This isn't new! Wrong proofs have appeared in print forever. It is also not ONLY due to privilege: mistakes can be made, and they're usually very hidden. In fact, ArXiV has diminished the number of wrong proofs in print because some get caught at the preprint stage. 4/
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I minded how all examples were about men, yet this wasn't remarked, and how the author describes the original mistake in Wiles' proof as "were found" : brilliant people worked very hard to find the mistake, the system (sometimes?/most of the time?) works. 5/
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There are other methods: we should encourage people, especially young ones, to publish complete proofs of incompletely proved stuff. This has happened in the past (I published a correction to someone's correction to someone's paper) we just need to make it easier. 6/
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Yes, it is bad that "some people know" but we now have plenty of avenues to get out of this. MathOverflow is a good place to startm as are social media of every kind. Again, imperfect but improving. 7/
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Finally, but should have been first "maths that isn't 100% correct is worthless" is an incredibly bad viewpoint. A lot of maths started on wobbly legs, and in fact it's a key part of how maths is the product of a community not individuals. 8/
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There are people who are good at having ideas, people who are good atspotting mistakes, people who are good at fixing proofs, people who are good at writing up clearly. Sometime (rarely) they work together, and you get very good things from the beginning. 9/
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More often they're not, and it takes years, or decades, and papers and people to go from the forst spark to a complete proof which is also readable. Because honestly, unreadable maths doesn't help much either. 10/
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Am I against computer aided proofs? Of course not! I am happy to have a computer help me typeset my papers and check my computations, so I certainly will welcome when I can also get help in checking a proof. 11/
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Replying to @BarbaraFantechi
Rota said that that a proof must provide more insight into the problem being studied, or give more ideas, and that computer aided proofs fail at doing so. What are your thoughts on this?
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Replying to @cynicaldevil_
If I'm stuck on my way to a result I really care about because there is ONE lemma I can't prove* I am really grateful for ANY proof, whether I can understand it or not. 1/ *This happens all the time.
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More people should know that practically all mathematicians, for this very reason, lead lives of quiet desperation. This agonized, unrelenting longing for ANY way out of one's quandary -- any way whatsoever! -- is perhaps the single most recognizable mathematical emotion.
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