3 ms·

Given that you seem to know this space, I have been wondering: Was there ever any major flaw in an important mathematical proof that was taken as a given, and s

by hannob 5y ago

Given that you seem to know this space, I have been wondering: Was there ever any major flaw in an important mathematical proof that was taken as a given, and subsequently plenty of papers building on that turned out to be wrong as well? Like I don't mean "this proof has a gap in its justification, but the thing claimed likely is still true". I mean "we thought someone had a proof for X, but actually later someone else showed X isn't true".

Penyngton 5y ago
I'm not sure if this quite matches your request (I suppose much hinges on the word "important"), but here's a story of a fairly famous and long-standing error: https://www.jamesrmeyer.com/ffgit/godel-error-2.html https://www.jamesrmeyer.com/ffgit/godel-error-2.html Personally, I'd say the fact that someone bothered to discover it was false fifty years after it was published shows its importance. The short version is that Gödel claimed in a paper that he had an algorithm to determine satisfiability for a certain logic, but the algorithm actually worked for a slightly different logic instead. People basically took Gödel's word for it for fifty years until a logician called Goldfarb found the mistake. EDIT: As a disclaimer, I don't have any association with or endorsement of the website I've linked to. I found it just now because I needed a source for the story that I've known for many years (I think I first heard it in person, but it's definitely contained in the book `The Classical Decision Problem' by Börger, Grädel and Gurevich). I skimmed the post and it seemed to cover the relevant details, but that's the extent of my knowledge of the site and its contents.
dynrzk 5y ago
Somewhat famously, symplectic geometry had its fair bit of foundational issues.
Sniffnoy 5y ago
This[0] may be a good place to start, but I'm not sure if it contains proper examples of what you say (of serious collapse). E.g., I expect a lot of people probably relied on the false result mentioned by Matheus, but most of them could probably be repaired with the corrected statement. So it seems like this probably hasn't happened? OTOH, there was the Italian school of algebraic geometry, but that was more than one single flaw... [0] https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat...

by hannob 5y ago

Penyngton 5y ago

I'm not sure if this quite matches your request (I suppose much hinges on the word "important"), but here's a story of a fairly famous and long-standing error: https://www.jamesrmeyer.com/ffgit/godel-error-2.html https://www.jamesrmeyer.com/ffgit/godel-error-2.html Personally, I'd say the fact that someone bothered to discover it was false fifty years after it was published shows its importance. The short version is that Gödel claimed in a paper that he had an algorithm to determine satisfiability for a certain logic, but the algorithm actually worked for a slightly different logic instead. People basically took Gödel's word for it for fifty years until a logician called Goldfarb found the mistake. EDIT: As a disclaimer, I don't have any association with or endorsement of the website I've linked to. I found it just now because I needed a source for the story that I've known for many years (I think I first heard it in person, but it's definitely contained in the book `The Classical Decision Problem' by Börger, Grädel and Gurevich). I skimmed the post and it seemed to cover the relevant details, but that's the extent of my knowledge of the site and its contents.

dynrzk 5y ago

Somewhat famously, symplectic geometry had its fair bit of foundational issues.

Sniffnoy 5y ago

This[0] may be a good place to start, but I'm not sure if it contains proper examples of what you say (of serious collapse). E.g., I expect a lot of people probably relied on the false result mentioned by Matheus, but most of them could probably be repaired with the corrected statement. So it seems like this probably hasn't happened? OTOH, there was the Italian school of algebraic geometry, but that was more than one single flaw... [0] https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat...