Is Math Right or Left-Wing?
According to Keith Devlin, it's left-wing:
What is a proof? The question has two answers. The right wing (“right-or-wrong”, “rule-of-law”) definition is that a proof is a logically correct argument that establishes the truth of a given statement. The left wing answer (fuzzy, democratic, and human centered) is that a proof is an argument that convinces a typical mathematician of the truth of a given statement.
While valid in an idealistic sense, the right wing definition of a proof has the problem that, except for trivial examples, it is not clear that anyone has ever seen such a thing. The traditional examples of correct proofs that have been presented to students for over two thousand years are the geometric arguments Euclid presents in his classic text Elements, written around 350 B.C. But as Hilbert pointed out in the late 19th century, many of those arguments are logically incorrect. Euclid made repeated use of axioms that he had not stated, without which his arguments are not logically valid.
Toth thinks that this situation will occur more and more often in mathematics. He says it is similar to the situation in experimental science - other scientists acting as referees cannot certify the correctness of an experiment, they can only subject the paper to consistency checks. He thinks that the mathematical community will have to get used to this state of affairs.
When it comes down to it, mathematics, for all that it appears to be the most right wing of disciplines, turns out in practice to be left wing to the core.
Strange. That sounds deregulated to me…