RichardKennaway comments on Open Thread: August 2009 - Less Wrong

5 Post author: taw 01 August 2009 03:06PM

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Comment author: anonym 04 August 2009 06:26:22AM 0 points [-]

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. There are social and other non-mathematical reasons that influence how and why some ideas are accepted while others are rejected only to be accepted later, and vice versa.

It's an interesting question whether this will always be the case or if it will converge on something approaching unanimously accepted truth and aesthetic criteria. Personally, I think mathematics is intrinsically an artistic endeavor and that the aesthetic aspect of it will never disappear. And where there is aesthetics, there is also politics and other sausage-making activities...

Comment author: RichardKennaway 04 August 2009 08:40:39AM *  0 points [-]

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.