Timeline of computational mathematics: Difference between revisions

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== 1940s ==

* Monte Carlo simulation (voted one of the top 10 [[algorithm]]s of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.<ref>{{cite journal|last=Metropolis|first=N.|title=The Beginning of the Monte Carlo method|journal=Los Alamos Science|year=1987|volume=No. 15, Page 125|page=125–130|url=http://library.lanl.gov/cgi-bin/getfile?15-12.pdf}}. Accessed |access-date=5 mayMay 2012.}}</ref><ref>S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). [http://library.lanl.gov/cgi-bin/getfile?00329286.pdf Statistical methods in neutron diffusion]. Los Alamos Scientific Laboratory report LAMS–551.</ref><ref>N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335–341.</ref>

* Dantzig introduces the [[simplex method|simplex algorithm]] (voted one of the top 10 algorithms of the 20th century).<ref>{{cite web|title=SIAM News, November 1994.|url=http://www.stanford.edu/group/SOL/dantzig.html|accessdate=6 June 2012}} Systems Optimization Laboratory, Stanford University Huang Engineering Center (site host/mirror).</ref>

* First [[Computational Fluid Dynamics|hydro simulations]] at Los Alamos occurred.<ref>Richtmyer, R. D. (1948). Proposed Numerical Method for Calculation of Shocks. Los Alamos, NM: Los Alamos Scientific Laboratory LA-671.</ref><ref>A Method for the Numerical Calculation of Hydrodynamic Shocks.

Von Neumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, pp. 232–237</ref>

* Ulam and von Neumann introduce the notion of cellular automata.<ref>Von Neumann, J., Theory of Self-ReproduiingReproducing Automata, Univ. of Illinois Press, Urbana, 1966.</ref>

* [[Manchester Small-Scale Experimental Machine#First programs|A routine for the Manchester Baby]] written to factor a large number (2^18), one of the first in [[computational number theory]].<ref>[http://curation.cs.manchester.ac.uk/digital60/www.digital60.org/birth/manchestercomputers/mark1/manchester.html The Manchester Mark 1.]</ref> The Manchester group would make several other breakthroughs in [[Mersenne primes|this area]].<ref>[http://curation.cs.manchester.ac.uk/digital60/www.digital60.org/about/glossary/notes.html#mersenne Miscellaneous Notes: Mersenne Primes.] [http://www.cs.manchester.ac.uk/Digital60/Digital 60 Manchester - 60 years of the Modern Computer]{{Dead link|date=July 2018 |bot=InternetArchiveBot |fix-attempted=no }}, [[University of Manchester|Manchester Uni.]] CS Curation website.</ref><ref>[http://news.bbc.co.uk/2/hi/technology/7465115.stm One tonne 'Baby' marks its birth: Dashing times.] By Jonathan Fildes, Science and technology reporter, BBC News.</ref>

* LU decomposition technique first discovered.

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== 1970s ==

*Computer algebra replicates and extends the work of Delaunay in lunar theory.<ref>http://www.umiacs.umd.edu/~helalfy/pub/mscthesis01.pdf {{Bare URL PDF|date=March 2022}}</ref>

* Mandelbrot, from studies of the [[Fatou set|Fatou]], [[Julia set|Julia]] and [[Mandelbrot set]]s, coined and popularized the term 'fractal' to describe these structures' [[self-similarity]].<ref>B. Mandelbrot; ''Les objets fractals, forme, hasard et dimension '' (in French). Publisher: Flammarion (1975), {{ISBN|9782082106474}}; English translation ''Fractals: Form, Chance and Dimension.'' Publisher: Freeman, W. H & Company. (1977). {{ISBN|9780716704737}}.</ref><ref>Mandelbrot, Benoît B.; (1983). The Fractal Geometry of Nature. San Francisco: W.H. Freeman. {{ISBN|0-7167-1186-9}}.</ref>

*Kenneth Appel and Wolfgang Haken prove the [[four colour theorem]], the [[Computer-assisted proof#Theorems proved with the help of computer programs|first theorem to be proved by computer]].<ref>Kenneth Appel and Wolfgang Haken, "Every planar map is four colorable, Part I: Discharging," Illinois Journal of Mathematics 21: 429–490, 1977.</ref><ref>Appel, K. and Haken, W. "Every Planar Map is Four-Colorable, II: Reducibility." Illinois J. Math. 21, 491–567, 1977.

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==2000s==

*In computational group theory, [[Optimal solutions for Rubik's Cube|God's Number]] for the [[Rubik's cubeCube]] is shown to be 20.<ref>[http://blog.computationalcomplexity.org/2010/09/rubiks-cube-conjecture-proven-do-we.html The Rubik's Cube Conjecture PROVEN! (Do we care?)] Wednesday, September 08, 2010</ref><ref>[http://www.cube20.org God's Number is 20.]</ref>

*Mathematicians completely map the E8-group.<ref>[https://news.mit.edu/2007/e8 Math research team maps E8: Calculation on paper would cover Manhattan.] MIT News. Elizabeth A. Thomson, News Office; March 18, 2007.</ref><ref>[https://www.math.columbia.edu/~woit/wordpress/?p=534 E8 Media Blitz], [[Peter Woit]].</ref><ref>[https://www.huliq.com/15695/mathematicians-map-e8 Mathematicians Map E8.] {{Webarchive|url=https://web.archive.org/web/20150924032322/http://www.huliq.com/15695/mathematicians-map-e8 |date=2015-09-24 }} By Armine Hareyan 2007-03-20 02:21.</ref>

==2010s==

* Hales completes the proof of Kepler's conjecture.<ref>[http://blog.kleinproject.org/?p=742 What is the way of packing oranges? — Kepler’sKepler's conjecture on the packing of spheres.] Posted on May 26, 2015 by Antoine Nectoux. Klein Project Blog: Connecting mathematical worlds.</ref><ref>[https://code.google.com/p/flyspeck/wiki/AnnouncingCompletion Announcement of Completion.] Flyspeck Project, [[Google Code]].</ref><ref>[https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/ Proof confirmed of 400-year-old fruit-stacking problem.] [[New Scientist]], 12 August 2014.

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