Mike Shulman on why mathematics doesn't collapse when there are wrong proof and theorems out there https://mathoverflow.net/a/338620/4177 with nice examples from recent history.
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Replying to @HigherGeometer
Yes, all is fine until you get a whole subfield built on wobbly foundations, and no one knows what's true and what's not. See: (especially
) algebraic geometry pre Zariski/Weil/Grothendieck. Intuition is essential but rigour is also necessary.4 replies 0 retweets 18 likes -
Replying to @HigherGeometer @BarbaraFantechi
This, as Mumford has stressed, is a delicate issue. Even when the foundations are wobbly, almost invariably someone knows what's true and what's not. The Italian algebraic geometers were a mixed bag, but the best of them had uncanny insight, which not even Grothendieck eclipsed.
9:21 AM - 19 Aug 2019
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