each other?
https://annals.math.princeton.edu/2004/159-2/p03
https://annals.math.princeton.edu/2006/164-3/p10
ljl @ mathematicians, muh rigor
DYK that there are two papers in the Annals of Mathematics that contradict
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Wow, so do we have any idea what proportion of mathematical discoveries are based on shoddy foundations versus reproducible and checkable proofs? And which of the two papers in the OP is currently believed to be true?
http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf slide 6
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http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf slide 6
Kevin Buzzard is making all the noise because he is now deadwood and has stopped producing new mathematics. So he said, some old mathematics might be wrong we need to check it. So he ran LEAN to verify some undegraduate proofs and said THIS IS MATH!
Professor Buzzard, what if your LEAN code has a bug? Is it still math? Who would verify that your code has no bug?
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The more interesting pair of Annals papers is:
https://annals.math.princeton.edu/1994/140-2/p04
https://annals.math.princeton.edu/articles/12527in which the same guy proves both a theorem and its negation.
Anyway, it's well-known to "the experts" that the Tsuji paper mentioned here is wrong. It has not led to the collapse of algebraic geometry.
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The more interesting pair of Annals papers is:
https://annals.math.princeton.edu/1994/140-2/p04
https://annals.math.princeton.edu/articles/12527
in which the same guy proves both a theorem and its negation.
Anyway, it's well-known to "the experts" that the Tsuji paper mentioned here is wrong. It has not led to the collapse of algebraic geometry.Why hasn’t he retracted the earlier result lol?
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The more interesting pair of Annals papers is:
https://annals.math.princeton.edu/1994/140-2/p04
https://annals.math.princeton.edu/articles/12527
in which the same guy proves both a theorem and its negation.
Anyway, it's well-known to "the experts" that the Tsuji paper mentioned here is wrong. It has not led to the collapse of algebraic geometry.There are other papers that are wrong but never got retracted by Annals. A famous example is Daniel Biss' paper. Instead of retraction, they allowed Biss to post a note saying there's an unfixable error in his proof of Theorem XXX so "the theorem remains a conjecture". This is more egregious given that all other papers by Biss, including one in Inventiones, have all been exposed as wrong. Some have been retracted.
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The more interesting pair of Annals papers is:
https://annals.math.princeton.edu/1994/140-2/p04
https://annals.math.princeton.edu/articles/12527
in which the same guy proves both a theorem and its negation.
Anyway, it's well-known to "the experts" that the Tsuji paper mentioned here is wrong. It has not led to the collapse of algebraic geometry.There are other papers that are wrong but never got retracted by Annals. A famous example is Daniel Biss' paper. Instead of retraction, they allowed Biss to post a note saying there's an unfixable error in his proof of Theorem XXX so "the theorem remains a conjecture". This is more egregious given that all other papers by Biss, including one in Inventiones, have all been exposed as wrong. Some have been retracted.
Why did Biss quit math? Was he pushed out or he himself didn't want to continue after his high-profile missteps?
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There are other papers that are wrong but never got retracted by Annals. A famous example is Daniel Biss' paper. Instead of retraction, they allowed Biss to post a note saying there's an unfixable error in his proof of Theorem XXX so "the theorem remains a conjecture". This is more egregious given that all other papers by Biss, including one in Inventiones, have all been exposed as wrong. Some have been retracted.
I know of just one paper that has been formally retracted by Annals, though there are several, such as Biss', that are known to be wrong.
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each other?
https://annals.math.princeton.edu/2004/159-2/p03
https://annals.math.princeton.edu/2006/164-3/p10
ljl @ mathematicians, muh rigorA paper that corrects another paper in the same journal. We used to have those in economics as well until the powers that be decided they didn’t like to demonstrate their fallibility.