One example I would have added is those two lines from a paper published by Annals of mathematicspic.twitter.com/HOOK37pbdi
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One example I would have added is those two lines from a paper published by Annals of mathematicspic.twitter.com/HOOK37pbdi
C'est dommage que cela ne dise rien de la compréhension d'un résultat mathématique... bon courage pour comprendre les idées des futures preuves d'ordi...
How do we understand computer programs?
This is one reason I like working in a field (triangulations of 3-manifolds) with abundant computable examples. The theorem often comes with a computer implementation which has checked the theorem on thousands of examples.
In terms of computer-checkable proofs, how solid do you think the field of pl 3-manifold topology is? A lot of the work in my area relied heavily on very technical theorems from the 60s and 70s that I barely knew existed, and definitely never learned the proofs.
Some degree of bitterness is appropriate. The fast pace of development in arithmetic or derived geometry creates ever smaller inner circles which "know how things work". Gaitsgory-Rozenblyum's work is great; I want to use it, and some people do, but I don't feel confortable.
Wow
I know something of the culture of mathematics, but I didn’t think that the gaps in proofs or the trust-mechanisms in elders were this profound or widespread ...
A number of algorithms published in the literature have been shown to be incorrect (the first out-of-SSA comes to mind, then Shostak's method). I'm told many papers in the scheduling community have flaws. (Not to mention, of course, implementations thereof.)
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