korrents

korrents · Dwarkesh Podcast

Grant Sanderson (@3blue1brown) – AI disproved a famous math conjecture. Now what?

Grant Sanderson · 1h 33m · youtube.com ↗

23 korrents from this recording

1h
Grant Sanderson did not write this page.

Every claim below is a statement made in this recording, quoted word for word and linked to the second it was said, so you can hear it rather than take our word for it. The wording comes from the transcript published alongside the recording; the sentence above each quote is our reading of the claim, not their wording.

  1. 0:06:54 · watch on youtube.com↗

    Our reading

    If AI can build the new theory that crystallises how to think about a subject, it would be surprising if that capability did not spill into the rest of the economy.

    Their wordsthat like if it's capable of building mountains uh that are, you know, the correct new theory that like crystallizes how we should be thinking about a subject, that's just such a level of intelligence that then it starts to feel like it would be surprising if that didn't permeate into other aspects of the economy besides like just the mountain building for math itself.
    Interesting
  2. 4 min later

  3. 0:11:05 · watch on youtube.com↗

    Our reading

    AI learning to generate good conjectures will never show up as a benchmark being knocked down; it will show up as a shift in how mathematicians talk about the tools.

    Their wordsI think the way that you'd measure conjecture generating ability is going to be more subjective on like that tone shift where um it'll be mathematicians saying they're not just using it to like solve their problems, but as they step back and decide what their research field should even be that a conversation with such and such model like was genuinely helpful for that.
    Interesting
  4. 3 min later

  5. 0:14:26 · watch on youtube.com↗

    Our reading

    Group theory took a hundred years to travel from one man's hunch to something the mathematical community agreed was good, passing through many heads on the way.

    Their wordswhat makes the GAWA theory such an interesting example is you have um literally this 100-year segment of like an idea that like flows through many different people's heads before it like settles into something that the math community like agrees is good.
    Interesting
  6. 10 min later

  7. 0:24:12 · watch on youtube.com↗

    Our reading

    To reward the instinct that a new idea is worth having, training would have to score the smallness of the concepts a solution needs, not just whether it solved the problem.

    Their wordsUh but I don't think it's easy but I do think it's something you would have to do in order to uh reward the gawwa like instinct rather than just rewarding have you solved a problem.
    Interesting
  8. 9 min later

  9. 0:32:52 · watch on youtube.com↗

    Our reading

    A proof and an explanation are different things, and a theorem can stay an unsolved expository problem long after it is proved.

    Their wordsUm even if it's proven just like there is a difference between proof and explanation.
    Interesting
  10. 1 min later

  11. 0:33:59 · watch on youtube.com↗

    Our reading

    The people who come up with genuinely novel insights are also unusually clear communicators of them, against the assumption that expertise spoils explanation.

    Their wordsOne is it seems like there's a really strong correlation between the people who come up with genuinely novel insights and also who are actually quite clear in their communication of it.
    Interesting
  12. 1 min later

  13. 0:35:02 · watch on youtube.com↗

    Our reading

    He used to think explaining AI's results would be the mathematician's remaining job; he now expects AI to explain better than most humans, so that is not what is left.

    Their wordsI kind of suspect that actually they'll also be like quite good at doing that and probably just like better than most humans are at like doing the explanation half and distilling half and that's actually not what's left for the mathematicians is like digesting and and explaining what was going on.
    Interesting
  14. 2 min later

  15. 0:36:50 · watch on youtube.com↗

    Our reading

    Even if AI curates better, people will still want a human curator they have a relationship with, because wanting to learn something is a social phenomenon.

    Their wordsI think we would always still prefer like a human that we had a relationship with because the way that we get motivated to be interesting interested in things is a social phenomenon.
    Interesting

  17. 0:37:17 · watch on youtube.com↗

    Our reading

    The mathematician's role will shift towards curation — deciding which ideas are worth displaying — rather than proving or explaining.

    Their wordsSo my role and arguably that of like other mathematicians might actually just shift subtly into that curation direction of what ideas are are worth displaying.
    Interesting
  18. 4 min later

  19. 0:41:17 · watch on youtube.com↗

    Our reading

    Most of the useful mathematics AI produces over the next five years will be filling in connections that only somebody expert in several fields could draw.

    Their wordsbut that's my guess on what most of the useful progress uh from these models will look like like in the next five years is just really filling in that landscape of like connections that you can draw if you're an expert in multiple fields.
    Interesting
  20. 7 min later

  21. 0:48:12 · watch on youtube.com↗

    Our reading

    The advantage of digital minds may be the opposite of pooling knowledge: deliberately giving agents different contexts, which is a control humans do not have over themselves.

    Their wordsYou could imagine systematizing that or like having multiple different agents deliberately given different pieces of context and try to like compare and contrast there. Like we we don't have the same level of manipulation on our own context.
    Interesting
  22. 4 min later

  23. 0:52:03 · watch on youtube.com↗

    Our reading

    There is no correct heuristic for science, so what you need is many independent research programmes each running its own bias.

    Their wordsWhich actually goes to show you that you there's not a correct huristic for science. You actually just need multiple independent research programs with their own huristics.
    Interesting
  24. 7 min later

  25. 0:59:16 · watch on youtube.com↗

    Our reading

    Mathematics alone can be left running: point a prover at a formal library, walk away for ten years, and there will be something there when you come back.

    Their wordsThat's a very unique thing that math has that nothing else has where you could press go and then just like just just poor compute at it and like look away for 10 years and then come back and say like what do you have and there's there's going to be something, right?
    Interesting
  26. 6 min later

  27. 1:05:41 · watch on youtube.com↗

    Our reading

    A stream of AI-written papers with any error rate at all becomes insufferable, because finding the error costs more than the paper is worth even at ninety-nine percent.

    Their wordsIt becomes insufferable like as a mathematician because you you would basically be like I'm every single time I see one of these I kind of don't know if it's worth my time even if 99 out of 100 of them are right.
    Interesting

  29. 1:06:02 · watch on youtube.com↗

    Our reading

    Formalisation's real gift is the green check mark — knowing a hard proof is correct before you spend time on it — and every other field would kill for it.

    Their wordsAnd so having anything that's able to give you that green check mark that says even if this is going to be complicated to understand, even if it's going to be a pain, you at the very least know it is correct. Like every other field would kill for that, right?
    Interesting

  31. 1:06:27 · watch on youtube.com↗

    Our reading

    Lean is overrated as the reinforcement-learning environment behind recent AI progress in mathematics, but it should not be written out of the story.

    Their wordsAnd so I think you are right that lean is maybe overrated on the side of the importance of it being used as a VR environment for any kind of like just progress in math generally. But I I I definitely wouldn't write it out of the story.
    Interesting
  32. 4 min later

  33. 1:10:05 · watch on youtube.com↗

    Our reading

    Writing well means knowing the exact moment to be unpredictable, which is not the same as raising the temperature.

    Their wordslike when you're writing you sort of you sort of know in order for it to be good, you have to have an element of the unpredictable. And it's it's not just like increasing temperature in your mind or something, right? It's like knowing exactly the correct point when you want to make an unpredictable move.
    Interesting
  34. 7 min later

  35. 1:16:47 · watch on youtube.com↗

    Our reading

    In choosing what to learn, who is teaching it matters more than what it is, because your existing interests are fairly arbitrary and a good educator is not.

    Their wordsI feel like a relevant insight in learning was um recognizing that like who matters more than what. So, like advice to any college student when they're choosing what courses to take. Uh, care a little bit less about your pre-existing interests because they're kind of arbitrary right now. and care a little bit more about whether like the person teaching it is a good educator and someone you resonate with.
    Interesting

  37. 1:17:15 · watch on youtube.com↗

    Our reading

    After a book you loved, read that author's other books rather than another book on the same subject.

    Their wordsSo if there's a book you've liked before, read what else that author has written rather than reading another thing on that subject.
    Interesting
  38. 1 min later

  39. 1:17:56 · watch on youtube.com↗

    Our reading

    Good exposition is willing to say things that are a little bit wrong and fix them later, which is exactly what a crowd-sourced encyclopedia edits out.

    Their wordsAnd I think a good exposition you care a little bit less about like correctness on the way, but you can like deliberately craft things that are a little bit wrong that you correct along the way that gets like edited out in a crowd source environment.
    Interesting
  40. 1 min later

  41. 1:19:19 · watch on youtube.com↗

    Our reading

    The best use of an LLM for learning is as a souped-up search engine that points you at the right human-written resource.

    Their wordsSo in that sense basically using it like a very souped-up version of Google on like zero in on the right human written resource.
    Interesting
  42. 8 min later

  43. 1:27:39 · watch on youtube.com↗

    Our reading

    Anyone choosing a career should work out where the money comes from and what value they add; asking the question at all puts you ahead of your peers.

    Their wordsKnow where the money is coming from. Know where you plug into that. And like if you're just asking those questions, you're actually already like steps ahead of all of the other like fledgling perspective mathematicians.
    Interesting
  44. 4 min later

  45. 1:32:01 · watch on youtube.com↗

    Our reading

    It would be disappointing and surprising if the next five years of AI progress in mathematics produced no economically valuable improvements traceable to it.

    Their wordsbut it would be a little bit disappointing and a little bit surprising if there weren't over the next 5 years like, uh, economically valuable improvements that were made that were directly like referable to the like AI progress in math.
    Interesting