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An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space that it is mathematically consistent that parallel lines may diverge was found in his notes after his death.

During his analysis of astronomical data, he realised that measurement error produced a bell curve — and that shape is now known as a Gaussian distribution.

Of all the great mathematicians, Cantor most perfectly fulfils the Hollywood stereotype that a genius for maths and mental illness are somehow inextricable.

Cantor's most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others.

The result was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised.

He also became fixated on proving that the works of Shakespeare were in fact written by Francis Bacon. Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel.

He rarely published alone, preferring to collaborate — writing about 1, papers, with collaborators, making him the second-most prolific mathematician after Euler.

As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him; No 2 for those who have authored with mathematicians with an Erdös No 1, and so on.

The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles.

In , he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid.

Early computer scientists adored playing Life, earning Conway star status. He has made important contributions to many branches of pure maths, such as group theory, number theory and geometry and, with collaborators, has also come up with wonderful-sounding concepts like surreal numbers, the grand antiprism and monstrous moonshine.

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