Bertrand Russell (1872–1970) was a British philosopher, logician, and professional troublemaker who lived so long he seemed to belong to three centuries at once. He tried to prove that all of mathematics rests on pure logic, won a Nobel Prize in Literature, went to prison for his pacifism, and was still marching against nuclear weapons in his nineties.
Russell's most famous contribution to mathematics is a spanner he threw into the works.
Building on
Russell loved dressing his paradox up as a village puzzle: imagine a barber who shaves everyone who doesn't shave themselves — and no one else. So, does the barber shave himself? If he does, he shouldn't; if he doesn't, he must. The barber can't exist, and neither could the old wide-open notion of a set. Russell then spent a decade with Alfred North Whitehead writing Principia Mathematica, a monumental attempt to derive maths from logic — it takes them hundreds of pages just to prove that 1 + 1 = 2.