The following is a timeline of scientific computing, also known as computational science.

Before modern computers

18th century

* Simpson rediscovers

Simpson's rule In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads \int_a^b f(x) \, ...

, a century after

Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...

(who derived it in 1615 after seeing it used for wine barrels). * 1733 – The French naturalist Comte de Buffon poses his needle problem. * Euler comes up with a simple numerical method for integrands.

19th century

* First formulation of Gram-Schmidt orthogonalisation by Laplace, to be further improved decades later. * Babbage in 1822, began work on a machine made to compute/calculate values of polynomial functions automatically by using the method of finite differences. This was eventually called the

Difference engine A difference engine is an automatic mechanical calculator designed to tabulate polynomial, polynomial functions. It was designed in the 1820s, and was first created by Charles Babbage. The name, the difference engine, is derived from the method ...

. * Lovelace's note G on the

Analytical Engine The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine, which was a des ...

(1842) describes an algorithm for generating

Bernoulli numbers In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...

. It is considered the first algorithm ever specifically tailored for implementation on a computer, and thus the first-ever computer programme.Tom Stoppard’s “Arcadia,” at Twenty.
By Brad Leithauser.

The New Yorker ''The New Yorker'' is an American weekly magazine featuring journalism, commentary, criticism, essays, fiction, satire, cartoons, and poetry. Founded as a weekly in 1925, the magazine is published 47 times annually, with five of these issues ...

, August 8, 2013. The engine was never completed, however, so her code was never tested. * Adams-Bashforth method published. * In applied mathematics, Jacobi develops technique for solving numerical equations. * Gauss Seidel first published. * To help with computing tides, Harmonic Analyser is built in 1886.

1900s (decade)

* 1900 –

Runge Runge may refer to: Locations *Runge, Texas, a town, United States *Runge (crater), a lunar crater Mare Smythii Other uses *Runge Newspapers, a newspaper chain in Ontario, Canada *Inspector Heinrich Runge (though it is more often spelled a ...

’s work followed by

Martin Kutta Martin Wilhelm Kutta (; 3 November 1867 – 25 December 1944) was a German mathematician. Kutta was born in Pitschen, Upper Silesia (today Byczyna, Poland). He attended the University of Breslau from 1885 to 1890, and continued his studies in Mu ...

to invent the Runge-Kutta method for approximating integration for differential equations.

1910s (decade)

* 1910 – A-M Cholesky creates a matrix decomposition scheme. *

Richardson extrapolation In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A^\ast = \lim_ A(h). In essence, given the value of A(h) for several values of h, we ...

introduced.

1920s

* 1922 –

Lewis Fry Richardson Lewis Fry Richardson, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist, and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of si ...

introduces

numerical weather forecasting Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in ...

by manual calculation, using methods originally developed by

Vilhelm Bjerknes Vilhelm Friman Koren Bjerknes ( , ; 14 March 1862 – 9 April 1951) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use in num ...

as early as 1895. * 1926 –

Grete Hermann Grete Hermann (2 March 1901 – 15 April 1984) was a Germans, German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum m ...

publishes foundational paper for

computer algebra In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

, which established the existence of

algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...

(including complexity bounds) for many of the basic problems of

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...

, such as

ideal Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considere ...

membership for

polynomial ring In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) ...

s. *1926 Adams-Moulton method. * 1927 –

Douglas Hartree Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the c ...

creates what is later known as the

Hartree–Fock method In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. The Hartree–Fock method often a ...

, the first

ab initio quantum chemistry methods ''Ab initio'' quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excite ...

. However, manual solutions of the Hartree–Fock equations for a medium-sized atom were laborious and small molecules required computational resources far beyond what was available before 1950.

1930s

This decade marks the first major strides to a modern computer, and hence the start of the modern era. * Fermi's Rome physics research group (informal name ''

I ragazzi di Via Panisperna ' (''Via Panisperna Boys'') is an Italian movie by director Gianni Amelio, telling the enthusiasms, fears, joys and disappointments of the (private and professional) life of a well-known group of young men fond of physics and mathematics, who ...

'') develop statistical algorithms based on Comte de Buffon's work, that would later become the foundation of the

Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...

. See also

FERMIAC The Monte Carlo trolley, or FERMIAC, was an analog computer invented by physicist Enrico Fermi to aid in his studies of neutron transport. Operation The FERMIAC employed the Monte Carlo method to model neutron transport in various types of n ...

. * Shannon explains how to use electric circuits to do Boolean algebra in "

A Symbolic Analysis of Relay and Switching Circuits "A Symbolic Analysis of Relay and Switching Circuits" is the title of a master's thesis written by computer science pioneer Claude E. Shannon while attending the Massachusetts Institute of Technology (MIT) in 1937. In his thesis, Shannon, a dual ...

" *

John Vincent Atanasoff John Vincent Atanasoff, , (October 4, 1903 – June 15, 1995) was an American physicist and inventor from mixed Bulgarian-Irish origin, best known for being credited with inventing the first electronic digital computer. Atanasoff invented the ...

and

Clifford Berry Clifford Edward Berry (April 19, 1918 – October 30, 1963) helped John Vincent Atanasoff create the first digital electronic computer in 1939, the Atanasoff–Berry computer (ABC). Biography Clifford Berry was born April 19, 1918, in Gladbr ...

create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, from 1937-42. *

Complex number calculator George Robert Stibitz (April 30, 1904 – January 31, 1995) was a Bell Labs researcher internationally recognized as one of the fathers of the modern digital computer. He was known for his work in the 1930s and 1940s on the realization of Boolea ...

created by Stibitz.

1940s

* 1947 – Metropolis algorithm for Monte Carlo simulation (named one of the top-10

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s of the 20th century) invented at Los Alamos by von Neumann, Ulam and Metropolis. *

George Dantzig George Bernard Dantzig (; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics. Dantzig is known for his dev ...

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 __NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. Acco ...

, all from the Institute for Numerical Analysis at the

National Bureau of Standards The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

, 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 "Equation of State Calculations by Fast Computing Machines" is a scholarly article published by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller in the Journal of Chemical Physics in 1953. T ...

introduces the

Metropolis–Hastings algorithm In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. This seque ...

. *

Molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...

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 Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...

John Pasta John Robert Pasta (October 22, 1918 – June 5, 1981) was an American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physic ...

Stanislaw Ulam Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...

, and

Mary Tsingou Mary Tsingou (married name: Mary Tsingou-Menzel; born October 14, 1928) is an American physicist and mathematician of Greek descent. She was one of the first programmers on the MANIAC computer at Los Alamos National Laboratory and is best known ...

discover the

Fermi–Pasta–Ulam–Tsingou problem In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi ...

through computer simulations of a vibrating string. * A team led by

John Backus John Warner Backus (December 3, 1924 – March 17, 2007) was an American computer scientist. He directed the team that invented and implemented FORTRAN, the first widely used high-level programming language, and was the inventor of the Back ...

develops the FORTRAN compiler and programming language at IBM's research centre in

San Jose, California San Jose, officially San José (; ; ), is a major city in the U.S. state of California that is the cultural, financial, and political center of Silicon Valley and largest city in Northern California by both population and area. With a 2020 popul ...

. This sped the adoption of scientific programming,National Medal of Science citation: 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 The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

" by Ray Clough to describe the earlier methods of

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

Alexander Hrennikoff Alexander Pavlovich Hrennikoff (russian: Александр Павлович Хренников; 11 November 1896 — 31 December 1984) was a Russian-Canadian structural engineer, a founder of the Finite Element Method. Biography Alexander was b ...

and

Olgierd Zienkiewicz Olgierd Cecil Zienkiewicz (18 May 1921 – 2 January 2009) was a British academic of Polish descent, mathematician, and civil engineer. He was born in Caterham, England. He was one of the early pioneers of the finite element method. Since ...

structural analysis Structural analysis is a branch of Solid Mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and thei ...

. * 1961 –

John G.F. Francis John G.F. Francis (born 1934) is an English computer scientist, who in 1961 published the QR algorithm for computing the eigenvalues and eigenvectors of matrices, which has been named as one of the ten most important algorithms of the twentieth ...

and Vera Kublanovskaya invent

QR factorization In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix ''A'' into a product ''A'' = ''QR'' of an orthogonal matrix ''Q'' and an upper triangular matrix ''R''. QR decomp ...

(voted one of the top 10 algorithms of the 20th century). * 1963 –

Edward Lorenz Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and me ...

discovers the butterfly effect on a computer, attracting interest in

chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...

. * 1961 – Using computational investigations of the

3-body problem In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...

, Michael Minovitch formulates the

gravity assist In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the p ...

method. * 1964 – Molecular dynamics invented independently by

Aneesur Rahman Aneesur Rahman (24 August 1927 – 6 June 1987) pioneered the application of computational methods to physical systems. His 1964 paper on liquid argon studied a system of 864 argon atoms on a CDC 3600 computer, using a Lennard-Jones potential ...

. * 1965 –

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...

developed by James W. Cooley and

John W. Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribut ...

. * 1964 –

Walter Kohn Walter Kohn (; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998. The award recognized their contributions to the unde ...

, with

Lu Jeu Sham Lu Jeu Sham (Chinese: 沈呂九) (born April 28, 1938) is an American physicist. He is best known for his work with Walter Kohn on the Kohn–Sham equations. Biography Lu Jeu Sham's family was from Fuzhou, Fujian, but he was born in British Hong ...

and

Pierre Hohenberg Pierre C. Hohenberg (3 October 1934 – 15 December 2017) was a French-American theoretical physicist, who worked primarily on statistical mechanics. Hohenberg studied at Harvard, where he earned his bachelor's degree in 1956 and a master's degr ...

, instigates the development of

density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...

, for which he shares the 1998 Nobel Chemistry Prize with

John Pople Sir John Anthony Pople (31 October 1925 – 15 March 2004) was a British theoretical chemist who was awarded the Nobel Prize in Chemistry with Walter Kohn in 1998 for his development of computational methods in quantum chemistry. Early ...

. This contribution is arguably the earliest work to which Nobels were given for a computer program or computational technique. * First regression calculations in economics.

1970s

* 1975 – Benoit Mandelbrot coins the term "

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...

" to describe the

self-similarity __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...

found in the Fatou,

Julia Julia is usually a feminine given name. It is a Latinate feminine form of the name Julio and Julius. (For further details on etymology, see the Wiktionary entry "Julius".) The given name ''Julia'' had been in use throughout Late Antiquity (e.g ...

and

Mandelbrot set The Mandelbrot set () is the set of complex numbers c for which the function f_c(z)=z^2+c does not diverge to infinity when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc., remains bounded in absolute value. This ...

s. Fractals become the first

mathematical visualization Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it ...

tool extensively explored with computing. * 1977 –

Kenneth Appel Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana–Champaign, solved one of the most famous problems in mathematics, the four-c ...

and

Wolfgang Haken Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds. Biography Haken was born in Berlin, Germany. His father was Werner Haken, a physicist who had Max ...

prove the

four colour theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...

, the first theorem to be proved by computer.

1980s

Fast multipole method __NOTOC__ The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the ''n''-body problem. It does this by expanding the system Green's function using a multipole expansion, ...

(voted one of the top 10

of the 20th century) invented by Vladimir Rokhlin and

Leslie Greengard Dr. Leslie F. Greengard is an American mathematician, physicist and computer scientist. He is co-inventor with Vladimir Rokhlin Jr. of the fast multipole method (FMM) in 1987, recognized as one of the top-ten algorithms of the 20th century. Gree ...

. *

Car–Parrinello molecular dynamics Car–Parrinello molecular dynamics or CPMD refers to either a method used in molecular dynamics (also known as the Car–Parrinello method) or the computational chemistry software package used to implement this method. The CPMD method is one of th ...

developed by

Roberto Car Roberto Car (born 3 January 1947 in Trieste) is an Italian physicist and the Ralph W. Dornte *31 Professor in Chemistry at Princeton University, where he is also a faculty member in the Princeton Institute for the Science and Technology of Materia ...

and

Michele Parrinello Michele Parrinello (born 7 September 1945, Messina) is an Italian physicist particularly known for his work in molecular dynamics (the computer simulation of physical movements of atoms and molecules). Parrinello and Roberto Car were awarded the ...

1990s

* 1990 – In computational genomics and

sequence analysis In bioinformatics, sequence analysis is the process of subjecting a DNA, RNA or peptide sequence to any of a wide range of analytical methods to understand its features, function, structure, or evolution. Methodologies used include sequence alig ...

, the

Human Genome Project The Human Genome Project (HGP) was an international scientific research project with the goal of determining the base pairs that make up human DNA, and of identifying, mapping and sequencing all of the genes of the human genome from both a ...

, an endeavour to sequence the entire

human genome The human genome is a complete set of nucleic acid sequences for humans, encoded as DNA within the 23 chromosome pairs in cell nuclei and in a small DNA molecule found within individual mitochondria. These are usually treated separately as the n ...

, begins. * 1998 –

Kepler conjecture The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling s ...

is almost all but certainly proved algorithmically by Thomas Hales. * The appearance of the first research grids using

volunteer computing Volunteer computing is a type of distributed computing in which people donate their computers' unused resources to a research-oriented project, and sometimes in exchange for credit points. The fundamental idea behind it is that a modern desktop co ...

–

GIMPS The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client and ...

(1996), distributed.net (1997) and Seti@Home (1999).

2000s

* 2000 – The

completes a rough draft of

. * 2003 – The

completed. * 2002 – The

BOINC The Berkeley Open Infrastructure for Network Computing (BOINC, pronounced – rhymes with "oink") is an open-source middleware system for volunteer computing (a type of distributed computing). Developed originally to support SETI@home, it beca ...

architecture is launched in 2002.

2010s

Foldit Foldit is an online puzzle video game about protein folding. It is part of an experimental research project developed by the University of Washington, Center for Game Science, in collaboration with the UW Department of Biochemistry. The objective ...

players solve virus structure, one of the first cases of a game solving a scientific question. ----

References

External links

* SIAM (Society for Industrial and Applied Mathematics) News
Top 10 Algorithms of the 20th Century

The History of Numerical Analysis and Scientific Computing @ SIAM (Society for Industrial and Applied Mathematics)
* * *IEEE Milestones {{Subject bar, portal1=Science, portal3=Mathematics Computational science s s