Vincent Atanasoff and Clifford Berry create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, from 1937-42. Complex number calculator created by Stibitz. 1940s 1947 – Metropolis algorithm for Monte Carlo simulation (named one of the top-10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis. George Dantzig introduces the simplex method (named one of the top 10 algorithms of the 20th century) in 1947. Ulam and von Neumann introduce the notion of cellular automata. Turing formulated the LU decomposition method. A. W. H. Phillips invents the MONIAC hydraulic computer at LSE, better known as "Phillips Hydraulic Computer". First hydro simulations occurred at Los Alamos. 1950s First successful weather predictions on a computer occurred. 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. Named one of the top 10 algorithms of the 20th century. Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm. Molecular dynamics invented by Bernie Alder and Wainwright A S Householder invents his eponymous matrices and transformation method (voted one of the top 10 algorithms of the 20th century). 1953 – Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou discover the Fermi–Pasta–Ulam–Tsingou problem through computer simulations of a vibrating string. A team led by John Backus develops the FORTRAN compiler and programming language at IBM's research centre in San Jose, California. This sped the adoption of scientific programming, and is one of the oldest extant programming languages, as well as one of the most popular in science and engineering. 1960s 1960 – First recorded use of the term "finite element method" by Ray Clough to describe the earlier methods of Richard Courant, Alexander Hrennikoff and Olgierd Zienkiewicz in structural analysis. 1961 – John G.F. Francis and Vera Kublanovskaya invent QR factorization (voted one of the top 10 algorithms of the 20th century). 1963 – Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory. 1961 – Using computational investigations of the 3-body problem, Michael Minovitch formulates the gravity assist method. 1964 – Molecular dynamics invented independently by Aneesur Rahman. 1965 – fast Fourier transform developed by James W. Cooley and John W. Tukey. 1964 – Walter Kohn, with Lu Jeu Sham and Pierre Hohenberg, instigates the development of density functional theory, for which he shares the