Timeline of computational mathematics

This is a timeline of key developments in computational mathematics.

1940s

1950s

1960s

1970s

1980s

1990s

2000s

  • In computational group theory, God's number is shown to be 20.[45][46]
  • Mathematicians completely map the E8-group.[47][48][49]

2010s

  • Hales completes the proof of Kepler's conjecture.[50][51][52]

See also

References

  1. Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. No. 15, Page 125.. Accessed 5 may 2012.
  2. S. Ulam, R. D. Richtmyer, and J. von Neumann(1947). Statistical methods in neutron diffusion. Los Alamos Scientific Laboratory report LAMS–551.
  3. N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335–341.
  4. "SIAM News, November 1994". Retrieved 6 June 2012. Systems Optimization Laboratory, Stanford University Huang Engineering Center (site host/mirror).
  5. Richtmyer, R. D. (1948). Proposed Numerical Method for Calculation of Shocks. Los Alamos, NM: Los Alamos Scientific Laboratory LA-671.
  6. A Method for the Numerical Calculation of Hydrodynamic Shocks. Von Neumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, pp. 232–237
  7. Von Neumann, J., Theory of Self-Reproduiing Automata, Univ. of Illinois Press, Urbana, 1966.
  8. The Manchester Mark 1.
  9. Miscellaneous Notes: Mersenne Primes. 60 Manchester - 60 years of the Modern Computer, Manchester Uni. CS Curation website.
  10. One tonne 'Baby' marks its birth: Dashing times. By Jonathan Fildes, Science and technology reporter, BBC News.
  11. Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Natl. Bur. Stand. 49, 409–436 (1952).
  12. Eduard Stiefel,U¨ ber einige Methoden der Relaxationsrechnung (in German), Z. Angew. Math. Phys. 3, 1–33 (1952).
  13. Cornelius Lanczos, Solution of Systems of Linear Equations by Minimized Iterations, J. Res. Natl. Bur. Stand. 49, 33–53 (1952).
  14. Cornelius Lanczos, An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators, J. Res. Natl. Bur. Stand. 45, 255–282 (1950).
  15. Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). "Equations of State Calculations by Fast Computing Machines". Journal of Chemical Physics. 21 (6): 1087–1092. Bibcode:1953JChPh..21.1087M. doi:10.1063/1.1699114.
  16. Unfortunately, Alder's thesis advisor was unimpressed, so Alder and Frankel delayed publication of their results until much later. Alder, B. J. , Frankel, S. P. , and Lewinson, B. A. , J. Chem. Phys., 23, 3 (1955).
  17. Stanley P. Frankel, Unrecognized Genius, HP9825.COM (accessed 29 Aug 2015).
  18. Fermi, E. (posthumously); Pasta, J.; Ulam, S. (1955) : Studies of Nonlinear Problems (accessed 25 Sep 2012). Los Alamos Laboratory Document LA-1940. Also appeared in 'Collected Works of Enrico Fermi', E. Segre ed. , University of Chicago Press, Vol.II,978–988,1965. Recovered 21 Dec 2012
  19. Ford, L. R.; Fulkerson, D. R. (1956). "Maximal flow through a network" . Canadian Journal of Mathematics. 8: 399–404.
  20. Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric Matrix" (PDF). Journal of the ACM. 5 (4): 339–342. doi:10.1145/320941.320947. MR 0111128.
  21. Alder, B. J.; T. E. Wainwright (1959). "Studies in Molecular Dynamics. I. General Method". J. Chem. Phys. 31 (2): 459. Bibcode 1959JChPh..31..459A. doi:10.1063/1.1730376
  22. J. G. F. Francis, "The QR Transformation, I", The Computer Journal, vol. 4, no. 3, pages 265–271 (1961, received Oct 1959) online at oxfordjournals.org;
    J. G. F. Francis, "The QR Transformation, II" The Computer Journal, vol. 4, no. 4, pages 332–345 (1962) online at oxfordjournals.org.
  23. Vera N. Kublanovskaya (1961), "On some algorithms for the solution of the complete eigenvalue problem," USSR Computational Mathematics and Mathematical Physics, 1(3), pages 637–657 (1963, received Feb 1961). Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).
  24. RW Clough, “The Finite Element Method in Plane Stress Analysis,” Proceedings of 2nd ASCE Conference on Electronic Computation, Pittsburgh, PA, Sept. 8, 9, 1960.
  25. Minovitch, Michael: "A method for determining interplanetary free-fall reconnaissance trajectories," Jet Propulsion Laboratory Technical Memo TM-312-130, pages 38-44 (23 August 1961).
  26. Christopher Riley and Dallas Campbell, Oct 22, 2012. "The maths that made Voyager possible". BBC News Science and Environment. Recovered 16 Jun 2013.
  27. Rahman, A (1964). "Correlations in the Motion of Atoms in Liquid Argon". Phys Rev. 136 (2A): A405–A41. Bibcode:1964PhRv..136..405R. doi:10.1103/PhysRev.136.A405.
  28. Lorenz, Edward N. (1963). "Deterministic Nonperiodic Flow" (PDF). Journal of the Atmospheric Sciences. 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  29. Zabusky, N. J.; Kruskal, M. D. (1965). "Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states". Phys. Rev. Lett. 15 (6): 240–243. Bibcode 1965PhRvL..15..240Z. doi:10.1103/PhysRevLett.15.240.
  30. http://www.merriam-webster.com/dictionary/soliton ; retrieved 3 nov 2012.
  31. Birch, Bryan; Swinnerton-Dyer, Peter (1965). "Notes on Elliptic Curves (II)". J. Reine Angew. Math. 165 (218): 79–108. doi:10.1515/crll.1965.218.79.
  32. Bruno Buchberger: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (PDF; 1,8 MB). 1965
  33. Verlet, Loup (1967). "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard−Jones Molecules". Physical Review. 159 (1): 98–103. Bibcode:1967PhRv..159...98V. doi:10.1103/PhysRev.159.98.
  34. Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Section 17.4. Second-Order Conservative Equations". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN 978-0-521-88068-8.
  35. Risch, R. H. (1969). "The problem of integration in finite terms". Transactions of the American Mathematical Society. American Mathematical Society. 139: 167–189. doi:10.2307/1995313. JSTOR 1995313. Risch, R. H. (1970). "The solution of the problem of integration in finite terms". Bulletin of the American Mathematical Society. 76 (3): 605–608. doi:10.1090/S0002-9904-1970-12454-5.
  36. http://www.umiacs.umd.edu/~helalfy/pub/mscthesis01.pdf
  37. 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.
  38. Mandelbrot, Benoît B.; (1983). The Fractal Geometry of Nature. San Francisco: W.H. Freeman. ISBN 0-7167-1186-9.
  39. Kenneth Appel and Wolfgang Haken, "Every planar map is four colorable, Part I: Discharging," Illinois Journal of Mathematics 21: 429–490, 1977.
  40. Appel, K. and Haken, W. "Every Planar Map is Four-Colorable, II: Reducibility." Illinois J. Math. 21, 491–567, 1977.
  41. Appel, K. and Haken, W. "The Solution of the Four-Color Map Problem." Sci. Amer. 237, 108–121, 1977.
  42. L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems, MIT, Cambridge, (1987).
  43. Rokhlin, Vladimir (1985). "Rapid Solution of Integral Equations of Classic Potential Theory." J. Computational Physics Vol. 60, pp. 187–207.
  44. L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comput. Phys., 73 (1987), no. 2, pp. 325–348.
  45. The Rubik's Cube Conjecture PROVEN! (Do we care?) Wednesday, September 08, 2010
  46. God's Number is 20.
  47. Math research team maps E8: Calculation on paper would cover Manhattan. MIT News. Elizabeth A. Thomson, News Office; March 18, 2007.
  48. E8 Media Blitz, Peter Woit.
  49. Mathematicians Map E8. Archived 2015-09-24 at the Wayback Machine By Armine Hareyan 2007-03-20 02:21.
  50. What is the way of packing oranges? — Kepler’s conjecture on the packing of spheres. Posted on May 26, 2015 by Antoine Nectoux. Klein Project Blog: Connecting mathematical worlds.
  51. Announcement of Completion. Flyspeck Project, Google Code.
  52. Proof confirmed of 400-year-old fruit-stacking problem. New Scientist, 12 August 2014.
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