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Ten advances in mathematics and theoretical computer science

openai.com

231–240 of 1000 posts

Re: Ten advances in mathematics and theoretical computer science

#231
At what point can we say AGI has been achieved? What is the test? AI is solving mathematical problems that humans have not been able to solve for decades. Is that not enough?

Sam Altman has said "If superintelligence can't discover novel physics, I don't think it's a superintelligence." Is that the test? How far away are we from AI discovering novel physics? It seems within reach.

Re: Ten advances in mathematics and theoretical computer science

#232
post #211
post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

I can see this being important if you only care about the results as evaluations of AI progress, but if what you care about is the math itself why should you care about the prompt or anything other than the proof?

Re: Ten advances in mathematics and theoretical computer science

#233

On the token limits etc - one assumes that OpenAI et al are able to “hire expert in field, and let them spend the equivalent of a million dollars of tokens” because they are not actually selling their complete compute 24 hrs a day, so the cost internally is a negligible (ish) electricity bill. Which is very suggestive - if after everything they are not fully loaded then the next gazillion data centres being built loo…

No such thing as free, even internally at a company. All such use of resources is accounted for, assigned a dollar value and billed to some department. Someone ran the numbers and figured that whatever they spent on these GPU cycles was worth it.

Re: Ten advances in mathematics and theoretical computer science

#234

Earlier quoted context omitted.

I love how people come up with creative ideas to prove the bubble. This one is even more ridiculous - that OpenAI had spare compute to advance mathematics proves that data centres will not be needed. WHAT. If anything it proves more data centres are needed. That's literally the only reasonable conclusion from this news.

Sorry I thought that a bubble was widely accepted. Are you arguing there is not an AI bubble, and that all the DC buildout is fine, going to be profitable etc? I am not looking for a online slanging match - just looking for a different point of view

It’s not obvious at all. If it were obvious to you, it would’ve been to OpenAI. It’s in their interest to accurately predict demand. The assumption that OpenAI/Sam is both really powerful but simultaneously ignorant to know what others know as obvious is well.. just strange. Especially strange when OpenAI has more information on models, breakthrough and usage patterns and we don’t.

I’m not participating in the slinging match but it’s very very weird that you think it’s some established thing that these companies won’t make profit. A lot of hubris must go in this kind of thought. Like.. do you all think everyone’s playing musical chairs?

Re: Ten advances in mathematics and theoretical computer science

#236
post #184
post #119

Earlier quoted context omitted.

It is comical at this point. Some people just can not stand the thought of AI actually delivering and are trying to find whatever ways to discredit it.

This isn't really about delivering - it's more about helping to understand the shape of problems that AI can solve right now. If they took 1000 problems and threw the model at it and it solved these ten, is there something we learn about these ten problems and the kinds of things that current AI is good at? That's very different from picking ten problems _at random_ and solving all of them successfully, which would s…

That's totally disjointed from anything in this thread. The main accusation is that openai is cherrypicking math problems and we should be against these results. As if a mathematical proof stops being provably correct because it was cherry picked

And frankly these "concerns" ignore reality. In any research phd course you're actively told to bite off something small and likely to be provable so that you can prove it (and publish it). Openai telling its computer to do that is no different that your phd advisor telling you that.

Re: Ten advances in mathematics and theoretical computer science

#237
post #230

Earlier quoted context omitted.

This is not at the top as it is actively flagged by people that can't psychologically cope with the advances of AI. Hacker News is no longer a web site of an elite.

We cannot psychologically stand that Redis is hyped by OpenAI: https://developers.openai.com/cookbook/examples/vector_datab... How are the sales going?

If you're actively throwing away brand new greenfield research because it was generated by a computer at a company that stans industry-spanning software so that you can stay mad at your pet celebrity project, you might be the problem.

Re: Ten advances in mathematics and theoretical computer science

#238
post #232
post #211

Earlier quoted context omitted.

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

I can see this being important if you only care about the results as evaluations of AI progress, but if what you care about is the math itself why should you care about the prompt or anything other than the proof?

Because the math isn't solely about the proof being correct. You don't need to take my word for it, here's one of the most famous living mathematicians' take on it: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...

Re: Ten advances in mathematics and theoretical computer science

#239
post #232
post #211

Earlier quoted context omitted.

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

I can see this being important if you only care about the results as evaluations of AI progress, but if what you care about is the math itself why should you care about the prompt or anything other than the proof?

Understanding the process that led to the proof helps to understand how to do further work on top of it, which is the goal of most mathematical research. It's not as though mathematicians are going to go launch a startup operationalizing their knowledge of how densely hyperspheres may be packed.

Re: Ten advances in mathematics and theoretical computer science

#240
post #211
post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

If the proofs are formally verified by a proof assistant (Agda, Roq, Lean, ⋯), I see no reason we would need to know how these came about. All the information needed is in the proof.
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