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Notes -
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.
How the hell did they decide to name it something so hard to pronounce.
It seems pretty simple to me.
It's actually closer to A-leh-they-ee-ah. It comes from a- (negation prefix) lethein (concealment, being unseen, or forgetting in the sense of the River of Lethe in Hades). I've always found it very philosophically interesting that the Greeks considered truth a negation of concealment rather than a purely positive category as we do.
I'm seeing four syllables for English and Greek.
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