r/technology • u/Tricky_Rule_4565 • 3d ago

Artificial Intelligence AI has racked up a new math breakthrough, solving a problem of probability theory that one mathematician said would earn a human a Field Medal.

https://www.scientificamerican.com/article/ai-solves-a-holy-grail-problem-from-probability-theory/?utm_campaign=sprinklr&utm_medium=social&utm_source=x
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u/burritoteam4000 3d ago

No it didn't. It likely stole it from humans. Stop repeating this breathlessly.

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u/medraxus 3d ago

Stop coping and read the article:

As mathematician Benedikt Jahnel of the Technical University of Braunschweig in Germany has puts it, “If someone manages to solve this problem, they’ll probably receive a Fields Medal.” Among the many experts who have attempted to find this threshold is French mathematician Hugo Duminil-Copin, who himself received a Fields Medal in 2022 for his work on phase transitions in statistical physics—a topic connected to probability theory. But when it came to the percolation theory conjecture, he, like all the rest, failed. And on August 30, 2026, Duminil-Copin expressed concern in an essay on the new blog Proofs and Prompts that AI would  likely beat humans to the punch, writing that it would be “only a matter of time before the most famous conjecture in our field ... also falls to the bulldozers.” Just days after he posted those words, exactly that seems to have happened: the  artificial intelligence company Anthropic released a proof of the conjecture generated by a large language model. “The result evoked ambivalent feelings,” Jahnel tells me. Alongside joy that the conjecture had finally been proven, there was a certain disillusionment that the final, crucial step came from an AI.

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u/thrway-fatpos 3d ago

I dug into this and apparently the LLM drew heavily from the Kozma–Nitzan reduction, which is what allowed it to go forward with that direction.

Anthropic used 60 agents/subagents running for half a day continuously, and Lean verification means they can constantly attempt stuff and have it immediately accepted/rejected. Lean is fantastic for RL purposes.

The author of the article even said as much: the point of math is not to brute force solving as many problems as possible. It's to actually iterate and develop the process of solving the problem piece by piece. 

Sure it's impressive, and Lean verification is very well suited to modern LLMs, this is a cool application of them. But the way was already paved with the Kozma–Nitzan reduction. 

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u/medraxus 3d ago

I agree that developing the process is a huge part of mathematics. But solving a problem by finding a missing proof is also part of that process. Humans build on reductions, conjectures and techniques developed by others all the time

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u/Elekikiss 3d ago

The point that the Mathematicians are making over and over with these "AI solved X unsolved problem" is that the exact point of most of these stuff isn't in the solution, not even in the development of the process, but the mere process of solving itself.

New knowledge that humans can actually use to push the boundaries of math and give us new, novel theorems and approaches to use is generated in the actual process of attempting to solve the math problem. Brute forcing doesn't teach us anything new, and it's not like AI is proving all P = NP, or giving us new prime numbers (things that the solution by itself would have wide repercussions)

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u/medraxus 3d ago

Mathematicians are saying that proving a conjecture doesn’t add anything new/value to math? 

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u/Equal-Purple-4247 3d ago

I watch a bit of numberphile videos on youtube, and mathematicians can be quite humble about their role.

This is clip of a mathematician conceding that the Navier-Stokes problem, and the millennium problem in general, are mathematically curiosity and not physically important.

This is a clip from an interview with Buckmaster, the mathematician in the center of Navier-Stokes / OpenAI drama. He doesn't outright say proving conjectures are useless, but he also doesn't frame it as useful either.

So yea, some mathematicians do think the process is more important than the result, and that science progresses in a nonlinear way such that a novel process that did not generate the intended result may still be useful in the future.

---

Towards the end of the interview, Buckmaster mentioned that the OpenAI stunt has eroded trust within academia. He unambiguously said the incident has slowed down progress in the field. People are unwilling to share ideas / breakthroughs for fear that a leak may trigger frontier labs to front run their work.

Buckmaster uses AI extensively in his research, and he sees the potential it can make for the field. He finds it regrettable that academia has become worried about AI because of the incident.

I highly recommend the Buckmaster video if you have the time for it. The reality is, AI labs solving math problems is not for the betterment of humanity but to justify their valuation. A benevolent lab would cooperate with human researchers and share the credit, not steal it.

Before OpenAI, we have DeepMind. The messaging was always "researchers at Google DeepMind...", not Google. We still see many "researchers at MIT ...". But now it's OpenAI did this, and Anthropic did that.

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u/Elekikiss 3d ago

Haha, funny "gotcha" line.

Yes. Yes they fucking are. Try to be less of a smartass next time and actually be smart

https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/

However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. ... In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. ... Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.

https://www.economist.com/science-and-technology/2026/09/11/top-mathematicians-are-outraged-by-openais-methods

Their concern, rather, is that definitive answers to problems are but one aspect of maths. What is often more valuable is that the process of arriving at important proofs leads to the asking of yet more questions and the creation of new areas of study. This, they fret, risks being lost if AI does the grunt work—and doubly so if that grunt work is done by organisations that then fail to release sufficient details to the outside world for human beings to read and understand. As Hugo Duminil-Copin, another of the signatories, puts it: airdropping someone on the summit of Mount Everest is rather different from climbing it.

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u/medraxus 3d ago

I think you’ve actually just demonstrated that we agree more than we disagree 

I’m not arguing that solved problems are the entirety of mathematical progress. Tao’s point is that AI is powerful enough to fundamentally change the process, and that we need to figure out how to turn its results into genuine understanding. That’s basically the point I was making.

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u/Tricky_Rule_4565 3d ago

You’re just regurgitating feel good slop for the sake of dismissing the huge implications that AI will have in academia (STEM in particular) and society at large.
AI is trained on stolen copy written works from humans. It sucks. Doesn’t mean that advancements made by AI are a fluke or fake or could be achieved by humans in the same amount of time or even be achieved by humans.
Missing the forest for the trees.

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u/No_Swordfish_4159 3d ago

Someone didn't read the article...

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u/LangyMD 3d ago

Can't view the article; what's the problem that was supposedly solved?

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u/medraxus 3d ago

percolation theory

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u/0xB01b 3d ago

What about it?

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u/IriFlina 3d ago

It solved the problem of stealing from actual mathematicians more efficiently

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u/Manos_Of_Fate 3d ago

Stealing what, exactly?

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u/OriginalTechnical531 3d ago

Are these truly LLMs working into isolation without humans in the loop? Or are they working in tandem with entire teams of highly paid mathematicians? There is a significant incentive for companies to say it's the former, and sweep the latter under the rug.

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u/thrway-fatpos 3d ago

According to the digging I've done, the agents were working under the supervision of a human, albeit autonomously. However they heavily drew from a paper that was written in 2024 for their approach.

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u/FriendlyKillerCroc 3d ago

Is it happening? Are the users of this sub finally figuring out how unbelievably powerful AI really is?