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.
why aren't all 19 resolved? a statement only gets an assessment when the public record can support or contradict it. opinions and what-ifs never can, and 2 checkable ones are still open, waiting for their date. predictions held up or didn't; assertions are supported or contradicted. on every card: ▮▮▮▮▮ certainty · ▮▮▮▮▮ debate potential. speakers are clickable
Hong: Competitor's AI demo can be solved entirely by Lean's grind tactic
“We're talking about, for example, the grind tactic in Lean. It can currently handle a lot of mass proofs, like, at a very low level. And this is pretty shocking because I have seen, you know, actually another company working in the same space, like, you know, …”
Hong: Informal math systems will not achieve math AGI
“I'm going to say on the record, we do not believe that an informal math system is going to be the math AGI solution.”
Hong: DeepMind's Formal Math Slowdown Post-AlphaProof Was Non-Technical
“After AlphaProof, kind of like, we didn't see a lot of the formal math you know, results or kind of progress from Google DeepMind, and that's actually because of reasons that are not necessarily technical.”
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: Axiom Math will be worth $10 billion
“Because when we realize the dream, the company's gonna be worth ten billion.”
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: 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: Harmonic's Aristotle Verified an Erdős Problem Proof Found by GPT
“In fact, like, you know, GPT found a proof to an unsolved Erdos problem, and our competitor Harmonic, you know, Aristotle you know, verified it.”
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: DeepSeek dissolved its formal reasoning team over strategic shift
“And we have since, for example, Deep Seek All right. Like originally having a formal team and then later dissolve that team because of strategic direction change.”
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: AI Solved All Non-Combinatorics IMO Problems Across 2024 and 2025
“Across 24 and 25, AI models could solve all the problems that are not combinatorics.”
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: Claude plus AXLE is a go-to setup in Lean community
“And we have seen also, we have heard from a lot of the people that Claude plus Axel is kind of their go-to setup for now.”
Hong: Auto-generated blueprints will be the key bottleneck in formal math
“I think auto-generated Blueprint is going to be a technical bottleneck that many people are trying to solve around the same time.”
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…”