7 ms·

It seems like making progress on math is letting the AI run fully autonomously for a few days, occasionally asking it to keep going. I'm not sure people need t

It seems like making progress on math is letting the AI run fully autonomously for a few days, occasionally asking it to keep going. I'm not sure people need to organize a mathathon to wait for a computer to give a printout. They mainly need tokens.

charlieyu1 9d ago
Are they actually autonomous? I’d say subject knowledge at the prompt stage plays a large part towards getting proper results
- a2ff6eeb0 9d ago
  When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. And left it for a long time. Jarred isn't a mathematician, he's the maintainer of a janky JavaScript environment. Here's the transcript: https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e9548c3f44f.pdf https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e...
- hgoel 9d ago
  Prompting for some of the results was almost the "Computer, do a breakthrough. Make no mistakes." meme. Just someone telling the model to keep trying a couple of times. Unfortunately we don't actually know what kind of prompting was done for the more prominent results.
  - charlieyu1 9d ago
    It’s definitely not how I work, I’d need to read the model responses and set a direction for the model to go
    - deleted 9d ago
      [deleted]
    - hgoel 9d ago
      Same here, it's one thing if I'm just screwing around, but if I'm trying to do anything serious, I need to at least have a handle on what it's doing, and, when thinking traces are available, keeping track of any logical errors in the model's reasoning.
      - a2ff6eeb0 9d ago
        you know the thinking traces are redacted and summarized using another model, right? The actual thinking trace looks something like: 7♣-removal-IS-the-prerequisite-for-10♠/9♥!!)-⟹-OVERLAP-(ii)+(iv):-{6♠ J♦ 9♥ 2♣}-=-FOUR--—-UNLESS-7♣'s-seat-8♥-...-and-2♣-drains-only-at-crack-:-⟹-2♣-celled-+-9♥-celled-simultaneously-UNAVOIDABLE-in-t8-dig--—-BREAK:-9♥-drains-to-10♠-THE-MOMENT-10♠-is-free:-t8-dig-order:-[K♣→t2]-[2♣→cell]-[7♣→8♥-:-8♥-WHERE:-post-chunk-9♠-:-chunk-⟸-K♣--done-:-ORDER:-K♣→t2,-CHUNK→K♣-(cap-4!!:-cells-then:-{6♠ J♦ 9♥}-FULL--chunk-cap-=-1--—-F-F-F-F-F.-—-chunk-BEFORE-9♥-celling?!-:-9♥-celled-at-t1-dig-⟸-needed-for-5♣-⟸-4♥3♣-⟸-t2-dig-⟸-K♣-seat-⟸-chunk-:-⟹-chunkAFTER-9♥-celling-FORCED--:-chunk-cap-with-{6♠ J♦ 9♥}:-1--—-—-J♦-THE-NEW-CANCER.-—-⟹-J♦-celling-DELAYED-till-after-chunk?! :-J♦'s-celling-was-for-J♥→Q♠-(5♦-access-for-4♣):-DELAY-4♣-resolution:-4♣→CELLearly-(as-always)-then-4♣-cell→5♦-LATER-when-5♦-frees-!!!:-cells-rotation:-4♣-celled-[t2-dig-…-5♦-freed]:-5♦-freed-⟸-J♥→Q♠-⟸-J♦-celled-:-⟹-{6♠, 4♣, J♦}-overlap-window-until-4♣→5♦-drains:-then-{6♠ J♦}+1-rotator-:-—-AND-9♥?!-9♥-celled-[t1-dig…]:-OVERLAP-{6♠ 4♣ 9♥}-before-J♦-even-:-⟹-rotator-slot-SINGLE:-timeline-:-(1)-{6♠}+2:-…-(2)-+9♥-(t1-dig):-{6♠ 9♥}+1:-(3)-+4♣-(t2-dig):-{6♠ 9♥ 4♣}-FULL-:-(4)-NEED:-t6-dig-(9♦8♠→10♣--no-cell;-8♥→CELL--FULL)--—-8♥-alternative-seat-pre-chunk:-NONE-—-.-⟹-⟹-THE-TRIANGLE-{9♥ 4♣ 8♥}-verdammt.-—-⟹-dig-t6-BEFORE-t2?!:-(3')-+8♥:-{6♠ 9♥ 8♥}-FULL:-J♥→Q♠-⟸-J♦-cell--FULL--AAAAAAAAAAAARGH. Citation: https://www-cdn.anthropic.com/d00db56fa754a1b115b6dd7cb2e3c342ee809620.pdf https://www-cdn.anthropic.com/d00db56fa754a1b115b6dd7cb2e3c3..., section 6.2.2 You're not going to get a handle on what it's doing. The thinking traces are there to make you feel better about yourself.
        hgoel 9d ago
        I'm referring to models where the actual traces are available. Eg. I've been using a local Qwen3.8-Next-Flash lately.
jhonof 9d ago
I think the purpose of an event like this would be to optimize the process so that it isn't just occasionally asking an AI to keep going.
- a2ff6eeb0 9d ago
  That sounds like adding a bottleneck, unless you mean writing a harness that automatically asks the model to keep going, so that there's no humans involved at all?
MostlyStable 9d ago
That's how several major AI advancements have happened. I have seen no evidence that that is the fastest way to make progress right now. I expect that, much like chess engines, it will not take too long before AI is significantly better than AI + human. But right now, my bet is that we are still safely within the window where an AI + human mathematician team is still better than AI alone (at least for the case where the human has learned how to work effectively with the partner....something that this event could possible be good for teaching).
- a2ff6eeb0 9d ago
  I suspect that the best progress will be made by a team that purely spends their time taking a list of open problems and promoting "solve <problem>", without actually trying to understand anything. Just keep as many problems in flight as you can across as many sessions as you can. You can probably ask the AI to come up with a list of problems itself, and rank them by the likelihood of progress.
  - youoy 9d ago
    Then 20 years go by and you wake up one day with questions that you cannot get out of your mind: why did I start prompting the LLM for? Why did I need these random proofs for? What do i do with my repo with 2billion lines of Lean?

charlieyu1 9d ago

Are they actually autonomous? I’d say subject knowledge at the prompt stage plays a large part towards getting proper results

a2ff6eeb0 9d ago
When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. And left it for a long time. Jarred isn't a mathematician, he's the maintainer of a janky JavaScript environment. Here's the transcript: https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e9548c3f44f.pdf https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e...
hgoel 9d ago
Prompting for some of the results was almost the "Computer, do a breakthrough. Make no mistakes." meme. Just someone telling the model to keep trying a couple of times. Unfortunately we don't actually know what kind of prompting was done for the more prominent results.
- charlieyu1 9d ago
  It’s definitely not how I work, I’d need to read the model responses and set a direction for the model to go
  - deleted 9d ago
    [deleted]
  - hgoel 9d ago
    Same here, it's one thing if I'm just screwing around, but if I'm trying to do anything serious, I need to at least have a handle on what it's doing, and, when thinking traces are available, keeping track of any logical errors in the model's reasoning.
    - a2ff6eeb0 9d ago
      you know the thinking traces are redacted and summarized using another model, right? The actual thinking trace looks something like: 7♣-removal-IS-the-prerequisite-for-10♠/9♥!!)-⟹-OVERLAP-(ii)+(iv):-{6♠ J♦ 9♥ 2♣}-=-FOUR--—-UNLESS-7♣'s-seat-8♥-...-and-2♣-drains-only-at-crack-:-⟹-2♣-celled-+-9♥-celled-simultaneously-UNAVOIDABLE-in-t8-dig--—-BREAK:-9♥-drains-to-10♠-THE-MOMENT-10♠-is-free:-t8-dig-order:-[K♣→t2]-[2♣→cell]-[7♣→8♥-:-8♥-WHERE:-post-chunk-9♠-:-chunk-⟸-K♣--done-:-ORDER:-K♣→t2,-CHUNK→K♣-(cap-4!!:-cells-then:-{6♠ J♦ 9♥}-FULL--chunk-cap-=-1--—-F-F-F-F-F.-—-chunk-BEFORE-9♥-celling?!-:-9♥-celled-at-t1-dig-⟸-needed-for-5♣-⟸-4♥3♣-⟸-t2-dig-⟸-K♣-seat-⟸-chunk-:-⟹-chunkAFTER-9♥-celling-FORCED--:-chunk-cap-with-{6♠ J♦ 9♥}:-1--—-—-J♦-THE-NEW-CANCER.-—-⟹-J♦-celling-DELAYED-till-after-chunk?! :-J♦'s-celling-was-for-J♥→Q♠-(5♦-access-for-4♣):-DELAY-4♣-resolution:-4♣→CELLearly-(as-always)-then-4♣-cell→5♦-LATER-when-5♦-frees-!!!:-cells-rotation:-4♣-celled-[t2-dig-…-5♦-freed]:-5♦-freed-⟸-J♥→Q♠-⟸-J♦-celled-:-⟹-{6♠, 4♣, J♦}-overlap-window-until-4♣→5♦-drains:-then-{6♠ J♦}+1-rotator-:-—-AND-9♥?!-9♥-celled-[t1-dig…]:-OVERLAP-{6♠ 4♣ 9♥}-before-J♦-even-:-⟹-rotator-slot-SINGLE:-timeline-:-(1)-{6♠}+2:-…-(2)-+9♥-(t1-dig):-{6♠ 9♥}+1:-(3)-+4♣-(t2-dig):-{6♠ 9♥ 4♣}-FULL-:-(4)-NEED:-t6-dig-(9♦8♠→10♣--no-cell;-8♥→CELL--FULL)--—-8♥-alternative-seat-pre-chunk:-NONE-—-.-⟹-⟹-THE-TRIANGLE-{9♥ 4♣ 8♥}-verdammt.-—-⟹-dig-t6-BEFORE-t2?!:-(3')-+8♥:-{6♠ 9♥ 8♥}-FULL:-J♥→Q♠-⟸-J♦-cell--FULL--AAAAAAAAAAAARGH. Citation: https://www-cdn.anthropic.com/d00db56fa754a1b115b6dd7cb2e3c342ee809620.pdf https://www-cdn.anthropic.com/d00db56fa754a1b115b6dd7cb2e3c3..., section 6.2.2 You're not going to get a handle on what it's doing. The thinking traces are there to make you feel better about yourself.
      - hgoel 9d ago
        I'm referring to models where the actual traces are available. Eg. I've been using a local Qwen3.8-Next-Flash lately.

jhonof 9d ago

I think the purpose of an event like this would be to optimize the process so that it isn't just occasionally asking an AI to keep going.

a2ff6eeb0 9d ago
That sounds like adding a bottleneck, unless you mean writing a harness that automatically asks the model to keep going, so that there's no humans involved at all?

MostlyStable 9d ago

That's how several major AI advancements have happened. I have seen no evidence that that is the fastest way to make progress right now. I expect that, much like chess engines, it will not take too long before AI is significantly better than AI + human. But right now, my bet is that we are still safely within the window where an AI + human mathematician team is still better than AI alone (at least for the case where the human has learned how to work effectively with the partner....something that this event could possible be good for teaching).

a2ff6eeb0 9d ago
I suspect that the best progress will be made by a team that purely spends their time taking a list of open problems and promoting "solve <problem>", without actually trying to understand anything. Just keep as many problems in flight as you can across as many sessions as you can. You can probably ask the AI to come up with a list of problems itself, and rank them by the likelihood of progress.
- youoy 9d ago
  Then 20 years go by and you wake up one day with questions that you cannot get out of your mind: why did I start prompting the LLM for? Why did I need these random proofs for? What do i do with my repo with 2billion lines of Lean?