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Some here and elsewhere where mathematics is discussed, have championed the First Proof iniative as the best way to evaluate mathematical reasoning capabilities of LLMs.
It consists of ten lemmas working mathematicians encountered in their work, solved, but have not published the solutions.
Today Google published what its SotA mathematical reasoning model, Aletheia, managed to produce autonomously. Some have downplayed the capabilities of SotA models, probably due to not having access to Aletheia, instead thinking that 200 USD per month buys them the most mathematically capable artificial intelligence. This would explain the common trope of claiming that, to use an analogy, an LLM is only capable of producing the integral of ln(n)x^2 only if one gives it the hint to use integration by parts.
Anyway, Google's model managed to autonomously solve five problems, and one partially. Importantly, the models have a self-filtering feature, in that if the model is not sufficiently sure of correctness, it will output nothing, rather than something potentially wrong. "Prompters" of Aletheia did not take the "A" word lightly, they did not attemp to skirt it by giving the model hints:
Notably, "prompters" do not deny that the platonic ideal of a proof was not what the model produced:
Two Aletheias were prompted: one with base model Gemini 3 Deep Think, and one with the base model as described in the model link above. The latter outperformed the former by solving and partially solving two problems the former did not. The amount of compute and thus cost is not revelead in absolute terms, only in relation to solving EP1051.
Autonomy and hard coding outputting nothing if unsure[1], makes them poweful tools even in the hands of less plus smart users. As the former means guiding them is not required and the latrer that they are reliable.
[1]LLM's doing otherwise is the product of them being deployed to the mass market, as the masses want the machine to reply more than they want the reply to be 100% correct. This is thus an inrehent flaw of LLMs, them bullshitting baselessly, but a consequence of post-training/RL.
I suppose the snark is aimed at me. So I guess I'll start with the snark right back, first. My comment included multiple very hopeful things, and a big part of that was due to the linked post's discussion of Alethia's performance on First Proof, which you would have known if you had read either of them. This now is just the ArXiV version of it.
I am still quite very hopeful, and it's nice to see the actual proofs that were generated. It is quite unfortunate that I can't beat on the system with my own problems to get a personal feel for it. I also endorse pretty much everything @PokerPirate has said below up to this point.
Obvious remaining concerns are obvious. It still generated wrong proofs, when evaluated by experts. Many many many hours of evaluation work. That can plausibly be managed; wrong proofs are definitely out there. I will repeat my related concern that the ballgame is quite different when you're working on a problem where you don't already have a solution (that is, where you don't know that a solution exists). And as you mention, cost, question mark? They're unclear about it, and what they do have looks scary, especially if you look at the numbers floating around in their prior papers (also untethered from an absolute scale, but wild in a relative scale).
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