Vegetarian mystical leader and number-obsessive, he owes his standing
as the most famous name in maths due to a theorem about right-angled
triangles, although it now appears it probably predated him. He lived in
a community where numbers were venerated as much for their spiritual
qualities as for their mathematical ones. His elevation of numbers as
the essence of the world made him the towering primogenitor of Greek
mathematics, essentially the beginning of mathematics as we know it now.
And, famously, he didn't eat beans.

Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis Women are under-represented in mathematics, yet the history of the
subject is not exclusively male. Hypatia was a scholar at the library in
Alexandria in the 4th century CE. Her most valuable scientific legacy
was her edited version of Euclid's

*The Elements*, the most
important Greek mathematical text, and one of the standard versions for
centuries after her particularly horrific death: she was murdered by a
Christian mob who stripped her naked, peeled away her flesh with broken
pottery and ripped apart her limbs.

Girolamo Cardano

**(1501 -1576)**Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty Italian polymath for whom the term Renaissance man could have been
invented. A doctor by profession, he was the author of 131 books. He was
also a compulsive gambler. It was this last habit that led him to the
first scientific analysis of probability. He realised he could win more
on the dicing table if he expressed the likelihood of chance events
using numbers. This was a revolutionary idea, and it led to probability
theory, which in turn led to the birth of statistics, marketing, the
insurance industry and the weather forecast.

Leonhard Euler

**(1707- 1783)**Leonhard Euler (1707-1783). Photograph: Science and Society Picture Library The most prolific mathematician of all time, publishing close to 900
books. When he went blind in his late 50s his productivity in many areas
increased. His famous formula

*ei*π + 1 = 0, where

*e* is the mathematical constant sometimes known as Euler's number and

*i*
is the square root of minus one, is widely considered the most
beautiful in mathematics. He later took an interest in Latin squares –
grids where each row and column contains each member of a set of numbers
or objects once. Without this work, we might not have had sudoku.

Carl Friedrich Gauss

**(1777-1855)** Carl Friedrich Gauss (1777-1855). Photograph: Bettmann/CORBIS Known as the prince of mathematicians, Gauss made significant
contributions to most fields of 19th century mathematics. 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.

Georg Cantor

**(1845-1918)**Georg Ferdinand Cantor (1845-1918), German mathematician. Photograph: © Corbis 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

Paul Erdös

**(1913-1996)** Paul Erdos (1913-96). Public Domain 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 1,500
papers, with 511 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.

John Horton Conway

**(b1937)** John Horton Conway. Public Domain The Liverpudlian is best known for the serious maths that has come
from his analyses of games and puzzles. In 1970, 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.

Grigori Perelman

**(b1966)** Russian mathematician Grigory Perelman. Photograph: © EPA/Corbis Perelman was awarded $1m last month for proving one of the most
famous open questions in maths, the Poincaré Conjecture. But the Russian
recluse has refused to accept the cash. He had already turned down
maths' most prestigious honour, the Fields Medal in 2006. "If the proof
is correct then no other recognition is needed," he reportedly said. The
Poincaré Conjecture was first stated in 1904 by Henri Poincaré and
concerns the behaviour of shapes in three dimensions. Perelman is
currently unemployed and lives a frugal life with his mother in St
Petersburg.

Terry Tao

**(b1975)** Terry Tao. Photograph: Reed Hutchinson/UCLA An Australian of Chinese heritage who lives in the US, Tao also won
(and accepted) the Fields Medal in 2006. Together with Ben Green, he
proved an amazing result about prime numbers – that you can find
sequences of primes of any length in which every number in the sequence
is a fixed distance apart. For example, the sequence 3, 7, 11 has three
primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that
are 6 apart. While sequences like this of any length exist, no one has
found one of more than 25 primes, since the primes by then are more than
18 digits long.

Alex Bellos is the author of Alex's Adventures in Numberland