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Among the proposals to reform the standard introductory-physics curriculum is one that teaches the concept of energy before that of force, essentially "introductory Hamiltonian mechanics".
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The Hamilton–Jacobi equation provides yet another formulation of classical mechanics, one which makes it mathematically analogous to wave optics. This formulation also uses Hamiltonian functions, but in a different way than the formulation described above. The paths taken by bodies or collections of bodies are deduced from a function formula_124 of positions formula_125 and time formula_126. The Hamiltonian is incorporated into the Hamilton–Jacobi equation, a differential equation for formula_127. Bodies move over time in such a way that their trajectories are perpendicular to the surfaces of constant formula_127, analogously to how a light ray propagates in the direction perpendicular to its wavefront. This is simplest to express for the case of a single point mass, in which formula_127 is a function formula_130, and the point mass moves in the direction along which formula_127 changes most steeply. In other words, the momentum of the point mass is the gradient of formula_127:
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The relation to Newton's laws can be seen by considering a point mass moving in a time-independent potential formula_135, in which case the Hamilton–Jacobi equation becomes
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Interchanging the order of the partial derivatives on the left-hand side, and using the power and chain rules on the first term on the right-hand side,
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This is another re-expression of Newton's second law. The expression in brackets is a "total" or "material" derivative as mentioned above, in which the first term indicates how the function being differentiated changes over time at a fixed location, and the second term captures how a moving particle will see different values of that function as it travels from place to place:
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In statistical physics, the kinetic theory of gases applies Newton's laws of motion to large numbers (typically on the order of Avogadro's number) of particles. Kinetic theory can explain, for example, the pressure that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.
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The Langevin equation is a special case of Newton's second law, adapted for the case of describing a small object bombarded stochastically by even smaller ones. It can be writtenformula_142where formula_143 is a drag coefficient and formula_144 is a force that varies randomly from instant to instant, representing the net effect of collisions with the surrounding particles. This is used to model Brownian motion.
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Newton's three laws can be applied to phenomena involving electricity and magnetism, though subtleties and caveats exist.
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Coulomb's law for the electric force between two stationary, electrically charged bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge formula_145 exerts upon a charge formula_146 is equal in magnitude to the force that formula_146 exerts upon formula_145, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law.
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Electromagnetism treats forces as produced by "fields" acting upon charges. The Lorentz force law provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge formula_107 and to the strength of the electric field. In addition, a "moving" charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector cross product,formula_150
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If the electric field vanishes (formula_151), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a helix) around the magnetic field lines at the cyclotron frequency formula_152. Mass spectrometry works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the mass-to-charge ratio.
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Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the electromagnetic field is proportional to the Poynting vector.
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There is subtle conceptual conflict between electromagnetism and Newton's first law: Maxwell's theory of electromagnetism predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the speed of light and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of "space" and "time" in such a way that all inertial observers will agree upon the speed of light in vacuum.
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In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector, formula_153, where formula_27 is the body's rest mass and formula_143 is the Lorentz factor, which depends upon the body's speed. Alternatively, momentum and force can be represented as four-vectors.
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Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.
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General relativity is theory of gravity that advances beyond that of Newton. In general relativity, gravitational force is reimagined as curvature of spacetime. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express.
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The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.
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Quantum mechanics is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The conceptual underpinning of quantum physics is very different from that of classical physics. Instead of thinking about quantities like position, momentum, and energy as properties that an object "has", one considers what result might "appear" when a measurement of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The expectation value for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.
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The Ehrenfest theorem provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.
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The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics could encompass both.
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The subject of physics is often traced back to Aristotle; however, the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, and he used the same term for density and viscosity; he conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion. Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior. Yet a javelin continues moving after it leaves the hand of its thrower. Aristotle concluded that the air around the javelin must be imparted with the ability to move the javelin forward. John Philoponus, a Byzantine Greek thinker active during the sixth century, found this absurd: the same medium, air, was somehow responsible both for sustaining motion and for impeding it. If Aristotle's idea were true, Philoponus said, armies would launch weapons by blowing upon them with bellows. Philoponus argued that setting a body into motion imparted a quality, impetus, that would be contained within the body itself. As long as its impetus was sustained, the body would continue to move. In the following centuries, versions of impetus theory were advanced by individuals including Nur ad-Din al-Bitruji, Avicenna, Abu'l-Barakāt al-Baghdādī, John Buridan, and Albert of Saxony. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. (The intuition that objects move according to some kind of impetus persists in many students of introductory physics.)
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The modern concept of inertia is credited to Galileo. Based on his experiments, Galileo concluded that the "natural" behavior of a moving body was to keep moving, until something else interfered with it. Galileo recognized that in projectile motion, the Earth's gravity affects vertical but not horizontal motion. However, Galileo's idea of inertia was not exactly the one that would be codified into Newton's first law. Galileo thought that a body moving a long distance inertially would follow the curve of the Earth. This idea was corrected by Isaac Beeckman, René Descartes, and Pierre Gassendi, who recognized that inertial motion should be motion in a straight line.
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Christiaan Huygens, in his "Horologium Oscillatorium" (1673), put forth the hypothesis that "By the action of gravity, whatever its sources, it happens that bodies are moved by a motion composed both of a uniform motion in one direction or another and of a motion downward due to gravity." Newton's second law generalized this hypothesis from gravity to all forces.
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One important characteristic of Newtonian physics is that forces can act at a distance without requiring physical contact. For example, the Sun and the Earth pull on each other gravitationally, despite being separated by millions of kilometres. This contrasts with the idea, championed by Descartes among others, that the Sun's gravity held planets in orbit by swirling them in a vortex of transparent matter, "aether". Newton considered aetherial explanations of force but ultimately rejected them. The study of magnetism by William Gilbert and others created a precedent for thinking of "immaterial" forces, and unable to find a quantitatively satisfactory explanation of his law of gravity in terms of an aetherial model, Newton eventually declared, "I feign no hypotheses": whether or not a model like Descartes's vortices could be found to underlie the "Principia"'s theories of motion and gravity, the first grounds for judging them must be the successful predictions they made. And indeed, since Newton's time every attempt at such a model has failed.
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Johannes Kepler suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite. In his "Principles of Philosophy" (1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a plenum, that is, filled with matter, so all motion required a body to displace a medium as it moved. During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum. Christopher Wren would later deduce the same rules for elastic collisions that Huygens had, and John Wallis would apply momentum conservation to study inelastic collisions. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.
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Newton arrived at his set of three laws incrementally. In a 1684 manuscript written to Huygens, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called Galilean invariance, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the "Principia," with three primary laws and then other statements reduced to corollaries, during 1685.
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Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the "Principia," he had already developed calculus (which he called "the science of fluxions"), but in the "Principia" he made no explicit use of it, perhaps because he believed geometrical arguments in the tradition of Euclid to be more rigorous. Consequently, the "Principia" does not express acceleration as the second derivative of position, and so it does not give the second law as formula_156. This form of the second law was written (for the special case of constant force) at least as early as 1716, by Jakob Hermann; Leonhard Euler would employ it as a basic premise in the 1740s. Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics. Pierre-Simon Laplace's five-volume "Traité de mécanique céleste" (1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the "Principia" had left open, like a full theory of the tides.
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The concept of energy became a key part of Newtonian mechanics in the post-Newton period. Huygens' solution of the collision of hard spheres showed that in that case, not only is momentum conserved, but kinetic energy is as well (or, rather, a quantity that in retrospect we can identify as one-half the total kinetic energy). The question of what is conserved during all other processes, like inelastic collisions and motion slowed by friction, was not resolved until the 19th century. Debates on this topic overlapped with philosophical disputes between the metaphysical views of Newton and Leibniz, and variants of the term "force" were sometimes used to denote what we would call types of energy. For example, in 1742, Émilie du Châtelet wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax; living force is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work can be dissipated into heat. With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above.
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Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not developed until the late 19th and early 20th centuries. Vector algebra, pioneered by Josiah Willard Gibbs and Oliver Heaviside, stemmed from and largely supplanted the earlier system of quaternions invented by William Rowan Hamilton.
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Yale University is a private Ivy League research university in New Haven, Connecticut. Founded in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world.
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Chartered by the Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research.
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Yale is organized into fourteen constituent schools: the original undergraduate college, the Yale Graduate School of Arts and Sciences and twelve professional schools. While the university is governed by the Yale Corporation, each school's faculty oversees its curriculum and degree programs. In addition to a central campus in downtown New Haven, the university owns athletic facilities in western New Haven, a campus in West Haven, and forests and nature preserves throughout New England. , the university's endowment was valued at $42.3 billion, the second largest of any educational institution. The Yale University Library, serving all constituent schools, holds more than 15 million volumes and is the third-largest academic library in the United States. Students compete in intercollegiate sports as the Yale Bulldogs in the NCAA Division I – Ivy League.
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, 65 Nobel laureates, five Fields Medalists, four Abel Prize laureates, and three Turing Award winners have been affiliated with Yale University. In addition, Yale has graduated many notable alumni, including five U.S. presidents, 10 Founding Fathers, 19 U.S. Supreme Court Justices, 31 living billionaires, 54 College founders and presidents, many heads of state, cabinet members and governors. Hundreds of members of Congress and many U.S. diplomats, 78 MacArthur Fellows, 252 Rhodes Scholars, 123 Marshall Scholars, 102 Guggenheim Fellows and nine Mitchell Scholars have been affiliated with the university. Yale is a member of the Big Three, along with Harvard and Princeton. Yale's current faculty include 67 members of the National Academy of Sciences, 55 members of the National Academy of Medicine, 8 members of the National Academy of Engineering, and 187 members of the American Academy of Arts and Sciences. The college is, after normalization for institution size, the tenth-largest baccalaureate source of doctoral degree recipients in the United States, and the largest such source within the Ivy League. It also is a top 10 (ranked seventh), after normalization for the number of graduates, baccalaureate source of some of the most notable scientists (Nobel, Fields, Turing prizes, or membership in National Academy of Sciences, National Academy of Medicine, or National Academy of Engineering).
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Yale traces its beginnings to "An Act for Liberty to Erect a Collegiate School", a would-be charter passed during a meeting in New Haven by the General Court of the Colony of Connecticut on October 9, 1701. The Act was an effort to create an institution to train ministers and lay leadership for Connecticut. Soon after, a group of ten Congregational ministers, Samuel Andrew, Thomas Buckingham, Israel Chauncy, Samuel Mather (nephew of Increase Mather), Rev. James Noyes II (son of James Noyes), James Pierpont, Abraham Pierson, Noadiah Russell, Joseph Webb, and Timothy Woodbridge, all alumni of Harvard, met in the study of Reverend Samuel Russell, located in Branford, Connecticut, to donate their books to form the school's library. The group, led by James Pierpont, is now known as "The Founders".
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Known from its origin as the "Collegiate School", the institution opened in the home of its first rector, Abraham Pierson, who is today considered the first president of Yale. Pierson lived in Killingworth (now Clinton). The school moved to Saybrook in 1703 when the first treasurer of Yale, Nathaniel Lynde, donated land and a building. In 1716, it moved to New Haven, Connecticut.
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Meanwhile, there was a rift forming at Harvard between its sixth president, Increase Mather, and the rest of the Harvard clergy, whom Mather viewed as increasingly liberal, ecclesiastically lax, and overly broad in Church polity. The feud caused the Mathers to champion the success of the Collegiate School in the hope that it would maintain the Puritan religious orthodoxy in a way that Harvard had not. Rev. Jason Haven, the minister at the First Church and Parish in Dedham, Massachusetts had been considered for the presidency on account of his orthodox theology and for "Neatness dignity and purity of Style [which] surpass those of all that have been mentioned," but was passed over due to his "very Valetudinary and infirm State of Health."
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In 1718, at the behest of either Rector Samuel Andrew or the colony's Governor Gurdon Saltonstall, Cotton Mather contacted the successful Boston-born businessman Elihu Yale to ask him for financial help in constructing a new building for the college. Through the persuasion of Jeremiah Dummer, Yale, who had made a fortune in Madras while working for the East India Company as the first president of Fort St. George (largely through secret contracts with Madras merchants that were illegal under Company policy), donated nine bales of goods, which were sold for more than £560, a substantial sum of money at the time. Cotton Mather suggested that the school change its name to "Yale College." The Welsh name Yale is the Anglicized spelling of the Iâl, which the family estate at Plas yn Iâl, near the village of Llandegla, was called.
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Meanwhile, a Harvard graduate working in England convinced some 180 prominent intellectuals to donate books to Yale. The 1714 shipment of 500 books represented the best of modern English literature, science, philosophy and theology at the time. It had a profound effect on intellectuals at Yale. Undergraduate Jonathan Edwards discovered John Locke's works and developed his original theology known as the "new divinity." In 1722 the rector and six of his friends, who had a study group to discuss the new ideas, announced that they had given up Calvinism, become Arminians, and joined the Church of England. They were ordained in England and returned to the colonies as missionaries for the Anglican faith. Thomas Clapp became president in 1745 and while he attempted to return the college to Calvinist orthodoxy, he did not close the library. Other students found Deist books in the library.
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Yale College undergraduates follow a liberal arts curriculum with departmental majors and is organized into a social system of residential colleges.
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Yale was swept up by the great intellectual movements of the period—the Great Awakening and the Enlightenment—due to the religious and scientific interests of presidents Thomas Clap and Ezra Stiles. They were both instrumental in developing the scientific curriculum at Yale while dealing with wars, student tumults, graffiti, "irrelevance" of curricula, desperate need for endowment and disagreements with the Connecticut legislature.
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Serious American students of theology and divinity, particularly in New England, regarded Hebrew as a classical language, along with Greek and Latin, and essential for the study of the Old Testament in the original words. The Reverend Ezra Stiles, president of the college from 1778 to 1795, brought with him his interest in the Hebrew language as a vehicle for studying ancient Biblical texts in their original language (as was common in other schools), requiring all freshmen to study Hebrew (in contrast to Harvard, where only upperclassmen were required to study the language) and is responsible for the Hebrew phrase אורים ותמים (Urim and Thummim) on the Yale seal. A 1746 graduate of Yale, Stiles came to the college with experience in education, having played an integral role in the founding of Brown University, in addition to having been a minister. Stiles' greatest challenge occurred in July 1779 when British forces occupied New Haven and threatened to raze the college. However, Yale graduate Edmund Fanning, secretary to the British general in command of the occupation, intervened and the college was saved. In 1803, Fanning was granted an honorary degree LL.D. for his efforts.
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As the only college in Connecticut from 1701 to 1823, Yale educated the sons of the elite. Punishable offenses for students included cardplaying, tavern-going, destruction of college property, and acts of disobedience to college authorities. During this period, Harvard was distinctive for the stability and maturity of its tutor corps, while Yale had youth and zeal on its side.
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The emphasis on classics gave rise to a number of private student societies, open only by invitation, which arose primarily as forums for discussions of modern scholarship, literature and politics. The first such organizations were debating societies: Crotonia in 1738, Linonia in 1753 and Brothers in Unity in 1768. Linonia and Brothers in Unity continue to exist today with commemorations to them can be found with names given to campus structures, like Brothers in Unity Courtyard in Branford College.
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The Yale Report of 1828 was a dogmatic defense of the Latin and Greek curriculum against critics who wanted more courses in modern languages, mathematics, and science. Unlike higher education in Europe, there was no national curriculum for colleges and universities in the United States. In the competition for students and financial support, college leaders strove to keep current with demands for innovation. At the same time, they realized that a significant portion of their students and prospective students demanded a classical background. The Yale report meant the classics would not be abandoned. During this period, all institutions experimented with changes in the curriculum, often resulting in a dual-track curriculum. In the decentralized environment of higher education in the United States, balancing change with tradition was a common challenge because it was difficult for an institution to be completely modern or completely classical. A group of professors at Yale and New Haven Congregationalist ministers articulated a conservative response to the changes brought about by the Victorian culture. They concentrated on developing a person possessed of religious values strong enough to sufficiently resist temptations from within, yet flexible enough to adjust to the 'isms' (professionalism, materialism, individualism, and consumerism) tempting him from without. William Graham Sumner, professor from 1872 to 1909, taught in the emerging disciplines of economics and sociology to overflowing classrooms of students. Sumner bested President Noah Porter, who disliked the social sciences and wanted Yale to lock into its traditions of classical education. Porter objected to Sumner's use of a textbook by Herbert Spencer that espoused agnostic materialism because it might harm students.
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Until 1887, the legal name of the university was "The President and Fellows of Yale College, in New Haven." In 1887, under an act passed by the Connecticut General Assembly, Yale was renamed to the present "Yale University."
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The Revolutionary War soldier Nathan Hale (Yale 1773) was the archetype of the Yale ideal in the early 19th century: a manly yet aristocratic scholar, equally well-versed in knowledge and sports, and a patriot who "regretted" that he "had but one life to lose" for his country. Western painter Frederic Remington (Yale 1900) was an artist whose heroes gloried in the combat and tests of strength in the Wild West. The fictional, turn-of-the-20th-century Yale man Frank Merriwell embodied this same heroic ideal without racial prejudice, and his fictional successor Frank Stover in the novel "Stover at Yale" (1911) questioned the business mentality that had become prevalent at the school. Increasingly the students turned to athletic stars as their heroes, especially since winning the big game became the goal of the student body, the alumni, and the team itself.
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Along with Harvard and Princeton, Yale students rejected British concepts about 'amateurism' in sports and constructed athletic programs that were uniquely American, such as football. The Harvard–Yale football rivalry began in 1875. Between 1892, when Harvard and Yale met in one of the first intercollegiate debates, and in 1909 (the year of the first Triangular Debate of Harvard, Yale and Princeton) the rhetoric, symbolism, and metaphors used in athletics were used to frame these early debates. Debates were covered on front pages of college newspapers and emphasized in yearbooks, and team members even received the equivalent of athletic letters for their jackets. There were also rallies to send off the debating teams to matches, but the debates never attained the broad appeal that athletics enjoyed. One reason may be that debates do not have a clear winner, as is the case in sports, and that scoring is subjective. In addition, with late 19th-century concerns about the impact of modern life on the human body, athletics offered hope that neither the individual nor the society was coming apart.
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In 1909–10, football faced a crisis resulting from the failure of the previous reforms of 1905–06, which sought to solve the problem of serious injuries. There was a mood of alarm and mistrust, and, while the crisis was developing, the presidents of Harvard, Yale, and Princeton developed a project to reform the sport and forestall possible radical changes forced by government upon the sport. Presidents Arthur Hadley of Yale, A. Lawrence Lowell of Harvard, and Woodrow Wilson of Princeton worked to develop moderate reforms to reduce injuries. Their attempts, however, were reduced by rebellion against the rules committee and the formation of the Intercollegiate Athletic Association. While the big three had attempted to operate independently of the majority, the changes pushed did reduce injuries.
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Starting with the addition of the Yale School of Medicine in 1810, the college expanded gradually from then on, establishing the Yale Divinity School in 1822, Yale Law School in 1822, the Yale Graduate School of Arts and Sciences in 1847, the now-defunct Sheffield Scientific School in 1847, and the Yale School of Fine Arts in 1869. In 1887, under the presidency of Timothy Dwight V, Yale College was renamed to Yale University, and the former name was subsequently applied only to the undergraduate college. The university would continue to expand greatly into the 20th and 21st century, adding the Yale School of Music in 1894, the Yale School of Forestry & Environmental Studies in 1900, the Yale School of Public Health in 1915, the Yale School of Architecture in 1916, the Yale School of Nursing 1923, the Yale School of Drama in 1955, the Yale School of Management in 1976, and the Jackson School of Global Affairs which is planned to open in 2022. The Sheffield Scientific School would also reorganize its relationship with the university to teach only undergraduate courses.
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Expansion caused controversy about Yale's new roles. Noah Porter, a moral philosopher, was president from 1871 to 1886. During an age of tremendous expansion in higher education, Porter resisted the rise of the new research university, claiming that an eager embrace of its ideals would corrupt undergraduate education. Many of Porter's contemporaries criticized his administration, and historians since have disparaged his leadership. Historian George Levesque argues Porter was not a simple-minded reactionary, uncritically committed to tradition, but a principled and selective conservative. Levesque continues, saying he did not endorse everything old or reject everything new; rather, he sought to apply long-established ethical and pedagogical principles to a rapidly changing culture. Levesque concludes, noting he may have misunderstood some of the challenges of his time, but he correctly anticipated the enduring tensions that have accompanied the emergence and growth of the modern university.
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Milton Winternitz led the Yale School of Medicine as its dean from 1920 to 1935. Dedicated to the new scientific medicine established in Germany, he was equally fervent about "social medicine" and the study of humans in their culture and environment. He established the "Yale System" of teaching, with few lectures and fewer exams, and strengthened the full-time faculty system; he also created the graduate-level Yale School of Nursing and the psychiatry department and built numerous new buildings. Progress toward his plans for an Institute of Human Relations, envisioned as a refuge where social scientists would collaborate with biological scientists in a holistic study of humankind, unfortunately, lasted for only a few years before the opposition of resentful anti-Semitic colleagues drove him to resign.
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Before World War II, most elite university faculties counted among their numbers few, if any, Jews, blacks, women, or other minorities; Yale was no exception. By 1980, this condition had been altered dramatically, as numerous members of those groups held faculty positions. Almost all members of the Faculty of Arts and Sciences—and some members of other faculties—teach undergraduate courses, more than 2,000 of which are offered annually.
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In 1793, Lucinda Foote passed the entrance exams for Yale College, but was rejected by the president on the basis of her gender. Women studied at Yale University as early as 1892, in graduate-level programs at the Yale Graduate School of Arts and Sciences. The first seven women to earn PhDs at Yale received their degrees in 1894: Elizabeth Deering Hanscom, Cornelia H. B. Rogers, Sara Bulkley Rogers, Margaretta Palmer, Mary Augusta Scott, Laura Johnson Wylie, and Charlotte Fitch Roberts. There is a portrait of these seven women in Sterling Memorial Library, painted by Brenda Zlamany.
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In 1966, Yale began discussions with its sister school Vassar College about merging to foster coeducation at the undergraduate level. Vassar, then all-female and part of the Seven Sisters—elite higher education schools that historically served as sister institutions to the Ivy League when most Ivy League institutions still only admitted men—tentatively accepted, but then declined the invitation. Both schools introduced coeducation independently in 1969. Amy Solomon was the first woman to register as a Yale undergraduate; she was also the first woman at Yale to join an undergraduate society, St. Anthony Hall. The undergraduate class of 1973 was the first class to have women starting from freshman year; at the time, all undergraduate women were housed in Vanderbilt Hall at the south end of Old Campus.
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A decade into co-education, student assault and harassment by faculty became the impetus for the trailblazing lawsuit Alexander v. Yale. In the late 1970s, a group of students and one faculty member sued Yale for its failure to curtail campus sexual harassment by especially male faculty. The case was partly built from a 1977 report authored by plaintiff Ann Olivarius, now a feminist attorney known for fighting sexual harassment, "A report to the Yale Corporation from the Yale Undergraduate Women's Caucus." This case was the first to use Title IX to argue and establish that the sexual harassment of female students can be considered illegal sex discrimination. The plaintiffs in the case were Olivarius, Ronni Alexander (now a professor at Kobe University, Japan), Margery Reifler (works in the Los Angeles film industry), Pamela Price (civil rights attorney in California), and Lisa E. Stone (works at Anti-Defamation League). They were joined by Yale classics professor John “Jack” J. Winkler, who died in 1990. The lawsuit, brought partly by Catharine MacKinnon, alleged rape, fondling, and offers of higher grades for sex by several Yale faculty, including Keith Brion, professor of flute and director of bands, political Science professor Raymond Duvall (now at the University of Minnesota), English professor Michael Cooke, and coach of the field hockey team, Richard Kentwell. While unsuccessful in the courts, the legal reasoning behind the case changed the landscape of sex discrimination law and resulted in the establishment of Yale's Grievance Board and the Yale Women's Center. In March 2011 a Title IX complaint was filed against Yale by students and recent graduates, including editors of Yale's feminist magazine Broad Recognition, alleging that the university had a hostile sexual climate. In response, the university formed a Title IX steering committee to address complaints of sexual misconduct. Afterwards, universities and colleges throughout the US also established sexual harassment grievance procedures.
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Yale, like other Ivy League schools, instituted policies in the early 20th century designed to maintain the proportion of white Protestants from notable families in the student body (see "numerus clausus"), and was one of the last of the Ivies to eliminate such preferences, beginning with the class of 1970.
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In 2006, Yale and Peking University (PKU) established a Joint Undergraduate Program in Beijing, an exchange program allowing Yale students to spend a semester living and studying with PKU honor students. In July 2012, the Yale University-PKU Program ended due to weak participation.
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In 2007 outgoing Yale President Rick Levin characterized Yale's institutional priorities: "First, among the nation's finest research universities, Yale is distinctively committed to excellence in undergraduate education. Second, in our graduate and professional schools, as well as in Yale College, we are committed to the education of leaders."
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In 2009, former British Prime Minister Tony Blair picked Yale as one location – the others being Britain's Durham University and Universiti Teknologi Mara – for the Tony Blair Faith Foundation's United States Faith and Globalization Initiative. As of 2009, former Mexican President Ernesto Zedillo is the director of the Yale Center for the Study of Globalization and teaches an undergraduate seminar, "Debating Globalization". As of 2009, former presidential candidate and DNC chair Howard Dean teaches a residential college seminar, "Understanding Politics and Politicians". Also in 2009, an alliance was formed among Yale, University College London, and both schools' affiliated hospital complexes to conduct research focused on the direct improvement of patient care—a growing field known as translational medicine. President Richard Levin noted that Yale has hundreds of other partnerships across the world, but "no existing collaboration matches the scale of the new partnership with UCL".
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In August 2013, a new partnership with the National University of Singapore led to the opening of Yale-NUS College in Singapore, a joint effort to create a new liberal arts college in Asia featuring a curriculum including both Western and Asian traditions.
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In 2017, having been suggested for decades, Yale University renamed Calhoun College, named for slave owner, anti-abolitionist, and white supremacist Vice President John C. Calhoun (it is now Hopper College, after Grace Hopper).
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In 2020, in the wake of protests around the world focused on racial relations and criminal justice reform, the #CancelYale tag was used on social media to demand that Elihu Yale's name be removed from Yale University. Most support for the change stemmed from politically conservative pundits, such as Mike Cernovich and Ann Coulter, satirizing perceived excesses of online cancel culture. Yale was president of Fort. St George in Madras, a fort of the East India Company in India, which was one of the biggest corporation in the world at the time. The company traded textiles, goods, diamonds, cotton, spices, among others, and was involved in the slave trade in India, with a private army of 260,000 soldiers, twice the size of Britain.
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His singularly large donation of paintings and books to the college led some critics to argue that Yale relied on money related to the slave-trade for its first scholarships and endowments.
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In August 2020, the US Justice Department sued Yale for alleged discrimination against Asian and white candidates on the basis of their race through affirmative action admission policies. In early February 2021, under the new Biden administration, the Justice Department withdrew the lawsuit. The group, Students for Fair Admissions, known for a similar lawsuit against Harvard alleging the same issue, plans to refile the lawsuit.
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The "Boston Globe" wrote that "if there's one school that can lay claim to educating the nation's top national leaders over the past three decades, it's Yale". Yale alumni were represented on the Democratic or Republican ticket in every U.S. presidential election between 1972 and 2004. Yale-educated presidents since the end of the Vietnam War include Gerald Ford, George H. W. Bush, Bill Clinton, and George W. Bush, and major-party nominees during this period include Hillary Clinton (2016), John Kerry (2004), Joseph Lieberman (vice president, 2000), and Sargent Shriver (vice president, 1972). Other Yale alumni who have made serious bids for the presidency during this period include Amy Klobuchar (2020), Tom Steyer (2020), Ben Carson (2016), Howard Dean (2004), Gary Hart (1984 and 1988), Paul Tsongas (1992), Pat Robertson (1988) and Jerry Brown (1976, 1980, 1992).
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Several explanations have been offered for Yale's representation in national elections since the end of the Vietnam War. Various sources note the spirit of campus activism that has existed at Yale since the 1960s, and the intellectual influence of Reverend William Sloane Coffin on many of the future candidates. Yale President Richard Levin attributes the run to Yale's focus on creating "a laboratory for future leaders," an institutional priority that began during the tenure of Yale Presidents Alfred Whitney Griswold and Kingman Brewster. Richard H. Brodhead, former dean of Yale College and now president of Duke University, stated: "We do give very significant attention to orientation to the community in our admissions, and there is a very strong tradition of volunteerism at Yale." Yale historian Gaddis Smith notes "an ethos of organized activity" at Yale during the 20th century that led John Kerry to lead the Yale Political Union's Liberal Party, George Pataki the Conservative Party, and Joseph Lieberman to manage the "Yale Daily News". Camille Paglia points to a history of networking and elitism: "It has to do with a web of friendships and affiliations built up in school." CNN suggests that George W. Bush benefited from preferential admissions policies for the "son and grandson of alumni", and for a "member of a politically influential family". "New York Times" correspondent Elisabeth Bumiller and "The Atlantic Monthly" correspondent James Fallows credit the culture of community and cooperation that exists between students, faculty, and administration, which downplays self-interest and reinforces commitment to others.
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During the 1988 presidential election, George H. W. Bush (Yale '48) derided Michael Dukakis for having "foreign-policy views born in Harvard Yard's boutique". When challenged on the distinction between Dukakis' Harvard connection and his own Yale background, he said that, unlike Harvard, Yale's reputation was "so diffuse, there isn't a symbol, I don't think, in the Yale situation, any symbolism in it" and said Yale did not share Harvard's reputation for "liberalism and elitism". In 2004 Howard Dean stated, "In some ways, I consider myself separate from the other three (Yale) candidates of 2004. Yale changed so much between the class of '68 and the class of '71. My class was the first class to have women in it; it was the first class to have a significant effort to recruit African Americans. It was an extraordinary time, and in that span of time is the change of an entire generation".
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The President and Fellows of Yale College, also known as the Yale Corporation, or board of trustees, is the governing body of the university and consists of thirteen standing committees with separate responsibilities outlined in the by-laws. The corporation has 19 members: three ex officio members, ten successor trustees, and six elected alumni fellows. The university has three major academic components: Yale College (the undergraduate program), the Graduate School of Arts and Sciences, and the twelve professional schools.
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Yale's former president Richard C. Levin was, at the time, one of the highest paid university presidents in the United States with a 2008 salary of $1.5 million. Yale's succeeding president Peter Salovey ranks 40th with a 2020 salary of $1.16 million.
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The Yale Provost's Office and similar executive positions have launched several women into prominent university executive positions. In 1977, Provost Hanna Holborn Gray was appointed interim president of Yale and later went on to become president of the University of Chicago, being the first woman to hold either position at each respective school. In 1994, Provost Judith Rodin became the first permanent female president of an Ivy League institution at the University of Pennsylvania. In 2002, Provost Alison Richard became the vice-chancellor of the University of Cambridge. In 2003, the dean of the Divinity School, Rebecca Chopp, was appointed president of Colgate University and later went on to serve as the president of the Swarthmore College in 2009, and then the first female chancellor of the University of Denver in 2014. In 2004, Provost Dr. Susan Hockfield became the president of the Massachusetts Institute of Technology. In 2004, Dean of the Nursing school, Catherine Gilliss, was appointed the dean of Duke University's School of Nursing and vice chancellor for nursing affairs. In 2007, Deputy Provost H. Kim Bottomly was named president of Wellesley College.
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Similar examples for men who have served in Yale leadership positions can also be found. In 2004, Dean of Yale College Richard H. Brodhead was appointed as the president of Duke University. In 2008, Provost Andrew Hamilton was confirmed to be the vice chancellor of the University of Oxford.
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Yale University staff are represented by several different unions. Clerical and technical workers are represented by Local 34, and service and maintenance workers are represented by Local 35, both of the same union affiliate UNITE HERE. Unlike similar institutions, Yale has consistently refused to recognize its graduate student union, Local 33 (another affiliate of UNITE HERE), citing claims that the union's elections were undemocratic and how graduate students are not employees; the move to not recognize the union has been criticized by the American Federation of Teachers. In addition, officers of the Yale University Police Department are represented by the Yale Police Benevolent Association, which affiliated in 2005 with the Connecticut Organization for Public Safety Employees. Yale security officers joined the International Union of Security, Police and Fire Professionals of America in late 2010, even though the Yale administration contested the election. In October 2014, after deliberation, Yale security decided to form a new union, the Yale University Security Officers Association, which has since represented the campus security officers.
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Yale has a history of difficult and prolonged labor negotiations, often culminating in strikes. There have been at least eight strikes since 1968, and "The New York Times" wrote that Yale has a reputation as having the worst record of labor tension of any university in the U.S. Moreover, Yale has been accused by the AFL–CIO of failing to treat workers with respect, as well as not renewing contracts with professors over involvement in campus labor issues. Yale has responded to strikes with claims over mediocre union participation and the benefits of their contracts.
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Yale's central campus in downtown New Haven covers and comprises its main, historic campus and a medical campus adjacent to the Yale–New Haven Hospital. In western New Haven, the university holds of athletic facilities, including the Yale Golf Course. In 2008, Yale purchased the 17-building, former Bayer HealthCare complex in West Haven, Connecticut, the buildings of which are now used as laboratory and research space. Yale also owns seven forests in Connecticut, Vermont, and New Hampshire—the largest of which is the Yale-Myers Forest in Connecticut's Quiet Corner—and nature preserves including Horse Island.
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Yale is noted for its largely Collegiate Gothic campus as well as several iconic modern buildings commonly discussed in architectural history survey courses: Louis Kahn's Yale Art Gallery and Center for British Art, Eero Saarinen's Ingalls Rink and Ezra Stiles and Morse Colleges, and Paul Rudolph's Art & Architecture Building. Yale also owns and has restored many noteworthy 19th-century mansions along Hillhouse Avenue, which was considered the most beautiful street in America by Charles Dickens when he visited the United States in the 1840s. In 2011, Travel+Leisure listed the Yale campus as one of the most beautiful in the United States.
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Many of Yale's buildings were constructed in the Collegiate Gothic architecture style from 1917 to 1931, financed largely by Edward S. Harkness, including the Yale Drama School. Stone sculpture built into the walls of the buildings portray contemporary college personalities, such as a writer, an athlete, a tea-drinking socialite, and a student who has fallen asleep while reading. Similarly, the decorative friezes on the buildings depict contemporary scenes, like a policemen chasing a robber and arresting a prostitute (on the wall of the Law School), or a student relaxing with a mug of beer and a cigarette. The architect, James Gamble Rogers, faux-aged these buildings by splashing the walls with acid, deliberately breaking their leaded glass windows and repairing them in the style of the Middle Ages, and creating niches for decorative statuary but leaving them empty to simulate loss or theft over the ages. In fact, the buildings merely simulate Middle Ages architecture, for though they appear to be constructed of solid stone blocks in the authentic manner, most actually have steel framing as was commonly used in 1930. One exception is Harkness Tower, tall, which was originally a free-standing stone structure. It was reinforced in 1964 to allow the installation of the Yale Memorial Carillon.
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Other examples of the Gothic style are on the Old Campus by architects like Henry Austin, Charles C. Haight and Russell Sturgis. Several are associated with members of the Vanderbilt family, including Vanderbilt Hall, Phelps Hall, St. Anthony Hall (a commission for member Frederick William Vanderbilt), the Mason, Sloane and Osborn laboratories, dormitories for the Sheffield Scientific School (the engineering and sciences school at Yale until 1956) and elements of Silliman College, the largest residential college.
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The oldest building on campus, Connecticut Hall (built in 1750), is in the Georgian style. Georgian-style buildings erected from 1929 to 1933 include Timothy Dwight College, Pierson College, and Davenport College, except the latter's east, York Street façade, which was constructed in the Gothic style to coordinate with adjacent structures.
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The Beinecke Rare Book and Manuscript Library, designed by Gordon Bunshaft of Skidmore, Owings & Merrill, is one of the largest buildings in the world reserved exclusively for the preservation of rare books and manuscripts. The library includes a six-story above-ground tower of book stacks, filled with 180,000 volumes, that is surrounded by large translucent Vermont marble panels and a steel and granite truss. The panels act as windows and subdue direct sunlight while also diffusing the light in warm hues throughout the interior. Near the library is a sunken courtyard, with sculptures by Isamu Noguchi that are said to represent time (the pyramid), the sun (the circle), and chance (the cube). The library is located near the center of the university in Hewitt Quadrangle, which is now more commonly referred to as "Beinecke Plaza."
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Alumnus Eero Saarinen, Finnish-American architect of such notable structures as the Gateway Arch in St. Louis, Washington Dulles International Airport main terminal, Bell Labs Holmdel Complex and the CBS Building in Manhattan, designed Ingalls Rink, dedicated in 1959, as well as the residential colleges Ezra Stiles and Morse. These latter were modeled after the medieval Italian hill town of San Gimignano – a prototype chosen for the town's pedestrian-friendly milieu and fortress-like stone towers. These tower forms at Yale act in counterpoint to the college's many Gothic spires and Georgian cupolas.
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Notable nonresidential campus buildings and landmarks include Battell Chapel, Beinecke Rare Book Library, Harkness Tower, Ingalls Rink, Kline Biology Tower, Osborne Memorial Laboratories, Payne Whitney Gymnasium, Peabody Museum of Natural History, Sterling Hall of Medicine, Sterling Law Buildings, Sterling Memorial Library, Woolsey Hall, Yale Center for British Art, Yale University Art Gallery, Yale Art & Architecture Building, and the Paul Mellon Centre for Studies in British Art in London.
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Yale's secret society buildings (some of which are called "tombs") were built both to be private yet unmistakable. A diversity of architectural styles is represented: Berzelius, Donn Barber in an austere cube with classical detailing (erected in 1908 or 1910); Book and Snake, Louis R. Metcalfe in a Greek Ionic style (erected in 1901); Elihu, architect unknown but built in a Colonial style (constructed on an early 17th-century foundation although the building is from the 18th century); Mace and Chain, in a late colonial, early Victorian style (built in 1823). (Interior moulding is said to have belonged to Benedict Arnold);Manuscript Society, King-lui Wu with Dan Kiley responsible for landscaping and Josef Albers for the brickwork intaglio mural. Building constructed in a mid-century modern style; Scroll and Key, Richard Morris Hunt in a Moorish- or Islamic-inspired Beaux-Arts style (erected 1869–70); Skull and Bones, possibly Alexander Jackson Davis or Henry Austin in an Egypto-Doric style utilizing Brownstone (in 1856 the first wing was completed, in 1903 the second wing, 1911 the Neo-Gothic towers in rear garden were completed); St. Elmo, (former tomb) Kenneth M. Murchison, 1912, designs inspired by Elizabethan manor. Current location, brick colonial; and Wolf's Head, Bertram Grosvenor Goodhue, erected 1923–1924, Collegiate Gothic.
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Yale's Office of Sustainability develops and implements sustainability practices at Yale. Yale is committed to reduce its greenhouse gas emissions 10% below 1990 levels by 2020. As part of this commitment, the university allocates renewable energy credits to offset some of the energy used by residential colleges. Eleven campus buildings are candidates for LEED design and certification. Yale Sustainable Food Project initiated the introduction of local, organic vegetables, fruits, and beef to all residential college dining halls. Yale was listed as a Campus Sustainability Leader on the Sustainable Endowments Institute's College Sustainability Report Card 2008, and received a "B+" grade overall.
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Yale is the largest taxpayer and employer in the City of New Haven, and has often buoyed the city's economy and communities. Yale, however, has consistently opposed paying a tax on its academic property. Yale's Art Galleries, along with many other university resources, are free and openly accessible. Yale also funds the New Haven Promise program, paying full tuition for eligible students from New Haven public schools.
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Yale has a complicated relationship with its home city; for example, thousands of students volunteer every year in myriad community organizations, but city officials, who decry Yale's exemption from local property taxes, have long pressed the university to do more to help. Under President Levin, Yale has financially supported many of New Haven's efforts to reinvigorate the city. Evidence suggests that the town and gown relationships are mutually beneficial. Still, the economic power of the university increased dramatically with its financial success amid a decline in the local economy.
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Several campus safety strategies have been pioneered at Yale. The first campus police force was founded at Yale in 1894, when the university contracted city police officers to exclusively cover the campus. Later hired by the university, the officers were originally brought in to quell unrest between students and city residents and curb destructive student behavior. In addition to the Yale Police Department, a variety of safety services are available including blue phones, a safety escort, and 24-hour shuttle service.
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In the 1970s and 1980s, poverty and violent crime rose in New Haven, dampening Yale's student and faculty recruiting efforts. Between 1990 and 2006, New Haven's crime rate fell by half, helped by a community policing strategy by the New Haven Police and Yale's campus became the safest among the Ivy League and other peer schools.
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In 2004, the national non-profit watchdog group Security on Campus filed a complaint with the U.S. Department of Education, accusing Yale of under-reporting rape and sexual assaults.
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In April 2021, Yale announced that it will require students to receive a COVID-19 vaccine as a condition of being on campus during the fall 2021 term.
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Undergraduate admission to Yale College is considered "most selective" by "U.S. News". In 2022, Yale accepted 2,234 students to the Class of 2026 out of 50,015 applicants, for an acceptance rate of 4.46%. 98% of students graduate within six years.
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Through its program of need-based financial aid, Yale commits to meet the full demonstrated financial need of all applicants. Most financial aid is in the form of grants and scholarships that do not need to be paid back to the university, and the average need-based aid grant for the Class of 2017 was $46,395. 15% of Yale College students are expected to have no parental contribution, and about 50% receive some form of financial aid. About 16% of the Class of 2013 had some form of student loan debt at graduation, with an average debt of $13,000 among borrowers. For 2019, Yale ranked second in enrollment of recipients of the National Merit $2,500 Scholarship (140 scholars).
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Half of all Yale undergraduates are women, more than 39% are ethnic minority U.S. citizens (19% are underrepresented minorities), and 10.5% are international students. 55% attended public schools and 45% attended private, religious, or international schools, and 97% of students were in the top 10% of their high school class. Every year, Yale College also admits a small group of non-traditional students through the Eli Whitney Students Program.
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Yale University Library, which holds over 15 million volumes, is the third-largest university collection in the United States. The main library, Sterling Memorial Library, contains about 4 million volumes, and other holdings are dispersed at subject and location libraries.
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Rare books are found in several Yale collections. The Beinecke Rare Book Library has a large collection of rare books and manuscripts. The Harvey Cushing/John Hay Whitney Medical Library includes important historical medical texts, including an impressive collection of rare books, as well as historical medical instruments. The Lewis Walpole Library contains the largest collection of 18th‑century British literary works. The Elizabethan Club, technically a private organization, makes its Elizabethan folios and first editions available to qualified researchers through Yale.
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Yale's museum collections are also of international stature. The Yale University Art Gallery, the country's first university-affiliated art museum, contains more than 200,000 works, including Old Masters and important collections of modern art, in the Swartwout and Kahn buildings. The latter, Louis Kahn's first large-scale American work (1953), was renovated and reopened in December 2006. The Yale Center for British Art, the largest collection of British art outside of the UK, grew from a gift of Paul Mellon and is housed in another Kahn-designed building.
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The Peabody Museum of Natural History in New Haven is used by school children and contains research collections in anthropology, archaeology, and the natural environment. The Yale University Collection of Musical Instruments, affiliated with the Yale School of Music, is perhaps the least-known of Yale's collections because its hours of opening are restricted.
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The museums once housed the artifacts brought to the United States from Peru by Yale history professor Hiram Bingham in his Yale-financed expedition to Machu Picchu in 1912 – when the removal of such artifacts was legal. The artifacts were restored to Peru in 2012.
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The "U.S. News & World Report" ranked Yale third among U.S. national universities for 2016, as it had for each of the previous sixteen years. Yale University is accredited by the New England Commission of Higher Education.
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Internationally, Yale was ranked 11th in the 2016 Academic Ranking of World Universities, tenth in the 2016–17 Nature Index for quality of scientific research output, and tenth in the 2016 CWUR World University Rankings. The university was also ranked sixth in the 2016 Times Higher Education (THE) Global University Employability Rankings and eighth in the Academic World Reputation Rankings. In 2019, it ranked 27th among the universities around the world by "SCImago Institutions Rankings".
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Yale is a member of the Association of American Universities (AAU) and is classified among "R1: Doctoral Universities – Very high research activity". According to the National Science Foundation, Yale spent $990 million on research and development in 2018, ranking it 15th in the nation.
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