John Vincent Atanasoff and Clifford Berry create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, from 1937 to 1942.
1940s
Nuclear bomb and ballistics simulations at Los Alamos and BRL, respectively.
Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis.
Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm. Also, important earlier independent work by Alder and S. Frankel.
Fermi, Ulam and Pasta with help from Mary Tsingou, discover the Fermi–Pasta–Ulam problem.
W Kohn instigates the development of density functional theory (with LJ Sham and P Hohenberg), for which he shares the Nobel Chemistry Prize (1998). This contribution is arguably the first Nobel given for a computer programme or computational technique.
Frenchman Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Delambre, by Cowell and Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics, and the Verlet list.
1970s
Veltman's calculations at CERN lead him and t'Hooft to valuable insights into renormalizability of electroweak theory. The computation has been cited as a key reason to the award of the Nobel prize to both.
Hardy, Pomeau and de Pazzis introduced the first lattice gas model, abbreviated as the HPP model after its authors. These later evolve into lattice Boltzmann models.
Wilson shows that continuum QCD is recovered for an infinitely large lattice with its sites infinitesimally close to one another, thereby beginning lattice QCD.
1980s
Italian physicists Car and Parrinello invent the Car–Parrinello method.
Fast multipole method invented by Rokhlin and Greengard (voted one of the top 10 algorithms of the 20th century).
