In his doctorate the 22-year-old Carl Friedrich Gauss, subsequently recognized as one of the most brilliant of mathematicians, proves the fundamental theorem of algebra

English mathematician Charles Babbage builds a sophisticated calculating machine, which he calls a 'difference engine'

English mathematician George Boole describes Boolean algebra in his pamphlet Mathematical Analysis of Logic

Georg Cantor lays the foundations of set theory with his paper On a Characteristic Property of All Real Algebraic Numbers

German mathematician Gottlob Frege publishes Grundlagen der Arithmetik ('Foundations of Arithmetic'), linking mathematics and logic

Alfred North Whitehead and Bertrand Russell complete a work of mathematical logic, Principia Mathematica

Wolfgang Pauli announces his mathematical proof of the existence of the particle subsequently known as the neutrino

Alan Turing publishes a paper introducing the computability theory as a branch of mathematical logic

John von Neumann establishes game theory as a mathematical discipline with his book Theory of Games and Economic Behaviour

British mathematician Andrew Wiles publishes, in Annals of Mathematics, his proof of Fermat's Last Theorem

Thomas Hales proves the Kepler Conjecture, named after the astronomer who first put it forward in his 1611 paper On the six-cornered snowflake

Yasumasa Kanada sets his 11th world record in calculating the number of digits in the decimal expansion of Π, reaching 1.2411 trillion