1500

1500		Babylonians establish the metric of flat 2-dimensional space by observation, in their efforts to keep track of land for legal and economic purposes.
-518		Pythagoras, a Greek educated by mystics in Egypt and Babylon, founds community of men and women calling themselves mathematikoi, in southern Italy. They believe that reality is in essence mathematical. Pythagoras noted that vibrating lyre strings with harmonious notes have lengths that are proportional by a whole number. The Pythagorean theorem proves by reasoning what the Babylonians figured out by measurement 1000 years earlier.
-387		Plato, after traveling to Italy and learning about the Pythagoreans, founds his Academy in Athens, and continues to develop the idea that reality must be expressible in mathematical terms. But Athens at that time has developed a notoriously misogynist culture. Unlike his role model Pythagoras, whose school developed many women mathematikoi, Plato does not allow women to participate.
-300		Euclid of Alexandria, a gifted teacher, produces Elements, one of the top mathematics textbooks of recorded history, which organizes the existing Mediterranean understanding of geometry into a coherent logical framework.
-225		Ionian mathematician Apollonius writes Conics, and introduces the terms ellipse, parabola and hyperbola to describe conic sections.
-140		Nicaean mathematician and astronomer Hipparchus develops what will be known as trigonometry.
150		The Almagest by Alexandrian astronomer and mathematician Claudius Ptolemy asserts that the Sun and planets orbit around the Earth in perfect circles. Ptolemy's work is so influential that will become official church doctrine when the Christians later come to rule Europe.
415		As a glorious 2000 years of ancient Mediterranean mathematics and science comes to a close, Hypatia of Alexandria, a renowned teacher, mathematician, astronomer, and priestess of Isis, is kidnapped from a public religious procession and brutally murdered by a mob of angry Christian monks.
628		Hindu mathematician-astronomer Brahmagupta writes Brahma- sphuta- siddhanta (The Opening of the Universe). Hindu mathematicians develop numerals and start investigating number theory.
830		The spread of Islam leads to the spread of written Arabic language. As ancient Greek and Hindu works are translated into Arabic, a culture of mathematics and astronomy develops. The peak of this cultural flowering is represented by Arabic mathematician Al-Khworizmi, working at the House of Wisdom in Baghdad, who develops what will be known as algebra in his work Hisab al-jabr w'al-muqabala.
1070		Iranian poet, mathematician and astronomer Omar Khayyam begins his Treatise on Demonstration of Problems of Algebra, classifying cubic equations that could be solved by conic sections. Khayyam was such a brilliant poet that history has nearly forgotten that he was also a brilliant scientist and mathematician. The moving finger writes...
1120		Adelard of Bath translates works of Euclid and Al-Khworizmi into Latin and introduces them to European scholars.
1482		Euclid's Elements is published using the revolutionary new technology of the printing press, leading to a revolution in education and scholarship as information becomes more difficult for authorities to control.
1543		Copernicus publishes De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres) asserting that the Earth and planets revolve about the Sun. The Catholic Church has accorded an official holy status to Ptolemy's geocentric Universe. Copernicus avoids prosecution as a heretic by waiting until the end of his own life to publish his controversial claims.
1589		Pisa University mathematics instructor Galileo Galilei studies the motion of objects and begins a book De Motu (On Motion) which he never finishes.
1602		Galileo observes that the period of a swinging pendulum is independent of the amplitude of the swing.
1609		Johannes Kepler claims in the journal Astronomia Nova that the orbit of Mars is an ellipse with the Sun at one focus, and sweeps out equal areas in equal time. He will later generalize these into his famous Three Laws of Planetary Motion.
1609		Galileo makes his first telescope. His observations of the moon show that it looks like a very large lumpy rock, not a divinely smooth and perfect shining Platonic heavenly orb. This discovery has enormously distressing cultural reverberations for Western culture and religion.
1614		Scottish theologian John Napier, who does mathematics as a hobby, publishes his discovery of the logarithm in his work Mirifici logarithmorum canonis descriptio.
1615		Kepler's mother, Frau Katharina Kepler, is accused of witchcraft by a local prostitute. European witch hunting was at its peak during Kepler's career, and witch hunting was supported by all levels of society, including secular officials and intellectuals in universities. Kepler spends the next several years making legal appeals and hiding his mother from legal authorities seeking to torture her into confessing to witchcraft. Examining an accused witch *ad torturam* was a standard court procedure during this era.
1620		Under court order, Kepler's mother is kidnapped in the middle of the night from her daughter's home and taken to prison. Kepler spends the next year appealing to the duke of Württemberg to prevent his imprisoned mother from being examined *ad torturam*.
1621		On September 28, Katharina Kepler is taken from her prison cell into the torture room, shown the instruments of torture and ordered to confess. She replies "Do with me what you want. Even if you were to pull one vein after another out of my body, I would have nothing to admit," and says the Lord's Prayer. She is taken back to prison. She is freed on October 4 upon order of the duke, who rules that her refusal to confess under threat of torture proves her innocence. He also orders her accusers to pay the cost of her trial and imprisonment.
1622		After having spent most of the last seven years under the legal threat of imminent torture, Katharina Kepler dies on April 13, still being threatened with violence from those who insist she is a witch.
1624		Pope Urban VIII promises Galileo that he is allowed write about Copernican heliocentrism if he treats it as an abstract proposition.
1628		Kepler uses Napier's logarithms to compute a set of astronomical tables, the Rudolphine Tables, whose accuracy is so impressive that it leads to the quiet acceptance of the heliocentric solar system by everyone in the shipping industry.
1629		Basque mathematician Pierre de Fermat, the founder of modern number theory, begins his brilliant career by reconstructing the work of Apollonius on conic sections . Fermat and Descartes pioneer the application of algebraic methods to solving problems in geometry.
1632		Galileo publishes Dialogue concerning the two greatest world systems, which argues convincingly for the Copernican view that the Earth and planets revolve around the Sun.
1633		The Inquisition calls Galieo to Rome to answer charges of heresy against the Catholic Church.
1637		Descartes publishes his revolutionary Discours de la méthode (Discourse on Method) containing three essays on the use of reason to search for the truth. In the third essay Descartes describes analytic geometry, and uses the letters (x,y,z) for the coordinate system that will later bear his name.
1642		Galileo dies at his villa in Florence, still under house arrest from charges of heresy.
1663		Cambridge mathematician Isaac Barrow delivers lectures on modern methods of computing tangents that inspire his student Isaac Newton towards developing calculus
1665		Newton's "miraculous years" in math and physics, when he discovers the derivative, which he sees as a ratio of velocities called fluxions, and the integral, which he sees as a fluent of the fluxions. Newton shows that the fluent and fluxion are inversely related, a result now called the *Fundamental Theorem of Calculus*. Newton also develops his ideas on optics and gravitation. He tries to publish his work in 1671, but the publisher goes bankrupt.
1683		Jacob Bernoulli, who studied mathematics and astronomy against the wishes of his career-minded parents, teaches Newtonian mechanics at the University of Basel, and turns mathematical physics into a family business.
1684		Leibniz publishes the beginning of his work on differential and integral calculus. He discovers the Fundamental Theorem of Calculus in his own way. Leibniz originates most of the current calculus notation including the integral sign. He portrays an integral as a sum of infinitesimals, a concept rejected by Newton.
1687		Newton publishes Principia Mechanica after Edmund Halley convinces Newton to write up his alleged proof that an inverse square force law leads to elliptical orbits. Newton's Laws of Motion and Law of Gravitation lead to the development of theoretical physics itself. This event marks a permanent change in the relationship between human beings and the Universe.
1693		Newton has a nervous breakdown after his close companion Fatio De Duillier becomes ill and has to return to Switzerland.
1696		Brachistochrone problem solved by Jacob and Johann Bernoulli, an early result in the calculus of variations.
1712		Thanks to a campaign waged by Newton, a commission appointed by Royal Society of London President Isaac Newton rules that Leibniz is guilty of plagiarism against Newton in the discovery of calculus. English mathematics and theoretical physics go into decline because those loyal to Newton are hesitant to adopt Leibniz' infinitesimal and his clean, intuitively appealing notation.
1736		Leonhard Euler begins the field of topology when he publishes his solution of the Konigsberg Bridge problem.
1738		Hydrodynamics by Daniel Bernoulli
1748		The multitalented Euler begins the fields of mathematical analysis and analytical mechanics with Introductio in analysin infinitorum. Euler introduces the formula e^ix = cos x + i sin x
1758		Joseph-Louis Lagrange finds the complete general solution to the Newtonian equations of motion for a vibrating string, which explains the harmonic relations observed by Pythagoras 22 centuries ago.
1770		Hyperbolic trigonometry -- cosh, sinh -- is developed.
1772		Henry Cavendish, a wealthy but paranoid recluse, discovers that the electrostatic force is described by an inverse square law similar to gravity, but doesn't tell anyone in the science community.
1788		Lagrange further develops the analytical mechanics of Euler when he publishes Mécanique Analytique, revealing Newtonian mechanics to be a rich field of exploration for mathematicians.
1789		Aristocrat Charles-Augustin de Coulomb, hiding from the French Revolution after the storming of the Bastille, shows that the electrostatic force between electric charges was very well described by an inverse square law, in full analogy with Newtonian gravity. This becomes known as Coulomb's Law, even though Henry Cavendish was the first one to demonstrate it.
1793		Lagrange is arrested during the Reign of Terror, but is rescued by Antoine-Laurent Lavoisier, the founder of modern chemistry. Unfortunately, Lavoisier's career in chemistry is ended when he is taken to meet Madame Guillotine on May 8, 1794.
1799		Pierre-Simon Laplace publishes his work Traité du Mécanique Céleste (Treatise on Celestial Mechanics) using differential equations to solve problems in planetary motion and fluid flow.
	1807		After serving as a member of the Revolutionary Committee that terrorized France, sent Coulomb into hiding, arrested Lagrange and guillotined Lavoisier, a repentant Jean Baptiste Joseph Fourier causes controversy with his memoir On the Propagation of Heat in Solid Bodies. His former teachers Laplace and Lagrange object to his use of infinite trigonometric series, which we now call Fourier series. Fourier later wins the Paris Institute Mathematics Prize for solving the problem of heat propagation, over the repeated objections of Laplace and Lagrange.
	1817		Johann Karl Friedrich Gauss begins working on non-Euclidean geometry, and lays the foundations of differential geometry, but doesn't publish because he is afraid of the controversy that would result.
	1820		Danish physicist Hans Christian Oersted studied the way an electric current in a wire could move the magnetic needle of a compass, which strongly suggested that electricity and magnetism were related somehow.
	1823		Transylvanian mathematician János Bolyai, despite being warned against it by his father, tosses out Euclid's Fifth Axiom and shows that non-Euclidean geometry is possible. Gauss calls him a genius of the first order, but then crushes the young man by telling him he discovered it years ago but failed to publish due to his own fear of controversy.
	1826		Elliptic functions are developed by Gauss, Jacobi and Abel.
	1826		In his book Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience. André Marie Ampère gave a mathematical derivation of the magnetic force between two parallel wires with electric current, what we now call Ampère's Law.
	1827		Ohm's Law of electrical resistance is published in his book Die galvanische Kette, mathematisch bearbeitet.
	1827		Augustin-Louis Cauchy develops the calculus of residues, beginning his work in mathematics that made complex analysis one of the most important analytical tools of modern theoretical physics, including string theory.
	1828		Self-educated English mill worker George Green publishes his work on the use of potential theory to solve partial differential equations, and develops one of the most powerful mathematical technologies in theoretical physics -- the Green function.
	1829		Russian mathematician Nikolai Ivanovich Lobachevsky publishes his independent discovery of non-Euclidean geometry in the Kazan Messenger. Years later, one of his physics students will become known to history as Lenin's father.
	1831		Evariste Galois develops the nascent group theory with his work on the permutation group.
	1831		Michael Faraday discovers magnetic induction, now known as Faraday's Law, where moving magnetism creates electricity, and this result increases support for the idea of a unified theory of electricity and magnetism.
	1829		French mathematician Joseph Liouville begins to work on boundary value problems in partial differential equations, leading to Sturm-Liouville theory. He then develops the study of conformal transformations, and later proves the Liouville Theorem regarding the invariance of the measure of phase space under what will later be called Hamiltonian flow.
	1834		William Rowan Hamilton applies his mathematical development of characteristic functions in optics to mechanics and the enormous and potent mathematical technology of Hamiltonian dynamics is born.
	1840		Karl Weierstrass begins his work on elliptic functions.
	1843		After a period of emotional distress and alcohol abuse, Hamilton finally deduces the noncommutative multiplication rule for quaternions. His first publication on the subject is to carve the quaternion formula into a bridge.
	1844		Hermann Grassmann develops exterior algebra and the Grassmannian.
	1851		Bernhard Riemann submits his Ph.D. thesis to his supervisor Gauss. In his thesis he describes what is now called a Riemann surface, an essential element in understanding string theory.
	1854		George Boole develops Boolean logic in Laws of Thought.
	1871		Norwegian mathematician Marius Sophus Lie publishes work on Lie algebras, opening up the field of differential topology and paving the way for gauge field theory 100 years later.
	1873		James Clerk Maxwell publishes a set of equations from which all of the observed laws of electromagnetism could be derived through mathematics. These equations turn out to have solutions that describe waves traveling through space with a speed that agrees with the measured speed of light. Maxwell makes the bold conclusion that light therefore must consist of electromagnetic waves, writing that he could "scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."
	1874		Cantor invents set theory.
	1878		William Clifford develops Clifford algebras from the work of Grassmann and Hamilton.
	1878		Arthur Cayley writes The theory of groups, where he proved that every finite group can be represented as a group of permutations.
	1883		Wilhelm Killing works on n-dimensional non-Euclidean geometry and Lie algebras, work that later results in the concept of a Killing vector, a powerful tool in differential geometry, quantum gauge field theory, supergravity and and string theory.
	1884		Heinrich Hertz rewrites Maxwell's Equations in a more elegant notation where the symmetry between electricity and magnetism was obvious. Hertz then creats the first radio waves and microwaves in his laboratory and shows that these electromagnetic waves behaved just as observable optical light behaved, proving that light was electromagnetic radiation, as Maxwell had predicted.
	1884		Ludwig Boltzmann makes a theoretical derivation of black body radiation using Maxwell's equations and thermodynamics, confirming the 1879 result measured experimentally by Josef Stefan. Their result, the Stefan-Boltzmann Law, is not quite right, and the correct solution in the next century will mark the beginning of quantum theory.
	1887		Michelson and Morley measure the Earth's velocity through the ether to be zero, strongly suggesting that there is no ether, and that the velocity of light is the same for all observers, a result whose full implications have changed the world forever.
	1894		Elie Cartan classifies simple Lie algebras
	1895		Henri Poincaré publishes Analysis Situs, and gives birth to the field of algebraic topology.
	1897		Electron discovered by J.J. Thompson.
	1899		Hendrik Lorentz becomes the third person, after Voigt and FitzGerald, to write down the relativistic coordinate transformations that will bear his name. The Lorentz transformations leave the speed of light invariant, as suggested by the Michelson-Morley experiment.
	1899		David Hilbert's Grundlagen der Geometrie (Foundations of Geometry) is published, putting modern geometry on a solid rigorous foundation.
	Max Planck makes his quantum hypothesis -- that energy is carried by indistinguishable units called quanta, rather than flowing in a pure continuum. This hypothesis leads to a successful derivation of the black body radiation law, now called Planck's Law, although in 1901 the quantum hypothesis as yet had no experimental support. The unit of quantum action is now called Planck's constant.
	1905			Swiss patent clerk Albert Einstein proposes Planck's quantum hypothesis as the physics underlying the photoelectric effect. Planck wins the Nobel Prize in 1918, and Einstein in 1921, for developing quantum theory, one of the two most important developments in 20th century physics.
	1905			Einstein publishes his simple, elegant Special Theory of Relativity, making mincemeat of his competition by relying on only two ideas: 1. The laws of physics are the same in all inertial frames, and 2. The speed of light is the same for all inertial observers.
	1905			Poincaré shows that Lorentz transformations in space and time plus rotations in space form a group, which comes to be known as the Lorentz group. The Lorentz group plus translations in space form a group called the Poincaré group.
	1907			Minkowski publishes Raum und Zeit (Space and Time), and establishes the idea of a spacetime continuum
	1909			Hilbert's work on integral equations later leads to the concept of a Hilbert space in quantum mechanics
	1915			Emmy Noether publishes Noether's Theorem, discovering the relationship between symmetries and conserved currents that was crucial to the later development of quantum gauge field theory and string theory
	1915			Einstein, with Hilbert in stiff competition, publishes his stunning General Theory of Relativity, and is lucky enough to be able to find observational support for his theory right away, in the perihelial advance of Mercury, and the deflection of starlight by the Sun.
	1916			German astrophysicist Karl Schwarzschild, serving on the Russian front in WWI, mails Einstein his paper on the Schwarzschild metric and Einstein presents it at a meeting of the Prussian Academy of Sciences. Six months and another major paper later, Schwarzschild dies of illness on the front.
	1921			Theodor Kaluza follows Einstein's advice and publishes his highly unorthodox ideas about unifying gravity with electromagnetism by adding an extra dimension of space that is compactified into a small circle. Kaluza-Klein compactification will become a rich subject of exploration in particle theory 60 years later.
	1925			Werner Heisenberg shows that his quantized probability operators form a non-commutative algebra. Born and Jordan point out to him that this is a matrix algebra, and the matrix formulation of quantum mechanics is born. He gets the Nobel Prize in 1932.
	1924			Louis duc de Broglie proposes the particle-wave duality of the electron in his doctoral thesis at the Sorbonne. He gets the Nobel Prize in 1929.
	1926			After learning of the work of de Broglie, Erwin Schrödinger develops his wave equation version of quantum mechanics, and unravels its relationship to the matrix formulation of quantum mechanics by Heisenberg. He shares the Nobel Prize with Dirac in 1933.
	1926			Young Cambridge math student Paul Dirac discovers the operator algebra behind Heisenberg's Uncertainty Principle for his doctoral thesis.
	1927			Heisenberg discovers the Uncertainty Principle that bears his name.
	1928			Dirac introduces a relativistic quantum equation for the electron, an equation now known as the Dirac equation. His equation predicts the discovery of the positron, and he shares the Nobel Prize with Schrodinger in 1933.
	1928			Werner Heisenberg, Hermann Weyl and Eugene Wigner begin an exploration of symmetry groups in quantum mechanics that has far-reaching consequences.
	1929			Edwin Hubble, with the help of his mule driver Humason, observes the redshift of distant galaxies and concludes that the Universe is expanding.
	1931			Einstein stops using the cosmological constant to keep the Universe from expanding.
	1931			Dirac shows that the existence of magnetic monopoles would lead to electric charge quantization.
	1931			Georges De Rham goes to work on his famous theorem in cohomology and characteristic classes, results that would become very important in string theory.
	1935			Young physicist Subramahnyan Chandrasekhar is attacked by famous astronomer Arthur Eddington for his report that there is a stellar mass limit beyond which collapse to what we now call a black hole is inevitable. Chandrasekhar wins the Nobel Prize in 1983 for his work on stellar evolution.
	1938			Wigner constructs a class of irreducible unitary representations of the Lorentz group
	1939			Elements de Mathematique, by Nicholas Bourbaki, pseudonym for a group of young mathematicians at the Ecole Normale in Paris, is begun. This extended set of works aims to set down in writing what is no longer in doubt, but rather on a boring and rigorous footing, in modern mathematics.
	1943			Chinese mathematician Shiing-Shen Chern begins his work on characteristic classes and fiber bundles that will become an important tool for understanding quantum gauge theories and string theory.
	1948			Richard Feynman, Julian Schwinger and Tomonaga Shin'ichiro report that the divergent integrals that plague the quantum gauge field theory of electrodynamics (QED) can be sensibly dealt with through the process of renormalization.
	1953			Based on particle scattering data, Murray Gell-Mann suggests that there is a new quantum number, called hypercharge, which we now call stangeness and recognize as a part of the quark model coming from the strange quark. Gell-Mann receives the Nobel Prize in 1969 for his work on the quark model.
	1954			Gell-Mann and Francis Low develop the idea that the physical content of a quantum theory should be invariant under a change of scale in the theory. This is called renormalization group, and it turns out to constrain quantum field theories enough to make it a very powerful tool for analyzing asymptotic behavior of quantum theories.
	1954			C.N. Yang and R. Mills develop non-Abelian gauge invariance, an idea that takes 17 years to gain acceptance, and then revolutionizes particle physics.
	1954			Eugenio Calabi conjectures the existence of a Kähler manifold with a Ricci-flat metric with a vanishing first Chern class, and a given complex structure and Kähler class. This funny-sounding stuff will eventually become of major importance in understanding superstring theory.
	1964			Cambridge mathematician Roger Penrose proves that a black hole spacetime must contain behind the black hole event horizon a singularity where spacetime physics ceases to make good sense.
	1964			Gell-Mann and George Zweig independently propose fundamental particles that Gell-Mann succeeds in naming "quarks".
	1964			Peter Higgs, Francois Englert and R. Brout suggest a method of breaking quantum gauge symmetry that is later called the Higgs mechanism.
	1967			In his paper A Model of Leptons, Steven Weinberg relies on Lie group theory combined with quantum field theory to explain the weak nuclear and electromagnetic forces in a single theory, using the Higgs mechanism to give mass to the weak bosons. Adbus Salam and Sheldon Glashow share the Nobel Prize with Weinberg in 1979 for Electroweak Theory.
	1967			Sidney Coleman and Jeffrey Mandula prove that well-behaved particle scattering theories can't have symmetry algebras that relate particles of different spin. But the strict consequences of the Coleman-Mandula Theorem were avoided by the supersymmetry algebras that were discovered a few years later.
	1968			Michael Atiyah and Isadore Singer begin their work on The Index of Elliptic Operators. They prove the Atiyah-Singer index theorem, a powerful mathematical result that will later be used extensively in theoretical physics.
	1968			Gabriele Veneziano begins modern string theory with his paper on the dual resonance model of the strong interactions.
	1970			Yoichiro Nambu, Leonard Susskind, and Holger Nielsen independently discover that the dual resonance model devised by Veneziano is based on the quantum mechanics of relativistic vibrating strings, and string theory begins.
	1971			Gerard 't Hooft publishes his proof that the electroweak gauge theory of Weinberg is renormalizable and a new chapter in theoretical physics begins -- the age of quantum gauge field theory.
	1971			Pierre Ramond, André Neveu and John Schwarz develop a string theory with fermions and bosons. Gervais and Sakita show that this theory obeys what turns out to be a supersymmetry algebra in two dimensions.
	1971			Ken Wilson publishes work using the renormalization group to understand the quantum behavior of systems undergoing phase transitions, this opens up the study of critical phenomena in particle physics and leads to greater understading of quark confinement. Wilson wins the Nobel Prize in 1981.
	1971			Soviet physicists Yuri Gol'fand and E. Likhtman extend the Poincaré algebra into a superalgebra and discover supersymmetry in four spacetime dimensions.
	1973			David Gross, David Politzer, Frank Wilczek and Gerard 't Hooft arrive at the conclusion that the coupling constant in non-abelian quantum gauge theories vanishes at high energy. This is called asymptotic freedom and is one of the major results in the history of quantum gauge field theory.
	1973			Quantum field theories with spacetime supersymmetry in four spacetime dimensions are discovered by Julius Wess and Bruno Zumino.
	1974			Stephen Hawking combines quantum field theory with classical general relativity and predicts that black holes radiate through particle emission, behave as thermodynamic objects, and decay with a finite lifetime into objects that we don't yet understand.
	1974			Magnetic monopole solutions of non-Abelian gauge field theories are found separately by 't Hooft and Moscow physicist Alexander Polyakov.
	1974			Joel Scherk and John Schwarz propose string theory as a theory of quantum gravity, an idea that takes ten years to be widely appreciated.
	1974			Howard Georgi and Sheldon Glashow propose SU(5) for a "Grand Unified Theory" (GUT) of all forces except gravity, the theory predicts that protons could decay.
	1975			Instanton solutions of Yang-Mills equations are discovered by Belavin, Polyakov, A. Schwarz and Tyupkin. This is exciting because instantons can tell us about non-perturbative physics that is not approachable by other means of calculation.
	1976			Shing-Tung Yau proves the Calabi conjecture and discovers the Calabi-Yau space, an important development for later progress in string theory.
	1980			Alan Guth puts forward the idea of an inflationary phase of the early Universe, before the Big Bang.
	1981			Michael Green and John Schwarz develop superstring theory.
	1981			After Schoen and Yau do it in a more traditional manner, Ed Witten uses supersymmetry to prove the positive mass conjecture.
	1982			Mathematician Karen Uhlenbeck shows that Yang-Mills instantons discovered by physicists can be used as a powerful analytical tool in abstract mathematics.
	1983			Witten and Luis Alvarez-Gaumé derive general formulas for gauge and gravitational anomalies in quantum field theories in any dimension. They show that the gravitational anomalies cancel in type IIB superstring theory.
	1983			Mathematics graduate student Simon Donaldson discovers exotic 4-manifolds, using instanton techniques learned in part from Uhlenbeck.
	1984			Michael Green and John Schwarz show that superstring theory is free from quantum anomalies if the spacetime dimension is 10 and the quantum gauge symmetry is SO(32) or E8 times E8.
	1984			Gross, Harvey, Martinec and Rohm find another class of anomaly-free superstring theories, and call it the heterotic string theory.
	1985			Candelas, Strominger, Horowitz and Witten propose the use of Calabi-Yau spaces for the extra dimensions in heterotic string theory.
	1991			Connes and Lott develop non-commutative geometry, which will find its way into the heart of string theorists at the turn of the millennium.
	1993			In search of an understanding of black hole entropy, 't Hooft suggests the idea that the information in a 3+1-dimensional system cannot be greater than what is need to store it as an image in 2+1 dimensions. Susskind generalizes this idea and applies it to string theory in his paper The World as a Hologram, and the Holographic Principle is born.
	1994			Nathan Seiberg and Ed Witten discover electric-magnetic duality in N=2 supersymmetric gauge theory in four spacetime dimensions, with very important applications in both mathematics and string theory.
	1995			Witten and Townsend introduce the idea of Type IIA superstring theory as a special limit of 11-dimensional supergravity theory with quantized membranes. This begins the M-theory revolution in superstring theory, and leads people to ponder the role of spacetime in string theory.
	1995			Andrew Wiles, with help from Richard Taylor, completes a rigorous proof of Fermat's Last Theorem.
	1995			Joseph Polchinski ignites the D-brane revolution in string theory with his paper describing extended objects in string theory formed by dual open strings with Dirichlet boundary conditions.
	1996			In their paper Microscopic Origin of Black Hole Entropy, Andy Strominger and Cumrun Vafa use D-branes to count the quantum states of an extreme black hole and their result matches the Bekenstein-Hawking value. This stimulates new respect for string theory from the relativity community.
	1997			Juan Maldacena finds that string theory in a background of five-dimensional anti-de Sitter space times a five-sphere obeys a duality relationship with superconformal field theory in four spacetime dimensions. The result, called AdS-CFT duality, opens up a new era of exploration in string theory.

Here is a very brief outline of the development of string theory, the details of which will eventually fill many large volumes written by many people directly and indirectly involved in this rich and fascinating story.
1921
	Electromagnetism can be derived from gravity in a unified theory if there are four space dimensions instead of three, and the fourth is curled into a tiny circle. Kaluza and Klein made this discovery independently of each other.
1970
	Three particle theorists independently realize that the dual theories developed in 1968 to describe the particle spectrum also describe the quantum mechanics of oscillating strings. This marks the official birth of string theory.
1971
	Supersymmetry is invented in two contexts at once: in ordinary particle field theory and as a consequence of introducing fermions into string theory. It holds the promise of resolving many problems in particle theory, but requires equal numbers of fermions and bosons, so it cannot be an exact symmetry of Nature.
1974
	String theory using closed strings fails to describe hadronic physics because the spin 2 excitation has zero mass. Oops, that makes it an ideal candidate for the missing theory of quantum gravity!! This marks the advent of string theory as a proposed unified theory of all four observed forces in Nature.
1976
	Supersymmetry is added to gravity, making supergravity. This progress is especially important to string theory, where gravity can't be separated from the spectrum of excitations.
1980
	String theory plus supersymmetry yields an excitation spectrum that has equal numbers of fermions and bosons, showing that string theory can be made totally supersymmetric. The resulting objects are called superstrings.
1984
	This was the year for string theory! Deadly anomalies that threatened to make the theory senseless were discovered to cancel each other when the underlying symmetries in the theory belong two special groups. Finally string theory is accepted by the mainstream physics community as an actual candidate theory uniting quantum mechanics, particle physics and gravity.
1991- 1995
	Interesting work on stringy black holes in higher dimensions leads to a revolution in understanding how different versions of string theory are related through duality transformations. This unlocks a surge of progress towards a deeper nonperturbative picture of string theory.
1996
	Using Einstein relativity and Hawking radiation, there were hints in the past that black holes have thermodynamic properties that need to be understood microscopically. A microscopic origin for black hole thermodynamics is finally achieved in string theory. String theory sheds amazing light on the entire perplexing subject of black hole quantum mechanics.