The following is a timeline of scientific computing, also known as computational science. Before modern computers 18th century Simpson rediscovers Simpson's rule, a century after Johannes Kepler (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. Lovelace's note G on the Analytical Engine (1842) describes an algorithm for generating Bernoulli numbers. It is considered the first algorithm ever specifically tailored for implementation on a computer, and thus the first-ever computer programme. 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’s work followed by Martin Kutta 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 introduced. 1920s 1922 – Lewis Fry Richardson introduces numerical weather forecasting by manual calculation, using methods originally developed by Vilhelm Bjerknes as early as 1895. 1926 – Grete Hermann publishes foundational paper for computer algebra, which established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. 1926 Adams-Moulton method. 1927 – Douglas Hartree creates what is later known as the Hartree–Fock method, the first ab initio quantum chemistry methods. 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) develop statistical algorithms based on Comte de Buffon's work, that would later become the foundation of the Monte Carlo method. See also FERMIAC. Shannon explains how to use electric circuits to do Boolean algebra in "A Symbolic Analysis of Relay and Switching Circuits" John