Founder / Reasoning Engines / Palo Alto
Tudor Achim
He taught a machine to win Math Olympiad gold - and then made it show every step of the work.
He taught a machine to win Math Olympiad gold - and then made it show every step of the work.
In July 2024, a small lab in Palo Alto put its system through the International Mathematical Olympiad problems and came back with gold-medal-level scores. So did OpenAI. So did Google DeepMind. The headline should have been the parity. The real story was the footnote: Harmonic submitted proofs that a machine could check line by line, written in the Lean 4 proof language, formally verified. No "trust me." Just proof.
Tudor Achim runs that lab. He cofounded Harmonic in 2023 with Vlad Tenev, the man better known for Robinhood, and pointed the whole thing at an idea he calls Mathematical Superintelligence - AI that reasons through mathematics instead of predicting the next plausible-sounding word. The bet underneath it is blunt: language models guess, mathematics proves, and the future belongs to the side that can tell the difference.
Today Aristotle, Harmonic's system, is the first consumer-facing product built on that premise. You can ask it a hard problem and get back an answer that comes with a certificate of correctness. For most of computing history that combination - useful and provably right - has been a fantasy. Achim is treating it as a roadmap.
"Mathematics is the fundamental toolkit to understand the world."
"Hallucinations are the engine of creativity."
"Within 2 or 3 years, AI mathematicians will surpass human mathematicians for any specific task."
Before the funding rounds and the Olympiad scores, there was a keyboard. Achim trained as a competitive pianist at Carnegie Mellon's music preparatory school, the kind of place where a demanding teacher decides how your afternoons go for years at a stretch. He credits that apprenticeship for a trait that turns out to be load-bearing in his current work: the willingness to sit with a hard problem long past the point where it stops being fun.
He swapped the recital hall for computer science, also at Carnegie Mellon, where he took his B.S. Then came a PhD in computational biology that he started and walked away from - the first of several comfortable paths he declined to finish. He landed at Quora, where he led machine learning work on the news feed, the ranking and recommendation machinery that decides what a few hundred million people read next.
Next he cofounded Helm.ai, an autonomous-driving software company, and served as its CTO. Teaching cars to see is a brutal teacher of one lesson in particular: an AI that is usually right is not good enough when "wrong" has a body count. That standard - correctness you can stake something on - is the through-line from the steering wheel to the proof assistant.
Along the way he kept one foot in research, with a stint as a Stanford PhD student and a string of papers at ICML, AISTATS, NIPS and ICRA, on everything from constraint-satisfaction sampling to generating protein structures with diffusion models. The titles are dense. The pattern is not: he keeps circling back to the question of how a machine can reason its way to something true.
A standard chatbot predicts the next word. Sometimes the words are right; sometimes they are confident fiction. There is no built-in way to tell which.
Harmonic writes its answers as proofs in Lean 4, a language a computer can check. If the proof holds, the answer is correct - not likely, correct.
Using reinforcement learning, Aristotle generates its own synthetic problems, then verifies its solutions - learning from territory no human assigned it.
Here is the move that makes people sit up. Achim does not treat AI hallucinations as a disease to be cured. He calls them "the engine of creativity" - the part of the system willing to leap somewhere unexpected. The trick is not to stop the leaping. The trick is to put a verifier underneath, so that every wild guess gets caught, checked, and either kept because it is provably true or thrown out because it is not.
That is the whole bet in one sentence: let the model dream, then make it prove. It is also why Mathematical Superintelligence is not just a faster calculator. Achim's claim is that mathematics is "the fundamental toolkit to understand the world," and that an AI fluent in formal proof could eventually verify safety-critical software, attack open research problems, and - the ambition he says out loud - take a run at the Millennium Prize questions that have stumped humans for decades.
Harmonic is the product of two people you would not obviously seat together. Vlad Tenev built Robinhood, a company about putting financial markets in everyone's pocket. Achim spent his career on the unglamorous frontier of getting machines to be correct under pressure - ranking systems, perception stacks for cars, sampling algorithms with names only a referee could love. Together they decided the most valuable thing to build was not another chatbot but a reasoning engine that could not lie to you about a number.
The capital agreed. Sequoia and Index Ventures led early rounds, with a roster that runs from Kleiner Perkins and Paradigm to angels as varied as the actor Jared Leto. The $100M Series B in July 2025 and a subsequent Series C reportedly pushed total funding to around $295M - a war chest that, divided across a team of roughly forty, says something about how much compute and talent it takes to teach a machine to prove.
The International Mathematical Olympiad is the hardest pre-university math competition on earth - six problems, two days, partial credit for elegance and full credit for proof. When OpenAI and DeepMind announced gold-medal-level results, the world noticed. When Harmonic announced the same, the world should have noticed something sharper. The large labs reported answers a panel of humans graded. Harmonic reported answers a computer could grade, because each one arrived as a machine-checkable proof in Lean 4.
That distinction is the entire point of Achim's company. An ungraded olympiad answer is a claim. A formally verified one is a fact. For a forty-person team to reach that bar at the same level as labs with thousands of researchers and far larger budgets is the kind of result that rewires how investors and competitors think about what a focused approach can do. Aristotle, the system that did it, then became the first such engine handed to the public - so anyone could ask a hard question and get back not just an answer but the receipt.
It is worth dwelling on the philosophy, because Achim does. He is not promising an AI that never has a strange idea. He wants the strange ideas - that is where new mathematics comes from. What he refuses to ship is a strange idea that nobody checked. Creativity on the front end, verification on the back end, and a willingness to throw away anything that fails the proof. It is an old engineering instinct dressed in new mathematics: measure twice, prove once.
Ask most founders where they'll be in three years and you get a revenue target. Achim gives you a deadline for human mathematicians: surpassed, he predicts, on any specific task. Harmonic's stated aim is AI that reasons through mathematics rather than language - eliminating hallucinations, verifying the software our lives depend on, and eventually opening problems no one has cracked.
It is a large claim from a small team. But the IMO result already did the thing skeptics said could not be done at this size: it tied the largest labs in the world and brought receipts. Whether the rest of the prediction lands, Achim has made the terms refreshingly clear. He is not asking to be believed. He is asking to be checked.