Timeline of computational mathematics

This is a timeline of key developments in computational mathematics.

1940s

• Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.^[1][2][3]
• Dantzig introduces the simplex algorithm (voted one of the top 10 algorithms of the 20th century).^[4]
• First hydro simulations at Los Alamos occurred.^[5][6]
• Ulam and von Neumann introduce the notion of cellular automata.^[7]
• A routine for the Manchester Baby written to factor a large number (2^18), one of the first in computational number theory.^[8] The Manchester group would make several other breakthroughs in this area.^[9]
• LU decomposition technique first discovered.

1950s

• Hestenes, Stiefel, and Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.^{[10][11][12][13]} Voted one of the top 10 algorithms of the 20th century.
• Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm.^[14] Also, important earlier independent work by Alder and S. Frankel.^[15][16]
• Enrico Fermi, Stanislaw Ulam, John Pasta, and Mary Tsingou, discover the Fermi–Pasta–Ulam–Tsingou problem.^[17]
• In network theory, Ford & Fulkerson compute a solution to the maximum flow problem.^[18]
• Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century).^[19]
• Molecular dynamics invented by Alder and Wainwright^[20]
• John G.F. Francis^[21] and Vera Kublanovskaya^[22] invent QR factorization (voted one of the top 10 algorithms of the 20th century).

1960s

• First recorded use of the term "finite element method" by Ray Clough,^[23] to describe the methods of Courant, Hrenikoff and Zienkiewicz, among others. See also here.
• Using computational investigations of the 3-body problem, Minovitch formulates the gravity assist method.^[24][25]
• Molecular dynamics was invented independently by Aneesur Rahman.^[26]
• Cooley and Tukey re-invent the Fast Fourier transform (voted one of the top 10 algorithms of the 20th century), an algorithm first discovered by Gauss.
• Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory.^[27]
• Kruskal and Zabusky follow up the Fermi–Pasta–Ulam–Tsingou problem with further numerical experiments, and coin the term "soliton".^[28][29]
• Birch and Swinnerton-Dyer conjecture formulated through investigations on a computer.^[30]
• Grobner bases and Buchberger's algorithm invented for algebra^[31]
• Frenchman Verlet (re)discovers a numerical integration algorithm,^[32] (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907,^[33] hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics.^[32]
• Risch invents algorithm for symbolic integration.^[34]

1970s

• Mandelbrot, from studies of the Fatou, Julia and Mandelbrot sets, coined and popularized the term 'fractal' to describe these structures' self-similarity.^[35][36]
• Kenneth Appel and Wolfgang Haken prove the four colour theorem, the first theorem to be proved by computer.^[37][38][39]

1980s

• Fast multipole method invented by Rokhlin and Greengard (voted one of the top 10 algorithms of the 20th century).^[40][41][42]

1990s

• The appearance of the first research grids using volunteer computing – GIMPS (1996) and distributed.net (1997).
• Kepler conjecture is almost all but certainly proved algorithmically by Thomas Hales in 1998.

2000s

• In computational group theory, God's Number for the Rubik's cube is shown to be 20.^[43][44]
• Mathematicians completely map the E8-group.^[45][46][47]

2010s

• Hales completes the proof of Kepler's conjecture.^[48][49][50]

See also

• Timeline of scientific computing
• Computational mathematics
• Timeline of algorithms
• Timeline of mathematics from the 20th century onwards
• Timeline of numerical analysis after 1945