Comment on Open Thread: August 2009

Richard_Kennaway
Tue, 04 Aug 2009 08:40:39 GMT

While mathematics certainly appears to me to be more of a meritocracy than the sciences, it's still the case that the notion of proof has changed over time -- and continues to change (witness Coq and friends) --, as have standards of rigor and what counts as mathematics.

The gold standard of what is a proof and what is not was achieved with the first-order predicate calculus a century ago and has not changed since. Leibniz' dream has been realised in this area. However, no-one troubles to explicitly use the perfect language of mathematical proof and nothing else, except when the act of doing so is the point. It is enough to be able to speak it, and thereafter to use its idioms to the extent necessary to clearly communicate one's ideas.

On the other hand, what proofs or theorems mathematicians find important or interesting will always be changing.

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