The Ledger
Every statement that passed quotation and attribution checks. Mix any filter with any other: certainty 1/5, debate potential 5/5, or both at once.
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Hong: Structured and formal data enables broad horizontal transfer learning
“If you have more structured and formal data, it's going to be a lot more horizontal than the specific vertical we are tackling.”
Hong: Axiom and Harmonic mistakenly claimed solved Erdős problems were new
“So actually what happened was our competitor, Harmonic, decided to publicize that they have solved unsolved problems, Erdos number one two four and four 81, and then we trusted their literature review, believing that these problems are really, truly unsolved. …”
Hong: Axiom Math has solved open research problems across math subfields
“We have good performance, you know, having solved open research questions and number theory, commutative algebra, algebraic geometry, some discrete math that come into Rx and probability.”
Hong: Scaling inference for formal math has almost no wall
“I think that we found scaling inference to have almost no wall recursively decomposing you know, approved goal into many sub goals and then learning to backtrack as well.”
Hong: Axiom Math will be worth $10 billion
“Because when we realize the dream, the company's gonna be worth ten billion.”
Hong: Formal verification TAM covers all AI-generated code, not niche applications
“No, that's not the TEM. The TEM is all code. The TEM is a right of first refusal on all AI-generated code. Like, right of first refusal, meaning, you know, you get to choose whether you want to verify it.”
Hong: AI for Math Will Fragment as Axiom and Harmonic Lead
“I expect fragmentation to start to happen as Axiom and Harmonic establish category leadership.”
Hong: Axiom's unmodified Putnam system achieved 99% on Verina benchmark
“And we actually recently, with no modification to the Putnam system, we saw a 99% out of the 189 problems, we saw a 187, we missed only two code-wisp-proof.”
Hong: Future coding will rely on automated test-generated specifications
“I think this is the future of coding. Yes, I think this is the future of coding. And I think this is where, you know, this is where I think even if we are supposed, like given the assumption that everything can be formally verified, you know, like studying sor…”
Hong: Commercial Pressure Risks Distracting AI Math Startups From Core Capability
“Potentially trying to prove commercial value is going to distract significantly from the core capability improvement.”
Hong: Lean-Based Systems Will Struggle With Highly Creative Combinatorics
“I think a Lean-based system will struggle in those very creative places, which is why we at Axiom actually also invest on something called mathematical discovery.”
Hong: Verification is the best first commercial market for Axiom
“The DNA of the company is math. We think that verification is the best first market.”
Hong: Training AI for mathematical elegance is an alignment problem
“At one point we're gonna get to there because, you know, I think the conjecture will probably depend on what, you know, will probably depend on what we mean by taste, elegance. Feels like an alignment problem to me, you know? Like, you know, who gets to say wh…”
Hong: Axiom Math to open source two mathematical discovery codebases
“We have some major news in the coming weeks, basically open sourcing entire code bases of mathematical discovery coming up.”
Hong: Each line of verified code currently takes 20 proof lines
“Currently, actually, you know, for each line of code written, there could be like 20 lines of proof.”
Hong: Axiom Math is 7-8 months old with about 30 employees
“We are like a seven, eight months old company, so it definitely means a lot to us. It's a really cool milestone. We're currently about like 30 people now, right?”
Hong: Axiom could not have solved Putnam problems in time without AXLE
“And without it, we couldn't have solved it with I think the eight problems within the time limit. Definitely not, not within the time limit.”
Hong: Axiom Math released AXLE, a Lean proof validation toolkit
“So we just released AXLE, A-X-L-E, stands for Axiom Lean Engine. And it's really a set of, kind of, proof validation and manipulation tools that are built for Lean in the language of Lean. So it's a bunch of metaprogramming tools.”
Hong: Axiom's Francois Charton Solved Decades-Old Math Conjectures
“Francois Charton, a member of technical staff at Axiom, and he previously have done Patent Boost and End-to-end, you know, settle this proof, a thirty-year-old conjecture by finding a counterexample found the solution to a one-hundred-and-thirty-year-old probl…”