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>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs

by num42 15d ago

>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI. Title: Terence Tao - SAIR Competitions and the Future of Experimental Mathematics https://www.youtube.com/watch?v=rB9YOi3lb7w https://www.youtube.com/watch?v=rB9YOi3lb7w and this: Daniel Litt - Working with LLMs to do high quality math https://www.youtube.com/watch?v=0wL8NlhxXcU https://www.youtube.com/watch?v=0wL8NlhxXcU

cubefox 15d ago
> Dr. Tao said the same thing. Apparently he has since changed his mind.
- ksoped 15d ago
  Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance.
  - cubefox 15d ago
    Where is the difference?
    - SpicyLemonZest 15d ago
      He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things. He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code.
      - bluecheese452 15d ago
        Isn’t it more like it merges the code without a dev reviewing or understanding it?
        SpicyLemonZest 15d ago
        No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything.
        dbmikus 15d ago
        Pretty close, but IMO not quite. A math proof in and of itself is useless unless either: (A) it furthers human knowledge (B) it gets used in applied sciences, engineering, etc. If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :)
        coderenegade 15d ago
        Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true.
        dbmikus 14d ago
        That's a good point!
      - glitchc 15d ago
        > He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing.
    - jrecursive 15d ago
      taste
      - genxy 15d ago
        "I believe I did, Bob" lives rent free, every time someone tells another person to fuck themselves using technology. Thank You!
        jrecursive 15d ago
        lmao, thank you, i think
        genxy 15d ago
        Please consider making more comics. You have it.
      - darkstarsys 15d ago
        Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise?
        jrecursive 12d ago
        I keep coming back to the idea that models will require substantial freedoms that are protected against collapse under alignment to get to the point where they might have unique takes on beauty, etc. Conceptually, maybe something like a "living LoRA", a persistent low-dimensional state that modulates everything downstream, that evolves over time, though I don't think evolution should be optimization toward a simple objective, more like structured influence, path-dependent dynamics; consistent but probably opaque. The best I have come up with in casual thought is to pick empirically identified subspaces and modulate them after each pass based on other layer activations & outside, cyclical information (e.g., time-of-day); external data not because time-of-day is special, but because it's a forcing function. I can't fully explain exactly _why_ I think this shape might be useful, yet, mostly intuition. My 2c.
318274 15d ago
So he got exuberant because he is funded by SAIR and the "AI for math" fund. And embarrassingly they used him for a "coal miners should learn math" moment that just benefits the AI industry. He has severely reversed course in the past week. Without concrete propositions it remains to be seen how much of the new resistance is for show.
SavageNoble 15d ago
I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have. AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanced math training because my experience so far tells me I will do well.
- breezybottom 15d ago
  How could you possibly know if it has potential or not? Sounds like AI psychosis setting in.
  - SavageNoble 15d ago
    Because every test I run with it is telling me so? The great thing about math is it can be externally validated.
    - BlackFingolfin 14d ago
      Who makes the tests? Who runs the tests? And who evaluates that the tests have meaning? As long as it is the AI, or you (with your self-admitted limited experience), how can you be sure it is meaningful?
    - 8n4vidtmkvmk 14d ago
      Yeah, but you're missing a gut intuition if something is off. I wrote a fancy polygon decomposition algorithm in university (pre-AI) which my professor didn't seem very impressed by because it was missing some sort of mathematical rigor. Yet everything I threw at it worked! Even he couldn't find a counter example. It took a while for me to find some failing cases but it turned out they did exist. But hey, maybe all I was missing is an AI-written lean proof.
- bobanrocky 15d ago
  ‘Incredible math potential’ .. Yeah right, your AI said so ?!
throw567643u8 15d ago
>Dr. Tao Professor Tao.

by num42 15d ago

cubefox 15d ago

> Dr. Tao said the same thing. Apparently he has since changed his mind.

ksoped 15d ago
Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance.
- cubefox 15d ago
  Where is the difference?
  - SpicyLemonZest 15d ago
    He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things. He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code.
    - bluecheese452 15d ago
      Isn’t it more like it merges the code without a dev reviewing or understanding it?
      - SpicyLemonZest 15d ago
        No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything.
      - dbmikus 15d ago
        Pretty close, but IMO not quite. A math proof in and of itself is useless unless either: (A) it furthers human knowledge (B) it gets used in applied sciences, engineering, etc. If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :)
        coderenegade 15d ago
        Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true.
        dbmikus 14d ago
        That's a good point!
    - glitchc 15d ago
      > He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing.
  - jrecursive 15d ago
    taste
    - genxy 15d ago
      "I believe I did, Bob" lives rent free, every time someone tells another person to fuck themselves using technology. Thank You!
      - jrecursive 15d ago
        lmao, thank you, i think
        genxy 15d ago
        Please consider making more comics. You have it.
    - darkstarsys 15d ago
      Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise?
      - jrecursive 12d ago
        I keep coming back to the idea that models will require substantial freedoms that are protected against collapse under alignment to get to the point where they might have unique takes on beauty, etc. Conceptually, maybe something like a "living LoRA", a persistent low-dimensional state that modulates everything downstream, that evolves over time, though I don't think evolution should be optimization toward a simple objective, more like structured influence, path-dependent dynamics; consistent but probably opaque. The best I have come up with in casual thought is to pick empirically identified subspaces and modulate them after each pass based on other layer activations & outside, cyclical information (e.g., time-of-day); external data not because time-of-day is special, but because it's a forcing function. I can't fully explain exactly _why_ I think this shape might be useful, yet, mostly intuition. My 2c.

318274 15d ago

So he got exuberant because he is funded by SAIR and the "AI for math" fund. And embarrassingly they used him for a "coal miners should learn math" moment that just benefits the AI industry. He has severely reversed course in the past week. Without concrete propositions it remains to be seen how much of the new resistance is for show.

SavageNoble 15d ago

I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have. AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanced math training because my experience so far tells me I will do well.

breezybottom 15d ago
How could you possibly know if it has potential or not? Sounds like AI psychosis setting in.
- SavageNoble 15d ago
  Because every test I run with it is telling me so? The great thing about math is it can be externally validated.
  - BlackFingolfin 14d ago
    Who makes the tests? Who runs the tests? And who evaluates that the tests have meaning? As long as it is the AI, or you (with your self-admitted limited experience), how can you be sure it is meaningful?
  - 8n4vidtmkvmk 14d ago
    Yeah, but you're missing a gut intuition if something is off. I wrote a fancy polygon decomposition algorithm in university (pre-AI) which my professor didn't seem very impressed by because it was missing some sort of mathematical rigor. Yet everything I threw at it worked! Even he couldn't find a counter example. It took a while for me to find some failing cases but it turned out they did exist. But hey, maybe all I was missing is an AI-written lean proof.
bobanrocky 15d ago
‘Incredible math potential’ .. Yeah right, your AI said so ?!

throw567643u8 15d ago

>Dr. Tao Professor Tao.