[The original artitle is published in SIAM News, Volume 33, Number 4, Barry A. Cipra, "The Best of the 20th Century: Editors Name Top 10 Algorithms"]
1946: John von Neumann, Stan Ulam, and Nick Metropolis, all at the Los Alamos Scientific Laboratory, cook up the Metropolis algorithm, also known as the Monte Carlo method.
1947: George Dantzig, at the RAND Corporation, creates the simplex method for linear programming.
1950: Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.
1951: Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations.
1957: John Backus leads a team at IBM in developing the Fortran optimizing compiler.
1959–61: J.G.F. Francis of Ferranti Ltd., London, finds a stable method for computing eigenvalues, known as the QR algorithm.
1962: Tony Hoare of Elliott Brothers, Ltd., London, presents Quicksort.
1977: Helaman Ferguson and Rodney Forcade of Brigham Young University advance an integer relation detection algorithm.
1987: Leslie Greengard and Vladimir Rokhlin of Yale University invent the fast multipole algorithm.