Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool at a narrow objective and see what sticks, then build on that or combine improvements.
Reading the article, that seems exactly how the discovery was made, an LLM used a "surprising connection" to go beyond the expected result. But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept.
A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation.
LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.
https://en.wikipedia.org/wiki/Qualified_immunity
Assuming you can still sue McDonalds I am not sure if this is a problem in the robotic llm case. I'm also trying to imagine a case where you would want to sue the llm and not the company. Given robots/llm don't have free will I'm not sure the problem with qualified immunity making police unaccountable applies.
There already exist a lot of similar conventions in corporate law. Generally, a main advantage of incorporation is protecting the people making the decisions from personal lawsuits.
Dystopia vibes from the fictional "Manna" people-management system. [0]
For those in academics, is OpenAI the vendor of choice?
They also offer grants you can apply for as a researcher. I'm sure other labs may have this too but I believe OpenAI was first to this.
Given that Google is the "web indexing company", finding hard to find things is natural for their models, and this is the only way I need these models for.
If I can't find it for a week digging the internet, I give it a colossal prompt, and it digs out what I'm looking for.
As far as academic research is concerned (e.g. this threads topic), I can't say.
I’m very out of my depth, but the structure of the proof seems to follow a pattern similar to a proof by contradiction. Where you’d say for example “assume for the sake of contradiction that the previously known limit is the highest possible” then prove that if that statement is true you get some impossible result.
When I'm learning about a new subject, I'll ask Claude to give me five papers that are relevant to what I'm learning about. Often three of the papers are either irrelevant or kind of shit, but that leaves 2/5 of them that are actually useful. Then from those papers, I'll ask Claude to give me a "dependency graph" by recursing on the citations, and then I start bottom-up.
This was game-changing for me. Reading advanced papers can be really hard for a variety of reasons, but one big one can simply be because you don't know the terminology and vernacular that the paper writers are using. Sometimes you can reasonably infer it from context, but sometimes I infer incorrectly, or simply have to skip over a section because I don't understand it. By working from the "lowest common denominator" of papers first, it generally makes the entire process easier.
I was already doing this to some extent prior to LLMs, as in I would get to a spot I didn't really understand, jump to a relevant citation, and recurse until I got to an understanding, but that was kind of a pain in the ass, so having a nice pretty graph for me makes it considerably easier for me to read and understand more papers.
I do not believe it will replace humans.
Why shouldn't it? Humans are poorly optimized for almost anything, and built on a substrate that's barely hanging together
And so do humans. Gotta stand on these shoulders of giants.
But AI is supercharging Math like there is no tomorrow.
1. Erdos 1196, GPT-5.4 Pro - https://www.scientificamerican.com/article/amateur-armed-wit...
There are a couple of other Erdos wins, but this was the most impressive, prior to the thread in question. And it's completely unsupervised.
Prompt - https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba...
2. Single-minus gluon tree amplitudes are nonzero , GPT-5.2 https://openai.com/index/new-result-theoretical-physics/
3. Frontier Math Open Problem, GPT-5.4 Pro and others - https://epoch.ai/frontiermath/open-problems/ramsey-hypergrap...
4. GPT-5.5 Pro - https://gowers.wordpress.com/2026/05/08/a-recent-experience-...
5. Claude's Cycles, Claude Opus 4.6 - https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cyc...
For example, these machines, if scaling intellect so fiercely that they are solving bespoke mathematics problems, should be able to generate mundane insights or unique conjectures far below the level of intellect required for highly advanced mathematics - and they simply do not.
Ask a model to give you the rundown and theory on a specific pharmacological substance, for example. It will cite the textbook and meta-analyses it pulls, but be completely incapable of any bespoke thinking on the topic. A random person pursuing a bachelor's in chemistry can do this.
Anything at all outside of the absolute facts, even the faintest conjecture, feels completely outside of their reach.
- It does not show an example of the new best solution, nor explain why they couldn't show an example (e.g. if the proof was not constructive)
- It does not even explain the previous best solution. The diagram of the rescaled unit grid doesn't indicate what the "points" are beyond the normal non-scaled unit grid. I have no idea what to take away from it.
- It's description of the new proof just cites some terms of art with no effort made to actually explain the result.
If this post were not on the OpenAI blog, I would assume it was slop. I understand advanced pure mathematics is complicated, but it is entirely possible to explain complicated topics to non-experts.
Who else disproved this longstanding conjecture before the model did so, since obviously it must have been in the training data since before?
Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules.
I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries.
So either “recombining existing material” isn’t disqualifying, or a lot of Fields Medals need to be returned.
Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibnitz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like art than a science.
For example, many belive that to sovle the Riemann Hypothesis, we likely need some new kind of math. Imo, it's unlikely that an LLM will somehow invent it.