A timeline of mathematics and theoretical physics

The Official String Theory Web Site:--> History --> Timeline (before 1800 / 1800-1899 / 1900 until today)

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.
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