a school while she was still working for the Robinsons. Various locations were considered, including the parsonage, but the project never materialised. Anne came home on the death of her aunt in early November 1842 while her sisters were in Brussels. Elizabeth Branwell left a £350 legacy (equivalent to £ in ) for each of her nieces. It was at the Long Plantation at Thorp Green in 1842 that Anne wrote her three-verse poem "Lines Composed in a Wood on a Windy Day", which was published in 1846 under the name Acton Bell. In January 1843 Anne returned to Thorp Green and secured a position for Branwell. He was to tutor Edmund, who was growing too old to be in Anne's care. Branwell did not live in the house as Anne did. Anne's vaunted calm appears to have been the result of hard-fought battles, balancing deeply felt emotions with careful thought, a sense of responsibility and resolute determination. All three Brontë sisters worked as governesses or teachers, and all experienced problems controlling their charges, gaining support from their employers, and coping with homesickness, but Anne was the only one who persevered and made a success of her work.
Back at the parsonage. Anne and Branwell taught at Thorp Green for the next three years. Branwell entered into a secret relationship with his employer's wife, Lydia Robinson. When Anne and Branwell returned home for the holidays in June 1845 Anne resigned. Anne gave no reason, but the reason may have been the relationship between her brother and Mrs Robinson. Branwell was dismissed when his employer found out about the relationship. Anne continued to exchange letters with Elizabeth and Mary Robinson. They came to visit Anne in December 1848. Anne took Emily to visit some of the places which Anne had become fond of. A plan to visit Scarborough fell through, but they went to York and saw York Minster. A book of poems. The Brontës were at home with their father during the summer of 1845. None had any immediate prospect of employment. Charlotte found Emily's poems, which had been shared only with Anne. Charlotte said that they should be published. Anne showed her own poems to Charlotte, and Charlotte "thought that these verses too had a sweet sincere pathos of their own". The sisters eventually reached an agreement. They told nobody what they were doing. With the money from Elizabeth Branwell they paid for publication of a collection of poems, 21 from Anne and 21 from Emily and 19 from Charlotte.
The book was published under pen names which retained their initials but concealed their sex. Anne's pseudonym was Acton Bell. "Poems by Currer, Ellis, and Acton Bell" was available for sale in May 1846. The cost of publication was 31 pounds and 10 shillings, about three-quarters of Anne's salary at Thorp Green. On 7 May 1846 the first three copies were delivered to Haworth Parsonage. The book achieved three somewhat favourable reviews, but was a commercial failure, with only two copies sold in the first year. Anne nonetheless found a market for her later poetry. The "Leeds Intelligencer" and "Fraser's Magazine" published her poem "The Narrow Way" under her pseudonym in December 1848. Four months earlier, Fraser's Magazine had published her poem "The Three Guides". Novels. "Agnes Grey". By July 1846 a package containing the manuscripts of each sister's first novel was making the rounds of London publishers. Charlotte had written "The Professor", Emily had written "Wuthering Heights", and Anne had written "Agnes Grey".
After some rejections "Wuthering Heights" and "Agnes Grey" were accepted by the publisher Thomas Cautley Newby. "The Professor" was rejected. It was not long before Charlotte had completed her second novel, "Jane Eyre". "Jane Eyre" was accepted immediately by Smith, Elder & Co. It was the first published of the sisters' novels, and an immediate and resounding success. Meanwhile, Anne and Emily's novels "lingered in the press". Anne and Emily were obliged to pay fifty pounds to help meet their publishing costs. Their publisher was galvanised by the success of "Jane Eyre" and published "Wuthering Heights" and "Agnes Grey" together in December 1847. They sold well, but "Agnes Grey" was outshone by Emily's more dramatic "Wuthering Heights". "The Tenant of Wildfell Hall". Anne's second novel, "The Tenant of Wildfell Hall", was published in the last week of June 1848. The novel challenged contemporary social and legal structures. In 1913, May Sinclair said that the slamming of Helen Huntingdon's bedroom door against her husband reverberated throughout Victorian England.
In the book Helen has left her husband to protect their son from his influence. She supports herself and her son in hiding by painting. She has violated social conventions and English law. Until the Married Women's Property Act 1870 was passed, a married woman had no legal existence independent from her husband and could not own property nor sue for divorce nor control the custody of her children. Helen's husband had a right to reclaim her and charge her with kidnapping. By subsisting on her own income she was stealing her husband's property since this income was legally his. Anne stated her intentions in the second edition, published in August 1848. She presented a forceful rebuttal to critics (among them Charlotte) who considered her portrayal of Huntingdon overly graphic and disturbing. Anne "wished to tell the truth". She explained: "When we have to do with vice and vicious characters, I maintain it is better to depict them as they really are than as they would wish to appear." Anne also castigated reviewers who speculated on the sex of authors and the perceived appropriateness of their writing. She was
London visit. In July 1848 Anne and Charlotte went to Charlotte's publisher George Smith in London to dispel the rumour that the "Bell brothers" were one person. Emily refused to go. Anne and Charlotte spent several days with Smith. Many years after Anne's death, he wrote in "The Cornhill Magazine" his impressions of her: The increasing popularity of the Bells' works led to renewed interest in "Poems by Currer, Ellis, and Acton Bell", originally published by Aylott and Jones. The remaining print run was bought by Smith and Elder, and reissued under new covers in November 1848. It still sold poorly. Family tragedies. Branwell's persistent drunkenness disguised the decline of his health and he died on 24 September 1848. His sudden death shocked the family. He was 31. The cause was recorded as chronic bronchitismarasmus, but was probably tuberculosis. The family suffered from coughs and colds during the winter of 1848, and Emily became very ill. She worsened over two months and rejected medical aid until the morning of 19 December. She was very weak and said that "if you will send for a doctor, I will see him now". But Emily died at about two o'clock that afternoon, aged 30.
Emily's death deeply affected Anne. Her grief undermined her physical health. Over Christmas Anne had influenza. Her symptoms intensified and in early January her father sent for a Leeds physician. The doctor diagnosed advanced consumption with little hope of recovery. Anne met the news with characteristic determination and self-control. However, in her letter to Ellen Nussey she expressed her frustrated ambitions: Unlike Emily, Anne took all the recommended medicines and followed the advice she was given. She also wrote her last poem, "A dreadful darkness closes in", in which she deals with being terminally ill. Her health fluctuated for months, but she grew thinner and weaker. Death. Anne seemed somewhat better in February. She decided to visit Scarborough to see if the change of location and the fresh sea air might benefit her. Charlotte was initially against the journey, fearing that it would be too stressful, but changed her mind after the doctor's approval and Anne's assurance that it was her last hope.
On 24 May 1849, Anne set off for Scarborough with Charlotte and Ellen Nussey. They spent a day and night in York en route. Here they escorted Anne in a wheelchair and did some shopping and visited York Minster. It was clear that Anne had little strength left. On Sunday 27 May, Anne asked Charlotte whether it would be easier to return home and die instead of remaining in Scarborough. A doctor was consulted the next day and said that death was close. Anne received the news quietly. She expressed her love and concern for Ellen and Charlotte, and whispered for Charlotte to "take courage". Anne died at about two o'clock in the afternoon on 28 May 1849, aged 29. Charlotte decided to "lay the flower where it had fallen". So Anne was buried in Scarborough. The funeral was held on 30 May. Patrick Brontë could not have made the journey if he had wished to. The former schoolmistress at Roe Head, Miss Wooler, was in Scarborough, and she was the only other mourner at Anne's funeral. Anne was buried in St Mary's churchyard, beneath the castle walls and overlooking the bay. Charlotte commissioned a stone to be placed over her grave with the inscription, When Charlotte visited the grave three years later she discovered multiple errors on the headstone and had it refaced, but it was still not free of error, for Anne was 29 when she died, not 28 as written.
In 2011 the Brontë Society installed a new plaque at Anne Brontë's grave. The original gravestone had become illegible at places and could not be restored. It was left undisturbed while the new plaque was laid horizontally, interpreting the fading words of the original and correcting its error. In April 2013 the Brontë Society held a dedication and blessing service at the gravesite to mark the installation of the new plaque. Reputation. After Anne's death, Charlotte addressed issues with the first edition of "Agnes Grey" for its republication, but she prevented republication of "The Tenant of Wildfell Hall". In 1850, Charlotte wrote that Subsequent critics paid less attention to Anne's work and some dismissed her as "a Brontë without genius". But since the mid-20th century her life and works have been given better attention. Biographies by Winifred Gérin (1959), Elizabeth Langland (1989) and Edward Chitham (1991), as well as Juliet Barker's group biography, "The Brontës" (1994; revised edition 2000), and work by critics such as Inga-Stina Ewbank, Marianne Thormählen, Laura C Berry, Jan B Gordon, Mary Summers, and Juliet McMaster has led to acceptance of Anne Brontë as a major literary figure. Sally McDonald of the Brontë Society said in 2013 that in some ways Anne "is now viewed as the most radical of the sisters, writing about tough subjects such as women's need to maintain independence and how alcoholism can tear a family apart." In 2016 Lucy Mangan championed Anne Brontë in the BBC's "Being the Brontës".
Augustine of Hippo Augustine of Hippo ( , ; ; 13 November 354 – 28 August 430), also known as Saint Augustine and in the Eastern Orthodox Church as Blessed Augustine, was a theologian and philosopher of Berber origin and the bishop of Hippo Regius in Numidia, Roman North Africa. His writings deeply influenced the development of Western philosophy and Western Christianity, and he is viewed as one of the most important Church Fathers of the Latin Church in the Patristic Period. His many important works include "The City of God", "On Christian Doctrine", and "Confessions". According to his contemporary, Jerome of Stridon, Augustine "established anew the ancient Faith". In his youth he was drawn to the Manichaean faith, and later to the Hellenistic philosophy of Neoplatonism. After his conversion to Christianity and baptism in 386, Augustine developed his own approach to philosophy and theology, accommodating a variety of methods and perspectives. Believing the grace of Christ was indispensable to human freedom, he helped formulate the doctrine of original sin and made significant contributions to the development of just war theory. When the Western Roman Empire began to disintegrate, Augustine imagined the Church as a spiritual City of God, distinct from the material Earthly City. The segment of the Church that adhered to the concept of the Trinity as defined by the Council of Nicaea and the Council of Constantinople closely identified with Augustine's "On the Trinity".
Augustine is recognized as a saint in the Catholic Church, the Eastern Orthodox Church, the Lutheran churches, and the Anglican Communion. He is also a preeminent Catholic Doctor of the Church and the patron of the Augustinians. His memorial is celebrated on 28 August, the day of his death. Augustine is the patron saint of brewers, printers, theologians, and a number of cities and dioceses. His thoughts profoundly influenced the medieval worldview. Many Protestants, especially Calvinists and Lutherans, consider him one of the theological fathers of the Protestant Reformation due to his teachings on salvation and divine grace. Protestant Reformers generally, and Martin Luther in particular, held Augustine in preeminence among early Church Fathers. From 1505 to 1521, Luther was a member of the Order of the Augustinian Eremites. In the East, his teachings are more disputed and were notably attacked by John Romanides, but other theologians and figures of the Eastern Orthodox Church have shown significant approbation of his writings, chiefly Georges Florovsky. The most controversial doctrine associated with him, the filioque, was rejected by the Eastern Orthodox Church. Other disputed teachings include his views on original sin, the doctrine of grace, and predestination. Though considered to be mistaken on some points, he is still considered a saint and has influenced some Eastern Church Fathers, most notably Gregory Palamas. In the Greek and Russian Orthodox Churches, his feast day is celebrated on 15 June.
Life. Background. Augustine of Hippo, also known as "Saint Augustine" or "Saint Austin", is known by various cognomens throughout the many denominations of the Christian world, including "Blessed Augustine" and the "Doctor of Grace" (). Hippo Regius, where Augustine was the bishop, was in modern-day Annaba, Algeria. Childhood and education. Augustine was born in 354 in the municipium of Thagaste (now Souk Ahras, Algeria) in the Roman province of Numidia. His mother, Monica or Monnica, was a devout Christian; his father Patricius was a pagan who converted to Christianity on his deathbed. He had a brother named Navigius and a sister whose name is lost but is conventionally remembered as Perpetua. Scholars generally agree that Augustine and his family were Berbers, an ethnic group indigenous to North Africa, but were heavily Romanized, speaking only Latin at home as a matter of pride and dignity. In his writings, Augustine mentions in passing his identity as a Roman African. For example, he refers to Apuleius as "the most notorious of us Africans," to Ponticianus as "a country man of ours, insofar as being African," and to Faustus of Mileve as "an African Gentleman".
Augustine's family name, Aurelius, suggests his father's ancestors were freedmen of the "gens Aurelia" given full Roman citizenship by the Edict of Caracalla in 212. Augustine's family had been Roman, from a legal standpoint, for at least a century when he was born. It is assumed that his mother, Monica, was of Berber origin, on the basis of her name, but as his family were "honestiores", an upper class of citizens known as honorable men, Augustine's first language was likely Latin. At the age of 11, Augustine was sent to school at Madaurus (now M'Daourouch), a small Numidian city about south of Thagaste. There he became familiar with Latin literature, as well as pagan beliefs and practices. His first insight into the nature of sin occurred when he and a number of friends stole pears from a neighbourhood garden. He tells this story in his autobiography, "Confessions". He realises that the pears were "tempting neither for its colour nor its flavour" – he was neither hungry nor poor, and he had enough of fruit which were "much better". Over the next few chapters, Augustine agonises over this past sin of his, recognising that one does not desire evil for evil's sake. Rather, "through an inordinate preference for these goods of a lower kind, the better and higher are neglected". In other words, man is drawn to sin when grossly choosing the lesser good over a greater good. Eventually, Augustine concludes that it was the good of the "companionship" between him and his accomplices that allowed him to delight in this theft.
At the age of 17, through the generosity of his fellow citizen Romanianus, Augustine went to Carthage to continue his education in rhetoric, though it was above the financial means of his family. Despite the good warnings of his mother, as a youth Augustine lived a hedonistic lifestyle for a time, associating with young men who boasted of their sexual exploits. The need to gain their acceptance encouraged inexperienced boys like Augustine to seek or make up stories about sexual experiences. It was while he was a student in Carthage that he read Cicero's dialogue "Hortensius" (now lost), which he described as leaving a lasting impression, enkindling in his heart the love of wisdom and a great thirst for truth. It started his interest in philosophy. Although raised Christian, Augustine became a Manichaean, much to his mother's chagrin. At about the age of 17, Augustine began a relationship with a young woman in Carthage. Though his mother wanted him to marry a person of his class, the woman remained his lover. He was warned by his mother to avoid fornication (sex outside marriage), but Augustine persisted in the relationship for over fifteen years, and the woman gave birth to his son Adeodatus (372–388), which means "Gift from God", who was viewed as extremely intelligent by his contemporaries. In 385, Augustine ended his relationship with his lover in order to prepare to marry a teenage heiress. By the time he was able to marry her, however, he had already converted to Christianity and decided to become a Christian priest and the marriage did not happen.
Augustine was, from the beginning, a brilliant student, with an eager intellectual curiosity, but he never mastered Greek – his first Greek teacher was a brutal man who constantly beat his students, and Augustine rebelled and refused to study. By the time he realized he needed to know Greek, it was too late; and although he acquired a smattering of the language, he was never eloquent with it. He did, however, become a master of Latin. Move to Carthage, Rome, and Milan. Augustine taught grammar at Thagaste during 373 and 374. The following year he moved to Carthage to conduct a school of rhetoric and remained there for the next nine years. Disturbed by unruly students in Carthage, he moved to establish a school in Rome, where he believed the best and brightest rhetoricians practised, in 383. However, Augustine was disappointed with the apathetic reception. It was the custom for students to pay their fees to the professor on the last day of the term, and many students attended faithfully all term, and then did not pay.
Manichaean friends introduced him to the prefect of the City of Rome, Symmachus, who had been asked by the imperial court at Milan to provide a rhetoric professor. Augustine won the job and headed north to take his position in Milan in late 384. Thirty years old, he had won the most visible academic position in the Latin world at a time when such posts gave ready access to political careers. Although Augustine spent ten years as a Manichaean, he was never an initiate or "elect", but an "auditor", the lowest level in this religion's hierarchy. While still at Carthage a disappointing meeting with the Manichaean bishop, Faustus of Mileve, a key exponent of Manichaean theology, started Augustine's scepticism of Manichaeanism. In Rome, he reportedly turned away from Manichaeanism, embracing the scepticism of the New Academy movement. Because of his education, Augustine had great rhetorical prowess and was very knowledgeable of the philosophies behind many faiths. At Milan, his mother's religiosity, Augustine's own studies in Neoplatonism, and his friend Simplicianus all urged him towards Christianity. This was shortly after the Roman emperor Theodosius I declared Christianity to be the only legitimate religion for the Roman Empire on 27 February 380 by the Edict of Thessalonica and then issued a decree of death for all Manichaean monks in 382. Initially, Augustine was not strongly influenced by Christianity and its ideologies, but after coming in contact with Ambrose of Milan, Augustine reevaluated himself and was forever changed.
Augustine arrived in Milan and visited Ambrose, having heard of his reputation as an orator. Like Augustine, Ambrose was a master of rhetoric, but older and more experienced. Soon, their relationship grew, as Augustine wrote, "And I began to love him, of course, not at the first as a teacher of the truth, for I had entirely despaired of finding that in thy Churchbut as a friendly man." Augustine was very much influenced by Ambrose, even more than by his own mother and others he admired. In his "Confessions", Augustine states, "That man of God received me as a father would, and welcomed my coming as a good bishop should." Ambrose adopted Augustine as a spiritual son after the death of Augustine's father. Augustine's mother had followed him to Milan and arranged a respectable marriage for him. Although Augustine acquiesced, he had to dismiss his concubine and grieved for having forsaken his lover. He wrote, "My mistress being torn from my side as an impediment to my marriage, my heart, which clave to her, was racked, and wounded, and bleeding." Augustine confessed he had not been a lover of wedlock so much as a slave of lust, so he procured another concubine since he had to wait two years until his fiancée came of age. However, his emotional wound was not healed. It was during this period that he uttered his famously insincere prayer, "Grant me chastity and continence, but not yet."
There is evidence Augustine may have considered this former relationship to be equivalent to marriage. In his "Confessions", he admitted the experience eventually produced a decreased sensitivity to pain. Augustine eventually broke off his engagement to his eleven-year-old fiancée but never renewed his relationship with either of his concubines. Alypius of Thagaste steered Augustine away from marriage, saying they could not live a life together in the love of wisdom if he married. Augustine looked back years later on the life at Cassiciacum, a villa outside of Milan where he gathered with his followers, and described it as "Christianae vitae otium" – the leisure of Christian life. Conversion to Christianity and priesthood. In late August of 386, at the age of 31, having heard of Ponticianus's and his friends' first reading of the life of Anthony of the Desert, Augustine converted to Christianity. As Augustine later told it, his conversion was prompted by hearing a child's voice say "take up and read" (). Resorting to the "sortes biblicae", he opened a book of St. Paul's writings ("Confessiones" 8.12.29) at random and read Romans 13:13–14: "Not in rioting and drunkenness, not in chambering and wantonness, not in strife and envying, but put on the Lord Jesus Christ, and make no provision for the flesh to fulfil the lusts thereof."
He later wrote an account of his conversion in his "Confessions" (), which has since become a classic of Christian theology and a key text in the history of autobiography. This work is an outpouring of thanksgiving and penitence. Although it is written as an account of his life, the "Confessions" also talks about the nature of time, causality, free will, and other important philosophical topics. The following is taken from that work: Ambrose baptized Augustine and his son Adeodatus, in Milan on Easter Vigil, 24–25 April 387. A year later, in 388, Augustine completed his apology "On the Holiness of the Catholic Church". That year, also, Adeodatus and Augustine returned home to Africa. Augustine's mother Monica died at Ostia, Italy, as they prepared to embark for Africa. Upon their arrival, they began a life of aristocratic leisure at Augustine's family's property. Soon after, Adeodatus, too, died. Augustine then sold his patrimony and gave the money to the poor. He only kept the family house, which he converted into a monastic foundation for himself and a group of friends. Furthermore, while he was known for his major contributions to Christian rhetoric, another major contribution was his preaching style.
After converting to Christianity, Augustine turned against his profession as a rhetoric professor in order to devote more time to preaching. In 391 Augustine was ordained a priest in Hippo Regius (now Annaba), in Algeria. He was especially interested in discovering how his previous rhetorical training in Italian schools would help the Christian Church achieve its objective of discovering and teaching the different scriptures in the Bible. He became a famous preacher (more than 350 preserved sermons are believed to be authentic), and was noted for combating the Manichaean religion, to which he had formerly adhered. He preached around 6,000 to 10,000 sermons when he was alive; however, there are only around 500 sermons that are accessible today. When Augustine preached his sermons, they were recorded by stenographers. Some of his sermons would last over one hour and he would preach multiple times throughout a given week. When talking to his audience, he would stand on an elevated platform; however, he would walk towards the audience during his sermons. When he was preaching, he used a variety of rhetorical devices that included analogies, word pictures, similes, metaphors, repetition, and antithesis when trying to explain more about the Bible. In addition, he used questions and rhymes when talking about the differences between people's life on Earth and Heaven as seen in one of his sermons that was preached in 412 AD. Augustine believed that the preachers' ultimate goal is to ensure the salvation of their audience.
In 395, he was made coadjutor Bishop of Hippo and became full Bishop shortly thereafter, hence the name "Augustine of Hippo"; and he gave his property to the church of Thagaste. He remained in that position until his death in 430. Bishops were the only individuals allowed to preach when he was alive and he scheduled time to preach after being ordained despite a busy schedule made up of preparing sermons and preaching at other churches besides his own. When serving as the Bishop of Hippo, his goal was to minister to individuals in his congregation and he would choose the passages that the church planned to read every week. As bishop, he believed that it was his job to interpret the work of the Bible. He wrote his autobiographical "Confessions" in 397–398. His work "The City of God" was written to console his fellow Christians shortly after the Visigoths had sacked Rome in 410. Augustine worked tirelessly to convince the people of Hippo to convert to Christianity. Though he had left his monastery, he continued to lead a monastic life in the episcopal residence.
Much of Augustine's later life was recorded by his friend Possidius, bishop of Calama (present-day Guelma, Algeria), in his "Sancti Augustini Vita". During this latter part of Augustine's life, he helped lead a large community of Christians against different political and religious factors which had a major influence on his writings. Possidius admired Augustine as a man of powerful intellect and a stirring orator who took every opportunity to defend Christianity against its detractors. Possidius also described Augustine's personal traits in detail, drawing a portrait of a man who ate sparingly, worked tirelessly, despised gossip, shunned the temptations of the flesh, and exercised prudence in the financial stewardship of his see. Death and sainthood. Shortly before Augustine's death, the Vandals, a Germanic tribe that had converted to Arianism, invaded Roman Africa. The Vandals besieged Hippo in the spring of 430 when Augustine entered his final illness. According to Possidius, one of the few miracles attributed to Augustine, the healing of an ill man, took place during the siege. Augustine has been cited to have excommunicated himself upon the approach of his death in an act of public penance and solidarity with sinners. Spending his final days in prayer and repentance, he requested the penitential Psalms of David be hung on his walls so he could read them and upon which led him to "[weep] freely and constantly" according to Possidius' biography. He directed the library of the church in Hippo and all the books therein should be carefully preserved. He died on 28 August 430. Shortly after his death, the Vandals lifted the siege of Hippo, but they returned soon after and burned the city. They destroyed all but Augustine's cathedral and library, which they left untouched.
Augustine was canonized by popular acclaim, and later recognized as a Doctor of the Church in 1298 by Pope Boniface VIII. His feast day is 28 August, the day on which he died. He is considered the patron saint of brewers, printers, theologians, and a number of cities and dioceses. He is invoked against sore eyes. Augustine is remembered in the Church of England's calendar of saints with a lesser festival on 28 August. Relics. According to Bede's "True Martyrology", Augustine's body was later translated or moved to Cagliari, Sardinia, by the Catholic bishops expelled from North Africa by Huneric. Around 720, his remains were transported again by Peter, bishop of Pavia and uncle of the Lombard king Liutprand, to the church of San Pietro in Ciel d'Oro in Pavia, to save them from frequent coastal raids by Saracens. In January 1327, Pope John XXII issued the papal bull "Veneranda Santorum Patrum", in which he appointed the Augustinians guardians of the tomb of Augustine (called "Arca"), which was remade in 1362 and elaborately carved with bas-reliefs of scenes from Augustine's life, created by Giovanni di Balduccio.
In October 1695, some workmen in the Church of San Pietro in Ciel d'Oro in Pavia discovered a marble box containing human bones (including part of a skull). A dispute arose between the Augustinian hermits (Order of Saint Augustine) and the regular canons (Canons Regular of Saint Augustine) as to whether these were the bones of Augustine. The hermits did not believe so; the canons affirmed they were. Eventually Pope Benedict XIII (1724–1730) directed the Bishop of Pavia, Monsignor Pertusati, to make a determination. The bishop declared that, in his opinion, the bones were those of Augustine. The Augustinians were expelled from Pavia in 1785, Augustine's ark and relics were brought to Pavia Cathedral in 1799. San Pietro fell into disrepair but was finally restored in the 1870s, under the urging of Agostino Gaetano Riboldi, and reconsecrated in 1896 when the relics of Augustine and the shrine were once again reinstalled. In 1842, a portion of Augustine's right arm (cubitus) was secured from Pavia and returned to Annaba. It now rests in the Saint Augustin Basilica within a glass tube inserted into the arm of a life-size marble statue of the saint.
Views and thought. Augustine's large contribution of writings covered diverse fields including theology, philosophy and sociology. Along with John Chrysostom, Augustine was among the most prolific scholars of the early church by quantity. Theology. Christian anthropology. Augustine was one of the first Christian ancient Latin authors with a very clear vision of theological anthropology. He saw the human being as a perfect unity of soul and body. In his late treatise "" (420) he exhorted respect for the body on the grounds it belonged to the very nature of the human person. Augustine's favourite figure to describe "body-soul" unity is marriage: "caro tua, coniunx tua – your body is your wife". Initially, the two elements were in perfect harmony. After the fall of humanity they are now experiencing dramatic combat with one another. They are two categorically different things. The body is a three-dimensional object composed of the four elements, whereas the soul has no spatial dimensions. Soul is a kind of substance, participating in reason, fit for ruling the body.
Augustine was not preoccupied, as Plato and Descartes were, in detailed efforts to explain the metaphysics of the soul-body union. It sufficed for him to admit they are metaphysically distinct: to be a human is to be a composite of soul and body, with the soul superior to the body. The latter statement is grounded in his hierarchical classification of things into those that merely exist, those that exist and live, and those that exist, live, and have intelligence or reason. Like other Church Fathers such as Athenagoras, Tertullian, Clement of Alexandria and Basil of Caesarea, Augustine "vigorously condemned the practice of induced abortion", and although he disapproved of abortion during any stage of pregnancy, he made a distinction between early and later abortions. He acknowledged the distinction between "formed" and "unformed" fetuses mentioned in the Septuagint translation of Exodus 21:22–23, which incorrectly translates the word "harm" (from the original Hebrew text) as "form" in the Koine Greek of the Septuagint. His view was based on the Aristotelian distinction "between the fetus before and after its supposed 'vivification. Therefore, he did not classify as murder the abortion of an "unformed" fetus since he thought it could not be known with certainty the fetus had received a soul.
Augustine held that "the timing of the infusion of the soul was a mystery known to God alone". However, he considered procreation as "one of the goods of marriage; abortion figured as a means, along with drugs which cause sterility, of frustrating this good. It lay along a continuum which included infanticide as an instance of 'lustful cruelty' or 'cruel lust.' Augustine called the use of means to avoid the birth of a child an 'evil work:' a reference to either abortion or contraception or both." Creation. In "City of God", Augustine rejected both the contemporary ideas of ages (such as those of certain Greeks and Egyptians) that differed from the Church's sacred writings. In "The Literal Interpretation of Genesis", Augustine argued that God had created everything in the universe simultaneously and not over a period of six days. He argued the six-day structure of creation presented in the Book of Genesis represents a logical framework, rather than the passage of time in a physical way – it would bear a spiritual, rather than physical, meaning, which is no less literal. One reason for this interpretation is the passage in Sirach 18:1, "creavit omnia simul" ("He created all things at once"), which Augustine took as proof that the days of Genesis 1 had to be taken non-literalistically. As additional support for describing the six days of creation as a heuristic device, Augustine thought the actual event of creation would be incomprehensible by humans and therefore needed to be translated.
Augustine also does not envision original sin as causing structural changes in the universe, and even suggests that the bodies of Adam and Eve were already created mortal before the Fall. Apart from his specific views, Augustine recognized that interpreting the creation story was difficult, and remarked that interpretations could change should new information come up. Ecclesiology. Augustine developed his doctrine of the Church principally in reaction to the Donatist sect. He taught there is one Church, but within this Church there are two realities, namely, the visible aspect (the institutional hierarchy, the Catholic sacraments, and the laity) and the invisible (the souls of those in the Church, who are either dead, sinful members or elect predestined for Heaven). The former is the institutional body established by Christ on earth which proclaims salvation and administers the sacraments, while the latter is the invisible body of the elect, made up of genuine believers from all ages, who are known only to God. The Church, which is visible and societal, will be made up of "wheat" and "tares", that is, good and wicked people (as per Mat. 13:30), until the end of time. This concept countered the Donatist claim that only those in a state of grace were the "true" or "pure" church on earth, and that priests and bishops who were not in a state of grace had no authority or ability to confect the sacraments.
Augustine's ecclesiology was more fully developed in "City of God". There he conceives of the church as a heavenly city or kingdom, ruled by love, which will ultimately triumph over all earthly empires which are self-indulgent and ruled by pride. Augustine followed Cyprian in teaching that bishops and priests of the Church are the successors of the Apostles, and their authority in the Church is God-given. The concept of Church invisible was advocated by Augustine as part of his refutation of the Donatist sect, though he, as other Church Fathers before him, saw the invisible Church and visible Church as one and the same thing, unlike the later Protestant reformers who did not identify the Catholic Church as the true church. He was strongly influenced by the Platonist belief that true reality is invisible and that, if the visible reflects the invisible, it does so only partially and imperfectly (see Theory of Forms). Others question whether Augustine really held to some form of an "invisible true Church" concept.
Eschatology. Augustine originally believed in premillennialism, namely that Christ would establish a literal 1,000-year kingdom prior to the general resurrection, but later rejected the belief, viewing it as carnal. During the medieval period, the Catholic Church built its system of eschatology on Augustinian amillennialism, where Christ rules the earth spiritually through his triumphant church. During the Reformation, theologians such as John Calvin accepted amillennialism. Augustine taught that the eternal fate of the soul is determined at death, and that purgatorial fires of the intermediate state purify only those who died in communion with the Church. His teaching provided fuel for later theology. Mariology. Although Augustine did not develop an independent Mariology, his statements on Mary surpass in number and depth those of other early writers. Even before the Council of Ephesus, he defended the Ever-Virgin Mary as the Mother of God, believing her to be "full of grace" (following earlier Latin writers such as Jerome) on account of her sexual integrity and innocence. Likewise, he affirmed that the Virgin Mary "conceived as virgin, gave birth as virgin and stayed virgin forever".
Natural knowledge and biblical interpretation. Augustine took the view that, if a literal interpretation contradicts science and humans' God-given reason, the biblical text should be interpreted metaphorically. While each passage of Scripture has a literal sense, this "literal sense" does not always mean the Scriptures are mere history; at times they are rather an extended metaphor. Original sin. Augustine taught that the sin of Adam and Eve was either an act of foolishness ("insipientia") followed by pride and disobedience to God or that pride came first. The first couple disobeyed God, who had told them not to eat of the Tree of the knowledge of good and evil (Gen 2:17). The tree was a symbol of the order of creation. Self-centeredness made Adam and Eve eat of it, thus failing to acknowledge and respect the world as it was created by God, with its hierarchy of beings and values. They would not have fallen into pride and lack of wisdom if Satan had not sown into their senses "the root of evil" ("radix Mali"). Their nature was wounded by concupiscence or libido, which affected human intelligence and will, as well as affections and desires, including sexual desire. In terms of metaphysics, concupiscence is not a state of being but a bad quality, the privation of good or a wound.
Augustine's understanding of the consequences of original sin and the necessity of redeeming grace was developed in the struggle against Pelagius and his Pelagian disciples, Caelestius and Julian of Eclanum, who had been inspired by Rufinus of Syria, a disciple of Theodore of Mopsuestia. They refused to agree original sin wounded human will and mind, insisting human nature was given the power to act, to speak, and to think when God created it. Human nature cannot lose its moral capacity for doing good, but a person is free to act or not act in a righteous way. Pelagius gave an example of eyes: they have capacity for seeing, but a person can make either good or bad use of it. Pelagians insisted human affections and desires were not touched by the fall either. Immorality, e.g. fornication, is exclusively a matter of will, i.e. a person does not use natural desires in a proper way. In opposition, Augustine pointed out the apparent disobedience of the flesh to the spirit, and explained it as one of the results of original sin, punishment of Adam and Eve's disobedience to God.
Augustine had served as a "Hearer" for the Manichaeans for about nine years, who taught that the original sin was carnal knowledge. But his struggle to understand the cause of evil in the world started before that, at the age of nineteen. By "malum" (evil) he understood most of all concupiscence, which he interpreted as a vice dominating people and causing in men and women moral disorder. Agostino Trapè insists Augustine's personal experience cannot be credited for his doctrine about concupiscence. He considers Augustine's marital experience to be quite normal, and even exemplary, aside from the absence of Christian wedding rites. As J. Brachtendorf showed, Augustine used Ciceronian Stoic concept of passions, to interpret Paul's doctrine of universal sin and redemption. The view that not only human soul but also senses were influenced by the fall of Adam and Eve was prevalent in Augustine's time among the Fathers of the Church. It is clear the reason for Augustine's distancing from the affairs of the flesh was different from that of Plotinus, a Neoplatonist who taught that only through disdain for fleshly desire could one reach the ultimate state of mankind. Augustine taught the redemption, i.e. transformation and purification, of the body in the resurrection.
Some authors perceive Augustine's doctrine as directed against human sexuality and attribute his insistence on continence and devotion to God as coming from his need to reject his own highly sensual nature as described in the "Confessions". Augustine taught that human sexuality has been wounded, together with the whole of human nature, and requires redemption of Christ. That healing is a process realized in conjugal acts. The virtue of continence is achieved thanks to the grace of the sacrament of Christian marriage, which becomes therefore a "remedium concupiscentiae" – remedy of concupiscence. The redemption of human sexuality will be, however, fully accomplished only in the resurrection of the body. The sin of Adam is inherited by all human beings. Already in his pre-Pelagian writings, Augustine taught that Original Sin is transmitted to his descendants by concupiscence, which he regarded as the passion of both soul and body, making humanity a "massa damnata" (mass of perdition, condemned crowd) and much enfeebling, though not destroying, the freedom of the will. Although earlier Christian authors taught the elements of physical death, moral weakness, and a sin propensity within original sin, Augustine was the first to add the concept of inherited guilt ("reatus") from Adam whereby an infant was eternally damned at birth.
Although Augustine's anti-Pelagian defence of original sin was confirmed at numerous councils, i.e. Carthage (418), Ephesus (431), Orange (529), Trent (1546) and by popes, i.e. Pope Innocent I (401–417) and Pope Zosimus (417–418), his inherited guilt eternally damning infants was omitted by these councils and popes. Anselm of Canterbury established in his "Cur Deus Homo" the definition that was followed by the great 13th-century Schoolmen, namely that Original Sin is the "privation of the righteousness which every man ought to possess," thus separating it from "concupiscence," with which some of Augustine's disciples had identified it, as later did Luther and Calvin. In 1567, Pope Pius V condemned the identification of Original Sin with concupiscence. Predestination. Augustine taught that God orders all things while preserving human freedom. Prior to 396, he believed predestination was based on God's foreknowledge of whether individuals would believe in Christ, that God's grace was "a reward for human assent". Later, in response to Pelagius, Augustine said that the sin of pride consists in assuming "we are the ones who choose God or that God chooses us (in his foreknowledge) because of something worthy in us", and argued that God's grace causes the individual act of faith.
Scholars are divided over whether Augustine's teaching implies double predestination, or the belief God chooses some people for damnation as well as some for salvation. Catholic scholars tend to deny he held such a view while some Protestants and secular scholars have held that Augustine did believe in double predestination. About 412, Augustine became the first Christian to understand predestination as a divine unilateral pre-determination of individuals' eternal destinies independently of human choice, although his prior Manichaean sect did teach this concept. Some Protestant theologians, such as Justo L. González and Bengt Hägglund, interpret Augustine's teaching that grace is irresistible, results in conversion, and leads to perseverance. In "On Rebuke and Grace" ("De correptione et gratia"), Augustine wrote: "And what is written, that He wills all men to be saved, while yet all men are not saved, may be understood in many ways, some of which I have mentioned in other writings of mine; but here I will say one thing: He wills all men to be saved, is so said that all the predestinated may be understood by it, because every kind of men is among them."
Speaking of the twins Jacob and Esau, Augustine wrote in his book "On the Gift of Perseverance", "[I]t ought to be a most certain fact that the former is of the predestinated, the latter is not." Sacramental theology. Also in reaction to the Donatists, Augustine developed a distinction between the "regularity" and "validity" of the sacraments. Regular sacraments are performed by clergy of the Catholic Church, while sacraments performed by schismatics are considered irregular. Nevertheless, the validity of the sacraments does not depend upon the holiness of the priests who perform them ("ex opere operato"); therefore, irregular sacraments are still accepted as valid provided they are done in the name of Christ and in the manner prescribed by the Church. On this point, Augustine departs from the earlier teaching of Cyprian, who taught that converts from schismatic movements must be re-baptised. Augustine taught that sacraments administered outside the Catholic Church, though true sacraments, avail nothing. However, he also stated that baptism, while it does not confer any grace when done outside the Church, does confer grace as soon as one is received into the Catholic Church.

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