La Habra High School
Math History Timeline

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20th Century ...
1914-present A.D.

1915	Einstein submits a paper giving a definitive version of the general theory of relativity.
1916	Sierpinski gives the first example of an absolutely normal number, that is a number whose digits occur with equal frequency in whichever base it is written.
1919	Hausdorff introduces the notion of "Hausdorff dimension", which is a real number lying between the topological dimension of an object and 3. It is used to study objects such as Koch's curve.
1919	Russell publishes Introduction to Mathematical Philosophy which had been largely written while he was in prison for anti-war activities.
1920	Fundamenta Mathematica is founded by Sierpinski and Mazurkiewicz.
1921	Borel publishes the first in a series of papers on game theory and becomes the first to define games of strategy.
1921	Emmy Noether publishes Idealtheorie in Ringbereichen which is of fundamental importance in the development of modern abstract algebra.
1922	Banach is awarded his habilitation for a thesis on measure theory. He begins his work on a development of normed vector spaces.
1922	Richardson publishes Weather Prediction by Numerical Process. He is the first to apply mathematics, in particular the method of finite differences, to predicting the weather. The calculations are prohibitive by hand calculation and only the development of computers will make his idea a reality.
1928	Von Neumann proves the minimax theorem in game theory.
1931	G D Birkhoff proves the general ergodic theorem. This will transform the Maxwell-Boltzmann kinetic theory of gases into a rigorous principle through the use of Lebesgue measure.
1931	Gödel publishes Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (On Formally Undecidable Propositions in Principia Mathematica and Related Systems). He proves fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved.
1931	Von Mises introduces the idea of a sample space into probability theory.
1932	Von Neumann publishes Grundlagen der Quantenmechanik on quantum mechanics.
1934	Zorn establishes "Zorn's lemma" so named (probably) by Tukey. It is equivalent to the axiom of choice.
1936	Turing publishes On Computable Numbers, with an application to the Entscheidungsproblem which describes a theoretical machine, now known as the "Turing machine". It becomes a major ingredient in the theory of computability.
1944	Von Neumann and Morgenstern publish Theory of Games and Economic Behaviour. The theory of games is used in the study of economics.
1949	Mauchly and John Eckert build the Binary Automatic Computer (BINAC). One of the major advances of this machine is that data is stored on magnetic tape rather than on punched cards.
1950	Hamming publishes a fundamental paper on error-detecting and error-correcting codes.
1955	Taniyama poses his conjecture on elliptic curves which will play a major role in the proof of Fermat's Last Theorem.
1961	Edward Lorenz discovers a simple mathematical system with chaotic behaviour. It leads to the new mathematics of chaos theory which is widely applicable.
1963	Cohen proves the independence of the axiom of choice and of the continuum hypothesis.
1975	Feigenbaum discovers a new constant, approximately 4.669201660910..., which is related to period-doubling bifurcations and plays an important part in chaos theory.
1975	Mandelbrot publishes Les objets fractals, forn, hasard et dimension which describe the theory of fractals.
1976	Appel and Haken show that the Four Colour Conjecture is true using 1200 hours of computer time to examine around 1500 configurations.
1977	Adleman, Rivest, and Shamir introduce public-key codes, a system for passing secret messages using large primes and a key which can be published.
1980	The classification of finite simple groups is complete.
1982	Mandelbrot publishes The fractal geometry of nature which develops his theory of fractal geometry more fully than his work of 1975.
1988	Elkies finds a counterexample to Euler's Conjecture with n = 4, namely 958004 + 2175194 + 4145604 = 4224814.
1994	Wiles proves Fermat's Last Theorem.
1999	Conrad and Taylor prove the "Taniyama-Shimura conjecture". Wiles proved a special case in 1993 on his way to giving a proof of Fermat's Last Theorem.
2000	At a meeting of the American Mathematical Society in Los Angeles "Mathematical Challenges of the 21st Century" were proposed. Unlike "Hilbert's problems" from 100 years earlier, these were given by a team of 30 leading mathematicians of whom eight were Fields Medal winners.

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