
Assistant Prof. @ChicagoBooth | OM & Applied AI | Most Cited Paper: Neural Collapse in AI Training | BSE @Princeton, PhD @Cornell, MS/PostDoc @Stanford
Chicago, IL
Joined November 2011
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XY Han retweeted
I was brought to tears on Sunday when the last milestone cleared. My father, a mathematician who passed in Jan, introduced me to the giants of group theory as a kid. The Classification of Finite Simple Groups (CFSG) defined my 80s college years. I can't believe I somehow got to be part of this human achievement. CFSG formalized in Lean. @leanprover
first, these results are mind blowing
second, can we appreciate how oai basically reinvented the academic peer review process from first principles?
XY Han retweeted
Many of you don't understand how serious this is, so let me break it down.
In computer science there is a famous kind of puzzle called 3-SAT. You are given a long list of yes-or-no switches and a set of rules about how they must be arranged, and you have to find a combination that satisfies every rule. The obvious way to solve it is to try every combination, but each new switch doubles the number of possibilities, so a puzzle with a few hundred switches would take longer than the age of the universe to brute force.
For decades, the smartest people in the field found clever tricks that made this a little faster, but every trick still hit the same wall: the time required kept exploding as the puzzle grew.
About 25 years ago, two computer scientists, Russell Impagliazzo and Ramamohan Paturi, working with Francis Zane, turned that wall into a formal idea.
They proposed the Exponential Time Hypothesis, which says this explosion is not a failure of human cleverness but a law of nature. No algorithm, however brilliant, will ever solve 3-SAT without the time blowing up exponentially. Nobody could prove it, but almost everyone believed it, and it became one of the foundations of modern computer science.
Researchers used it as a measuring stick. If you could show that solving some other problem quickly would also crack 3-SAT quickly, you had shown that problem was hopelessly hard too. Hundreds of papers, across scheduling, graphs, logic and much more, rest on this one assumption.
Now an internal AI model at OpenAI claims to have broken it. It says it found an algorithm that solves these puzzles meaningfully faster than the hypothesis allows, and it has checked the proof in a computer verification system called Lean.
And here is the remarkable part: the very people who proposed the hypothesis, Impagliazzo and Paturi, along with MIT's Ryan Williams, are now leading the public review of whether a machine has disproved their own idea.
So what happens next? If the disproof holds, a large part of theoretical computer science has to be revisited.
Every result that said "this problem cannot be solved faster, assuming ETH" loses its foundation, and researchers will have to work out which of those walls were real and which were simply where we stopped looking. It does not mean everything becomes easy. The new algorithm is still slow in absolute terms and this is not the famous P versus NP problem being solved.
But it means our map of what is possible was wrong in a place we were very confident about, and it was an AI that redrew it. If the disproof fails, the hypothesis survives and the field breathes out, but we will still have watched an AI produce serious, checkable work on one of the deepest questions in the discipline, closely enough that the founders of the idea had to take it seriously. Either way, something has shifted.
XY Han retweeted
After ETH falling, I woulnd't be surprised by an n^logn algorithm for 3SAT. Heck maybe even P=NP but in some absurd way that changes nothing in practice. Not dishing LLMs, they’re extraordinary! Just mad at myself for letting worst case complexity deter me from trying stuff.
XY Han retweeted
I made this prediction 3 years ago, in July 2023. Few attending my talk believed me back then.
In retrospect, replace was not quite the right word. AI won’t replace any fields. Instead, it will fundamentally reshape, and is already reshaping, fields by rewarding deep connections to real-world challenges and other disciplines.
We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
openai.com/index/building-sc…
XY Han retweeted
I didn’t realize until today that Anthropic CEO Dario Amodei started college at Caltech and would have been one of my students if he hadn’t skipped Physics 1 (since I was head TA at the time). Given that he did skip it, it’s virtually certain that I graded his placement exam.
gradually learning economists use the word "identification" the same way statisticians use the word "inference".
it sounds like and kind of is the english word but actually has a crazy amount of domain-specific connotations and those connotations make up the entirety of some ppl's careers
XY Han retweeted
I’ve lately been getting emails from prospective grad students with detailed questions about my papers and proposed approaches to extend them.
Sorry, not impressed. A year or two ago, I might have been, but somehow it’s never happened until now… 🤔
XY Han retweeted
One feature of Vibed ML papers is that they do some cool hack in Section 3-4 and then Section 5 is called “Theoretical Analysis” as if we understood how any of this works.




























