About once in a century the world produces a mathematics genius who blazes new trails. The Frenchman Galois was one of them; Euler, Gauss, Cantor, Gödel, a few others. John Horton Conway, inventor of the famous Game of Life, may be one.

1) They are always men (Hypatia, a 5th century Greek woman. may have been one; there have been no other qualifying women in modern times).

2) They all do their best work before the age of twenty.

These are not just brilliant mathematicians, they are off the scale. They're far too rare to draw any statistically valid conclusions from.