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AxiomProver is the first AI to solve research conjectures end-to-end
“It's probably the first AI to solve a research conjecture completely end-to-end and self-verifies. That means the output are fully verified, a hundred percent correct.”
AxiomProver achieved a perfect score on the 2025 Putnam math exam
“Eight within the time limit, and then 12 out of 12.”
Today's AI can solve math problems that take human researchers months
“I think that we are at a threshold of mathematical renaissance, which is to realize that there are so many unsolved problems that will currently take, say, researchers months to crack, or even technical lemmas in those really longstanding conjectures that we b…”
True AI reasoning engines require verifiable rewards for intermediate proof steps
“If you want to have a reasoning engine that really truly masters at logic and mathematical reasoning, then you need to somehow get verifiable reward for the proof steps.”
Axiom's proof verifier is 100 times faster than open-source alternatives
“So a lot of the sort of like verify, verify proof is actually, you know, one of our prover tools that's about to be released, and that's actually a hundred times faster than The other counterparts that are the open source, like effort, cloud comparator.”
AxiomProver autonomously proves theorems publishable in major mathematical journals
“Currently the batch of papers, Axiom Prover has autonomously proven and mathematicians have written You can probably get into Journal of Number Theory, Journal of Algebra, like that level.”
Axiom Math aims to solve a Fields Medal shortlist-worthy problem using AI
“I think that we really want Accent Prover to be able to solve one long-standing problem in mathematics that you can objectively, objectively say, even though if it's an AI, you know, or double-blind, whatever, that will be in the shortlist.”
AxiomProver could eventually solve the majority of human mathematical conjectures
“Everything that human mind Can conjecture, find interesting, find tasteful, could be solved by, hopefully, majority of them by accent prover.”
Generation and verification loops are the next major frontier of AI
“We still feel like we cannot fully elaborate and emphasize the thing that we are seeing that is the next frontier of AI. That is a generation and verification loop. That is the discovery of verified knowledge.”
AxiomProver has solved four research-level open mathematical problems
“Recently, I think like a couple of weeks ago, we just announced that action prover solved these four research level open problems.”
Axiom Math's AI system proves multiple open research conjectures every week
“We actually have actually a few more research conjectures that's being proven every week just by the supply of mathematicians you know, from the world, and we try to put those problems into use.”
Numerical AI benchmarks fail to evaluate underlying logical reasoning capabilities
“Like, you know, we have seen from, say, Frontier Math and other benchmark, which only compels a numerical answer that it doesn't actually necessarily reflect the model's capability in the logical reasoning.”
Mathematical reasoning is the foundational reasoning layer for AGI
“Our worldview is math reasoning is a true reasoning layer of AGI.”
AxiomProver self-improves by adding generated mathematical proofs to its skill library
“Action Prover learns to prove things, and it kind of self-improved in a way where all the things that it proved got fed back into it, into a kind of a skill library.”
Mathematical AI unlocks solutions for verification and optimization
“I think through solving math, we also realize that it can solve a lot of other problems, such as verification, such as optimization, et cetera.”
Axiom's AI generated Putnam math solutions that diverge from human proofs
“So we actually analyzed all 12 problem solutions of the Putnam exam, and we found that a lot of the solutions actually differ from the human solution.”
Lean-based AI provers favor mechanistic arguments over clever human-style solutions
“Because it is a, you know, lean based system, it is really good at sort of routine bookkeeping, and it will actually choose a lot of the more mechanistic, you know, arguments over the ones that require like a clever, say one picture solution.”
Auto-formalization is harder than translating between two programming languages
“And auto formalization, which is the sort of capability of converting the natural language reasoning to say the formal language. And that's harder than translation because it's different than say translating between two programming languages. You're translatin…”
Translating formal Lean code into English is easier than auto-formalization
“There's also auto-informalization, which is kind of translate back, I mean, from Lean to English. That's easier than auto-formalization, because most of the machines' AI have seen a lot more English than Lean.”
Axiom Math focuses on post-training reinforcement learning to achieve performance gains
“And I think that we shouldn't do pre-training. We shouldn't try to just only train from scratch. I think we're kind of focusing on post-training reinforcement learning can potentially get us better performance gain.”
The Lean theorem prover language is closer to Rust than to English
“I think the sort of gap between, say, for example, Lean and another, like, strongly typed language like Rust is a lot closer than the gap between Lean and English.”
The open-source Lean dataset contains only tens of millions of tokens
“It's only two-digit million number of tokens out there in the open, open world.”
Axiom Math will release its Lean tools on a public API
“We are actually gonna release them on a public, like, API on these, all these dozen of pools. Very, very soon. Beginning of March.”
Axiom Math tested transfer learning from mathematical reasoning to code verification
“So from Putnam Perfect Score, that was four months in, then two months later was the four research conjectures, and then, you know, during this middle, we also have tested something that is transfer learning from math to code verification, so another evaluatio…”
Domain experts grade the 2025 Putnam Competition as harder than IMO 2025
“Pundum 20 25 is by a lot of sort of experts grading harder than IMO 20 25, so it's the hardest reward Maths Olympiae test”
Math community AI skepticism stems from unverifiable informal language model outputs
“A lot of the, like, adverse reaction about from the math community about AI is actually coming from the fact that they cannot verify an informal solution.”
Almost all younger-generation mathematicians accept Lean as a formal proof verifier
“Almost all of the new school of mathematicians are accepting Lean.”
Mathematical difficulty spans solution creativity and object abstraction
“There are actually two axis of difficulty. One is how creative the solution is, and The other one, roughly speaking, is how abstract the mathematical object is.”
Only five humans have achieved a perfect Putnam score in 100 years
“Over the 100 year history of Putnam, there's only five human perfect scores.”