History of Mathematics

Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics.

In Babylonia mathematics developed from 2000 BC.

Number problems such as that of the Pythagorean triples (a, b, c) with a^b²=c² were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems. Quadratic equations were also studied and these examples led to a type of numerical algebra.

Geometric problems relating to similar figures, area and volume were also studied and values obtained for π.

The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC.

The major Greek progress in mathematics dated back to 300 BC - 200 AD. After that time mathematics flourished in Islamic countries in Iran, Syria and India, in particular.

From about the 11^th century Adelard of Bath, then later Fibonacci, brought the Islamic mathematics and its knowledge of Greek mathematics back into Europe.

Major progress in mathematics in Europe was made again at the beginning of the 16th century by Pacioli, then Cardan, Tartaglia and Ferrari with the algebraic solution of cubic and quartic equations. Copernicus and Galileo revolutionised the applications of mathematics to the study of the universe.

The 17^th century saw Napier, Briggs and others greatly extended the power of mathematics as a calculatory science with the discovery of logarithms.

Progress towards the calculus continued with Fermat, who, together with Pascal, began the mathematical study of probability.

Newton developed the calculus into a tool to push forward the study of nature. His work contained a wealth of new discoveries showing the interaction between mathematics, physics and astronomy. Newton's theory of gravitation and his theory of light took us into the 18^th century.

The most important mathematician of the 18^th century was Euler who, in addition to work in a wide range of mathematical areas, invented two new branches, namely the calculus of variations and differential geometry.

Toward the end of the 18^th century, Lagrange began to developa rigorous theory of functions and of mechanics.

The 19^th century saw rapid progress in mathematics. Fourier's work on heat was of fundamental importance. In geometry Pibcker produced fundamental work on analytic geometry and Steiner - in synthetic geometry.

Non-Euclidean geometry developed by Lobachevsky and Bolyai led to characterization of geometry by Riemann. Gauss, thought by some to be the greatest mathematician of all time, studied quadratic reciprocity and integer congruence. His work in differential geometry revolutionized the topic. He also contributed in a major way to astronomy and magnetism.

Cauchy, building on the work of Lagrange on functions, began rigorous analysis and began the study of the theory of functions of a complex variable. This work would continue through Weierstrass and Riemann.

Analysis was driven by the requirements of mathematical physics and astronomy. Lie's work on differential equations led to the study of topological groups and differential topology. Maxwell was to revolutionize the application of analysis to mathematical physics. Statistical mechanics was developed by Maxwell, Boltzmann and Gibbs. It led to ergodic theory.

(Adapted from the Internet sites)

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