Formal proof is a notion developed in the early part of the 20th century by logicians such as Bertrand Russell and Gottlob Frege, along with mathematicians such as David Hilbert (who can fairly be described as the father of modern mathematics) and Nicolas Bourbaki, the pseudonym of a group of French mathematicians who sought to place all of mathematics on a rigorous footing.
ECONOMIST: Just what does it mean to prove something?