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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

#41

Post by scrollop »

drakenot wrote: post #32
bgirard wrote: post #28

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 improv…

I think voice mode uses weaker models, just an FYI relative to the SOTA

Definitely, seems like gpt 3

Re: The AI revolution in math has arrived

#42

Post by keyle »

ambicapter wrote: post #6
maplethorpe wrote: post #3

Earlier quoted context omitted.

Altman has estimated one year until ChatGPT is capable of measuring time passed. https://tech.yahoo.com/ai/chatgpt/articles/chatgpt-fails-mis...

Sounds like Musk setting deadlines for Mars landings.

It's so hard to predict you know, these planets keep moving...

Re: The AI revolution in math has arrived

#44

Post by dogscatstrees »

zarzavat wrote: post #20
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…

It makes sense to me. Originally LLMs would get stuck in infinite loops generating tokens forever. This is bad, so we trained them to strongly prefer to stop once they reached the end of their answer. However, training models to stop also gave them "laziness", because they might prefer a shorter answer over a meandering answer that actually answered the user's question. Mathematics is unusual because it has an extern…

It was just yesterday that this top post [] was decrying the "peril of laziness lost", that LLMs inherently lack the virtue of laziness.

So which one are they?

[] https://news.ycombinator.com/item?id=47743628

Re: The AI revolution in math has arrived

#45

Post by yabutlivnWoods »

djsjajah wrote: post #31
yabutlivnWoods wrote: post #29

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.

You just failed the Turing test.

Fortunately for me equivalents to Turing exist: https://en.wikipedia.org/wiki/Turing_machine_equivalents

Re: The AI revolution in math has arrived

#46

Post by homarp »

4ajsH17 wrote: post #40

[flagged]

https://www.quantamagazine.org/about/ says "launched by the Simons Foundation in 2012"

and https://www.simonsfoundation.org/about/ has "Since its founding in 1994 by Jim and Marilyn Simons"

https://en.wikipedia.org/wiki/Jim_Simons explains how Jim Simons got rich.

The book 'The Man Who Solved the Market' - https://www.gregoryzuckerman.com/the-books/the-man-who-solve... is a nice read.

HN discussion on a review of the book - https://news.ycombinator.com/item?id=29392041

Re: The AI revolution in math has arrived

#47

Post by 440bx »

Boring mathematical reality here. This is nice and all that but as a (part time) corporate mathematician, I'd like an AI that organises conference trips, picks the best accommodation and food and gaslights the execs into approving it. Then fixes the perpetually broken coffee machine. Everything else for me starts on paper and is mostly undergrad level problems which I need to do by hand to keep my brain going for when I actually might need it one day. And with the geopolitical instability out there at the moment I'm not that willing to put my eggs into the basket.

Re: The AI revolution in math has arrived

#48

Post by LoganDark »

dogscatstrees wrote: post #44
zarzavat wrote: post #20

Earlier quoted context omitted.

It makes sense to me. Originally LLMs would get stuck in infinite loops generating tokens forever. This is bad, so we trained them to strongly prefer to stop once they reached the end of their answer. However, training models to stop also gave them "laziness", because they might prefer a shorter answer over a meandering answer that actually answered the user's question. Mathematics is unusual because it has an extern…

It was just yesterday that this top post [] was decrying the "peril of laziness lost", that LLMs inherently lack the virtue of laziness. So which one are they? [] https://news.ycombinator.com/item?id=47743628

I think laziness is not a minimum of effort. Laziness can actually be more effort towards a simpler or more practical solution, because those solutions are more pleasant in some way, and therefore more attractive to pursue.

Re: The AI revolution in math has arrived

#49

Post by bonesss »

dataviz1000 wrote: post #19
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…

I know why. Several people had problems with Sonnet burning through all their credits grinding on a problem it can't solve. Opus fixes this — it has a confidence threshold below which it exits the task instead of grinding. "I spent ~$100 last week testing both against multiplication. Sonnet at 37-digit × 37-digit (~10³⁷) never quits — 15+ minutes, 211KB of output, still actively decomposing numbers when I stopped it.…

So we have a bunch of imposter syndrome techies who would 5x with just a hint of encouragement, and now we’re trying to 2x them with LLMs, but in order to get there those same techies will have to gas up and inspire the LLM with the leadership and vision they themselves are wanting for?

The Universe seems against free lunches… if AGI is possible, finding a manager good enough to get the AGI to update its timesheet will not be (in practice).

Re: The AI revolution in math has arrived

#50

Post by doubledamio »

All these overly optimistic articles about AI solving maths problems are very annoying. Can we agree that maths is not about solving problems, but about understanding them by developing a language and the conditions for new insights? It is misleading because GPTs do provide easy access to new information, but they do not deepen understanding.

I think AI-assisted research will likely have a very negative net impact on mathematics in the long run by lowering the average level of understanding within the community.

Also, research directions are influenced by what people can solve, and this will slowly shift research toward purely algebraic/symbolic manipulations that mathematicians no longer fully keep track of.

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