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The AI revolution in math has arrived

quantamagazine.org

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Re: The AI revolution in math has arrived

#21

Post by p1dda »

gxs wrote: post #15
themafia wrote: post #7

There are several high value prizes for mathematical research. Let me know when an "AI" has earned one of them. Otherwise: > When Ryu asked ChatGPT, “it kept giving me incorrect proofs,” [...] he would check its answers, keep the correct parts, and feed them back into the model So you had a conversational calculator being operated by an actual domain expert. > With ChatGPT, I felt like I was covering a lot of ground…

Wow that was your takeaway? > “2025 was the year when AI really started being useful for many different tasks,” said Terence Tao I think I’ll go out on a limb and agree with Terrence Tao, I think the dude is well known in the math community, or something

I think he means useful for mathematicians getting paid shilling for AI models

Re: The AI revolution in math has arrived

#22

Post by lamasery »

CivBase wrote: post #18
dogscatstrees wrote: post #10

> As they did so, they also learned how to improve the prompts they gave AlphaEvolve. One key takeaway: The model seemed to benefit from encouragement. It worked better “when we were prompting with some positive reinforcement to the LLM,” Gómez-Serrano said. “Like saying ‘You can do this’ — this seemed to help. This is interesting. We don’t know why.” Four top logical people in the world are acknowledging this. It is…

This seems pretty obvious, no? It's pattern matching on training material. There is almost certainly an overlap between positivity and success in the training material. Positive prompts cause the pattern matching to weight towards positivity and therefor more successful material.

The training or system prompts have shoved the probabilities toward a space that tends to select “halt” sooner. You need to drag the probability weights around until they are less likely to reach “halt” so soon.

Nice language often sorta does this for whatever model(s) they looked at, and is also something people are likely to try. Probably lots and lots of nonsense token combos would work even better, but who’s gonna try sticking “gerontocratic green giant giraffes” on the end of their prompts to see if it helps?

Positive or negative language likely also prevents pulling the probabilities away from the correct topic, being so generic a thing. The above suggestion might only be ultra-effective if the topic is catalytic converters, for some reason, and push the thing into generating tokens about giraffes otherwise. How would you ever discover the dozens or thousands of more-effective but only-sometimes nonsense token combos? You’d need automation and a lot of brute force, or some better way to analyze the LLM’s database.

Re: The AI revolution in math has arrived

#24

Post by sm0ss117 »

Mathematics seems like the ideal candidate for AIs to achieve absurd results. It's a purely abstract grammar with true auto-verifiability. Even SWE has the requirement of interacting with real physical things. In math there's no external feedback required, you're solely bounded by the rate and quality of token generation.

Re: The AI revolution in math has arrived

#25

Post by jryle70 »

noobermin wrote: post #17
gxs wrote: post #15

Earlier quoted context omitted.

Wow that was your takeaway? > “2025 was the year when AI really started being useful for many different tasks,” said Terence Tao I think I’ll go out on a limb and agree with Terrence Tao, I think the dude is well known in the math community, or something

If anything his simping for AI models makes me more suspect of him than I ever was because my own eyes show me their limits.

Any chance your eyes are wrong? Or only people who disagree with you are.

Re: The AI revolution in math has arrived

#26

Post by themafia »

gxs wrote: post #15
themafia wrote: post #7

There are several high value prizes for mathematical research. Let me know when an "AI" has earned one of them. Otherwise: > When Ryu asked ChatGPT, “it kept giving me incorrect proofs,” [...] he would check its answers, keep the correct parts, and feed them back into the model So you had a conversational calculator being operated by an actual domain expert. > With ChatGPT, I felt like I was covering a lot of ground…

Wow that was your takeaway? > “2025 was the year when AI really started being useful for many different tasks,” said Terence Tao I think I’ll go out on a limb and agree with Terrence Tao, I think the dude is well known in the math community, or something

> go out on a limb and agree with Terrence Tao

Is AI his specialty?

> I think the dude is well known in the math community, or something

I believe this is called "appeal to authority." Which is why, instead of disagreeing with him, I suggested a more cogent endpoint that could be used to establish the facts the article's title suggests.

Re: The AI revolution in math has arrived

#28

Post by bgirard »

Last week I got together with my math alumni friend. We cracked some beers, we chatted with voice mode ChatGPT and toyed around with Collatz Conjecture and we sent some prompt to a coding agent to build visualizations and simulation. It was a lot of fun directing these agents while we bounced off ideas and the models could explore them.

I think with the right problem and the right agentic loop it’s clear to me improvements will speed up.

Re: The AI revolution in math has arrived

#29

Post by yabutlivnWoods »

We can define a Dyson Sphere in math.

We cannot build one.

AI outputting axiomatically valid syntax isn't going to be all that useful. It's possible to generate all axiomatically correct math with a for loop until the machine OOMs

Physics is not math and math is not physics.

Re: The AI revolution in math has arrived

#30

Post by drivebyhooting »

sm0ss117 wrote: post #24

Mathematics seems like the ideal candidate for AIs to achieve absurd results. It's a purely abstract grammar with true auto-verifiability. Even SWE has the requirement of interacting with real physical things. In math there's no external feedback required, you're solely bounded by the rate and quality of token generation.

This misses the mark on at least two accounts: 1. Proofs without human understanding have less value for mathematicians 2. At least for now, interestingness depends on human judgment. It is subjective and not as verifiable.
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