6 ms·

I was once in a presentation for a math PhD thesis. During the thesis, the evaluator of the thesis noticed a flaw in their proof. The student understood and the

by tchalla 3mo ago

I was once in a presentation for a math PhD thesis. During the thesis, the evaluator of the thesis noticed a flaw in their proof. The student understood and then asked “What now?” The evaluator prof simply shrugged.

simonreiff 3mo ago
That sounds like the worst "exam nightmare" scenario imaginable, but did the student get the PhD in the end?
- abdullahkhalids 3mo ago
  Mistakes in proofs are relatively common, but such a mistake doesn't automatically mean that the proof is entirely wrong. Many times, the mistake is just in the exposition, and can be fixed easily. Other times, the mistake is fixable and the fix is apparent. Perhaps the author forget to treat a relatively trivial edge case. In the first two cases, the student would likely just pass with minor corrections to be submitted soon. Sometimes, of course, the proof is just wrong. That is the dangerous case, which will cause either major corrections or failure.
  - recursivecaveat 3mo ago
    A few months after Andrew Wiles presented the proof for Fermat's last theorem, some mistakes were found that subsequently took him over a year to patch over. Imagine being 12 months into trying to put the pieces back together, after all the years of work and announcing your finding publicly.
    - reinitctxoffset 3mo ago
      I can recommend without reservation the book by Simon Singh, at least for a lay audience (don't know how an expert would experience it). It's understandably the natural place to get the dramatic tension from what at least purports to be a sober account with some momentum. It's reasonably consistent with the way it's treated on the lectures I've seen from Sir Andrew Wiles on YouTube. It sounds like a nightmare. He had intentionally set the proof up in a high stakes way, working in private, very quiet on what he was really doing. I gather this is not the done thing, eccentric at best kind of vibes, and I think by that point it was almost crackpot adjacent to even try seriously. His advisor forcefully pushed him off even trying earlier. So it's compound on the stakes. The beg reveal is intentionally as dramatic as possible. And then the questions start to land, most are minor clarifications, notation deficits, but one is sticky, one won't go away. Kept me up late reading about it.
- angry_octet 3mo ago
  Proof fix-ups are quite common, but if it was not possible, then no, not for that topic.
  - drnick1 3mo ago
    A Ph.D. is usually a collection of papers/chapters, so even if a fatal flaw is found in one of the chapters, it does not normally result in "failing the Ph.D." It just means that that particular paper isn't publishable. The bar for getting a Ph.D. is actually quite low; what is truly difficult is clearing the bar in terms of publications for academic positions and later tenure.
    - angry_octet 3mo ago
      You would have to go back and do more work though, and if you couldn't fix it you would have to do another defence. But yes, it is a different situation to actually getting a good post doc.
  - vintermann 3mo ago
    I guess there's no tradition for publishing "negative results" in mathematics? By that I mean not proof of something negative, but rather, "we tried this thing for ages and couldn't get it to work, but we couldn't prove that it could never work either". Probably there are understandable reasons for that... But I think "negative science" is really important, and soft results like "we tried that for a long time and it wasn't very fruitful" are actually very important for progress even if they're poorly attested in the written record. I guess in mathematics they come informally from your thesis advisor...
    - andoando 3mo ago
      I mean it would be ridiculously easy to make up any number of incorrect proofs. It would have to show something new and interesting.
    - jibal 3mo ago
      There are mathematical statements that have been shown to be undecidable (no proof for or against is possible) and such a demonstration is a huge deal.
angry_octet 3mo ago
A recording of a car crash: discovering on live radio/podcast that the central tenet of your book is wrong, and amateurishly so. Naomi Wolf 'death recorded' on BBC[1], skip to 5:51. After this the book was pulped and she had some sort of psychotic break during COVID and allied with ultra-right and COVID denialist loonies. [1] https://www.bbc.com/news/av/world-us-canada-48639663 https://www.bbc.com/news/av/world-us-canada-48639663
- globnomulous 3mo ago
  This is astonishing. How could a person go to the lengths of writing an entire book without ever looking up this sort of thing?
  - brohee 3mo ago
    The most astonishing thing is that she still holds the PhD whose thesis was the basis of the book. A stain on Oxford reputation.
  - somenameforme 3mo ago
    The term she mistook for meaning a death/execution had been recorded was "death recorded". So it's a mistake that could be made similarly to how one might confidently assume that a "public school" is a school which is a school that is either government funded or open to anybody in the local area. More generally I think people are inappropriately confident in general. When you go through history just about every century prior people believed many things that the next century would come to see as plainly false. People in modern times seemed to have stopped believing this was true, yet it's likely that people during every given century also stopped believing such was true, because what you believe "now" is always assumed to be correct. Nobody wants to believe they hold false beliefs, even though there's a practically 100% certainty that all of us do, and in quite healthy quantities.
    - NooneAtAll3 3mo ago
      ...what is public school then?
CurtMonash 3mo ago
I first heard that kind of story about a thesis defense at Princeton. The twist was that they had been short one person to judge it, so they roped in a professor who was available at that moment ... and he found a counterexample on the fly. The professor was John Milnor.
bananaflag 3mo ago
I personally know a story in this vein with a (sort of) happy ending. A PhD student discovered that a result of his professor would imply the solution to a big conjecture in another field. The people in that field then analyzed the prof's result and found that the proof was flawed. The student was still allowed to graduate based on this since the finding of the connection between fields was brilliant. Then he quit academia (not because of this story, he had planned it before). Then a year later the prof figured out how to fix the flaw in his proof and published a paper with his former student, thus solving the conjecture. The two are still on good terms, writing papers together.
- Xmd5a 3mo ago
  > The two are still on good terms, writing papers together. Why are you framing this like this? Do mathematician take these kind of things personally?
  - bananaflag 3mo ago
    Because I think the median reader would expect this sort of thing to come up at some point in the story.

by tchalla 3mo ago

simonreiff 3mo ago

That sounds like the worst "exam nightmare" scenario imaginable, but did the student get the PhD in the end?

abdullahkhalids 3mo ago
Mistakes in proofs are relatively common, but such a mistake doesn't automatically mean that the proof is entirely wrong. Many times, the mistake is just in the exposition, and can be fixed easily. Other times, the mistake is fixable and the fix is apparent. Perhaps the author forget to treat a relatively trivial edge case. In the first two cases, the student would likely just pass with minor corrections to be submitted soon. Sometimes, of course, the proof is just wrong. That is the dangerous case, which will cause either major corrections or failure.
- recursivecaveat 3mo ago
  A few months after Andrew Wiles presented the proof for Fermat's last theorem, some mistakes were found that subsequently took him over a year to patch over. Imagine being 12 months into trying to put the pieces back together, after all the years of work and announcing your finding publicly.
  - reinitctxoffset 3mo ago
    I can recommend without reservation the book by Simon Singh, at least for a lay audience (don't know how an expert would experience it). It's understandably the natural place to get the dramatic tension from what at least purports to be a sober account with some momentum. It's reasonably consistent with the way it's treated on the lectures I've seen from Sir Andrew Wiles on YouTube. It sounds like a nightmare. He had intentionally set the proof up in a high stakes way, working in private, very quiet on what he was really doing. I gather this is not the done thing, eccentric at best kind of vibes, and I think by that point it was almost crackpot adjacent to even try seriously. His advisor forcefully pushed him off even trying earlier. So it's compound on the stakes. The beg reveal is intentionally as dramatic as possible. And then the questions start to land, most are minor clarifications, notation deficits, but one is sticky, one won't go away. Kept me up late reading about it.
angry_octet 3mo ago
Proof fix-ups are quite common, but if it was not possible, then no, not for that topic.
- drnick1 3mo ago
  A Ph.D. is usually a collection of papers/chapters, so even if a fatal flaw is found in one of the chapters, it does not normally result in "failing the Ph.D." It just means that that particular paper isn't publishable. The bar for getting a Ph.D. is actually quite low; what is truly difficult is clearing the bar in terms of publications for academic positions and later tenure.
  - angry_octet 3mo ago
    You would have to go back and do more work though, and if you couldn't fix it you would have to do another defence. But yes, it is a different situation to actually getting a good post doc.
- vintermann 3mo ago
  I guess there's no tradition for publishing "negative results" in mathematics? By that I mean not proof of something negative, but rather, "we tried this thing for ages and couldn't get it to work, but we couldn't prove that it could never work either". Probably there are understandable reasons for that... But I think "negative science" is really important, and soft results like "we tried that for a long time and it wasn't very fruitful" are actually very important for progress even if they're poorly attested in the written record. I guess in mathematics they come informally from your thesis advisor...
  - andoando 3mo ago
    I mean it would be ridiculously easy to make up any number of incorrect proofs. It would have to show something new and interesting.
  - jibal 3mo ago
    There are mathematical statements that have been shown to be undecidable (no proof for or against is possible) and such a demonstration is a huge deal.

angry_octet 3mo ago

A recording of a car crash: discovering on live radio/podcast that the central tenet of your book is wrong, and amateurishly so. Naomi Wolf 'death recorded' on BBC[1], skip to 5:51. After this the book was pulped and she had some sort of psychotic break during COVID and allied with ultra-right and COVID denialist loonies. [1] https://www.bbc.com/news/av/world-us-canada-48639663 https://www.bbc.com/news/av/world-us-canada-48639663

globnomulous 3mo ago
This is astonishing. How could a person go to the lengths of writing an entire book without ever looking up this sort of thing?
- brohee 3mo ago
  The most astonishing thing is that she still holds the PhD whose thesis was the basis of the book. A stain on Oxford reputation.
- somenameforme 3mo ago
  The term she mistook for meaning a death/execution had been recorded was "death recorded". So it's a mistake that could be made similarly to how one might confidently assume that a "public school" is a school which is a school that is either government funded or open to anybody in the local area. More generally I think people are inappropriately confident in general. When you go through history just about every century prior people believed many things that the next century would come to see as plainly false. People in modern times seemed to have stopped believing this was true, yet it's likely that people during every given century also stopped believing such was true, because what you believe "now" is always assumed to be correct. Nobody wants to believe they hold false beliefs, even though there's a practically 100% certainty that all of us do, and in quite healthy quantities.
  - NooneAtAll3 3mo ago
    ...what is public school then?

CurtMonash 3mo ago

I first heard that kind of story about a thesis defense at Princeton. The twist was that they had been short one person to judge it, so they roped in a professor who was available at that moment ... and he found a counterexample on the fly. The professor was John Milnor.

bananaflag 3mo ago

I personally know a story in this vein with a (sort of) happy ending. A PhD student discovered that a result of his professor would imply the solution to a big conjecture in another field. The people in that field then analyzed the prof's result and found that the proof was flawed. The student was still allowed to graduate based on this since the finding of the connection between fields was brilliant. Then he quit academia (not because of this story, he had planned it before). Then a year later the prof figured out how to fix the flaw in his proof and published a paper with his former student, thus solving the conjecture. The two are still on good terms, writing papers together.

Xmd5a 3mo ago
> The two are still on good terms, writing papers together. Why are you framing this like this? Do mathematician take these kind of things personally?
- bananaflag 3mo ago
  Because I think the median reader would expect this sort of thing to come up at some point in the story.