

A timeline of mathematics and theoretical physics

1901 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.

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.

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Visit the extensive History of Mathematics site at the University of St. Andrews

Black Holes
Nobel Laureates in Physics
String Theory Origins of Supersymmetry by John H. Schwarz
Introduction to the Yuri Golfand Memorial Volume "Many Faces of the Superworld" by M. Shifman

For serious or the curious: The Mathematics of Fermat's Last Theorem

