4 ms·

> The Jacobian Conjecture Interestingly, Yitang Zhang of the twin-prime-conjecture fame spent 7 years working on the Jacobian conjecture under the advisor Tzuo

> The Jacobian Conjecture Interestingly, Yitang Zhang of the twin-prime-conjecture fame spent 7 years working on the Jacobian conjecture under the advisor Tzuong-Tsieng Moh at Purdue. A key step in his thesis used a corollary of Moh's. It turned out that the corollary was incorrect. As a result, Moh refused to write any recommendation letter for Zhang, and Zhang couldn't find any teaching or research job and ended up spending years working at a Subway[1]. Imagine Zhag had ChatGPT in 1986 when he started working on the Jacobian Conjecture. [1] Of course now this has become an inspiring story. That said, the story definitely invokes complex emotions. The best way to describe it is probably this Chinese poem, which I have no idea how to translate: 庾信平生最萧瑟，暮年诗赋动江关

derbOac 3mo ago
Inspiring? Because of the twin prime conjecture success following his time in the wilderness? I suppose so. I'm tired of tales like this in academics though. That's not a criticism of you for telling the tale, I'm just so tired of this kind of thing in academics in general. So, so, so much politics and public reputation management. Zhang should have never had to suffer like that. As my own research has drifted more into math, I've been surprised at how many assertions in the literature turn out to be false. Not just false, but propagated into the applied literature extensively, and even when you point out the problems a lot of defensiveness and denial about it along the lines of Zhang's story. I agree about wondering what would have happened if LLMs had been around in 1986. My guess is the outcome would have been the same for the same reasons? My experience with LLMs in proofs is they can be very helpful, but also very wrong. It's like having another person with another set of hunches about what path to go down.
- hintymad 3mo ago
  > So, so, so much politics and public reputation management. Zhang should have never had to suffer like that. Very true. Unfortunately, when there are people, there will be politics. I remember when reading Yau's autobiography, I kept marvel how much calculation, or "politics" if you will, that Yau mentioned or implied in the book. > My guess is the outcome would have been the same for the same reasons? At least Zhang didn't have to spend 7 years working on the Jacobian conjecture. He said in an interview that he always wanted to work on number theory. Moh asked him to work on Jacobian, and he obliged.
- somenameforme 3mo ago
  Planck's Principle: 'Science advances one funeral at a time.' [1] In his exact words: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it... An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarized with the ideas from the beginning: another instance of the fact that the future lies with the youth." And he said that having lived, as a outsized figure, through the late 19th to mid 20th century of physics, which was the absolute golden age for such. [1] - https://en.wikipedia.org/wiki/Planck's_principle https://en.wikipedia.org/wiki/Planck's_principle
  - bluGill 3mo ago
    The more important lesson for those of us are are "old" is to not get stuck in things that were learned in the past when they are found false. If you are not yet old, remember this - it is very likely you will old in a few years.
    - somenameforme 3mo ago
      It's more nuanced because many things are never really found false, or can't realistically be falsified. Planck was implicitly referencing the whole controversy over quantum mechanics, and how exactly to interpret it. None other than Einstein refused, all the way to his death, to accept a probabilistic interpretation in spite of all evidence pointing in that direction. He simply believed on a fundamental level that the universe must be deterministic. Many don't understand that many of his famous quotes like 'spooky action at a distance' or 'god doesn't play dice' were mocking probabilistic interpretations of quantum mechanics, like the Copenhagen Model - the one we still assume to this very day. Of course there even remains the possibility that at some point in the future he may even be proven correct. And at this point I'm playing into the very same mindset that essentially explains where Planck's Principle comes from, but perhaps such being a part of humanity is not an entirely bad thing. It's certainly been with us even as mankind has gone through unprecedented leaps of understanding and technological advancement.
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.
OG_BME 3mo ago
ChatGPT's idiomatic translation of the poem: Yu Xin’s was a life of utter desolation; in old age, his poems and rhapsodies stirred the riverlands.
- Eufrat 3mo ago
  I guess that works, it is always difficult to capture the cultural and linguistic melancholy of such poetry.
- zahlman 3mo ago
  Yu Xin's past was exquisitely tragic Ages passed; now his works betray magic
  - dash2 3mo ago
    I think the feminine rhyme sounds unintentionally comic.
- acchow 3mo ago
  Opus: No life ran more bleak and desolate than Yu Xin's — yet in his twilight years, his verses stirred the rivers and the passes.

derbOac 3mo ago

Inspiring? Because of the twin prime conjecture success following his time in the wilderness? I suppose so. I'm tired of tales like this in academics though. That's not a criticism of you for telling the tale, I'm just so tired of this kind of thing in academics in general. So, so, so much politics and public reputation management. Zhang should have never had to suffer like that. As my own research has drifted more into math, I've been surprised at how many assertions in the literature turn out to be false. Not just false, but propagated into the applied literature extensively, and even when you point out the problems a lot of defensiveness and denial about it along the lines of Zhang's story. I agree about wondering what would have happened if LLMs had been around in 1986. My guess is the outcome would have been the same for the same reasons? My experience with LLMs in proofs is they can be very helpful, but also very wrong. It's like having another person with another set of hunches about what path to go down.

hintymad 3mo ago
> So, so, so much politics and public reputation management. Zhang should have never had to suffer like that. Very true. Unfortunately, when there are people, there will be politics. I remember when reading Yau's autobiography, I kept marvel how much calculation, or "politics" if you will, that Yau mentioned or implied in the book. > My guess is the outcome would have been the same for the same reasons? At least Zhang didn't have to spend 7 years working on the Jacobian conjecture. He said in an interview that he always wanted to work on number theory. Moh asked him to work on Jacobian, and he obliged.
somenameforme 3mo ago
Planck's Principle: 'Science advances one funeral at a time.' [1] In his exact words: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it... An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarized with the ideas from the beginning: another instance of the fact that the future lies with the youth." And he said that having lived, as a outsized figure, through the late 19th to mid 20th century of physics, which was the absolute golden age for such. [1] - https://en.wikipedia.org/wiki/Planck's_principle https://en.wikipedia.org/wiki/Planck's_principle
- bluGill 3mo ago
  The more important lesson for those of us are are "old" is to not get stuck in things that were learned in the past when they are found false. If you are not yet old, remember this - it is very likely you will old in a few years.
  - somenameforme 3mo ago
    It's more nuanced because many things are never really found false, or can't realistically be falsified. Planck was implicitly referencing the whole controversy over quantum mechanics, and how exactly to interpret it. None other than Einstein refused, all the way to his death, to accept a probabilistic interpretation in spite of all evidence pointing in that direction. He simply believed on a fundamental level that the universe must be deterministic. Many don't understand that many of his famous quotes like 'spooky action at a distance' or 'god doesn't play dice' were mocking probabilistic interpretations of quantum mechanics, like the Copenhagen Model - the one we still assume to this very day. Of course there even remains the possibility that at some point in the future he may even be proven correct. And at this point I'm playing into the very same mindset that essentially explains where Planck's Principle comes from, but perhaps such being a part of humanity is not an entirely bad thing. It's certainly been with us even as mankind has gone through unprecedented leaps of understanding and technological advancement.

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.

OG_BME 3mo ago

ChatGPT's idiomatic translation of the poem: Yu Xin’s was a life of utter desolation; in old age, his poems and rhapsodies stirred the riverlands.

Eufrat 3mo ago
I guess that works, it is always difficult to capture the cultural and linguistic melancholy of such poetry.
zahlman 3mo ago
Yu Xin's past was exquisitely tragic Ages passed; now his works betray magic
- dash2 3mo ago
  I think the feminine rhyme sounds unintentionally comic.
acchow 3mo ago
Opus: No life ran more bleak and desolate than Yu Xin's — yet in his twilight years, his verses stirred the rivers and the passes.