The Economist examines what it means to prove something, and how formal logic and computers can be used to replace traditional mathemtical proofs.
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. This effort was subtle, but its upshot can be described simply. It is to replace, in proofs, standard mathematical reasoning which, in essence, relies on hand-waving arguments (it should be obvious to everyone that B follows from A) with formal logic.