Ankur Moitra
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Lex Fridman Podcast · #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis &…
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Did AI Prove the Unique Games Conjecture?
Ankur Moitra says a headlining result in the OpenAI drop is that the unique games conjecture is true. He had been on the side of the doubters, because the conjecture sounded too nice to be true.
Unique games strengthens the PCP theorem from the 1990s, a result that made the front page of the New York Times. A verifier can catch a false proof by inspecting only a constant number of random spots. If unique games holds, a huge set of problems has a best approximation algorithm, and that algorithm is simple.
Dor Minzer and Irit Dinur proved a weaker two-to-one games theorem that looked like a path humans might finish in another 10 or 20 years. The OpenAI release showed the full conjecture is t
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Why Does Ankur Moitra Say to Pretend You Already Won?
Ankur Moitra says the best way to live a rich and fulfilling life is to pretend you have already won, then figure out what you would do.
After a sabbatical in the Bay Area, living in Palo Alto while college stress sat in the cafes, he came back to MIT and was asked to give the convocation speech. The auditorium held freshmen and their families, 17-year-old kids who had already won the game of looking good on paper. He remembered starting college excited just to learn, filling little notebooks with a four-year plan so the classes would line up and he could take photonics as a sophomore. He had no idea what photonics was. It sounded fun and fancy. He sees the later path as endless optimizing:
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What Did Kamal Jain Say About Laptops and Markets?
Ankur Moitra cites Kamal Jain for the line he likes: if my laptop can't find it, then neither can the market. A Nash equilibrium is hard to compute, and that fact throws into question whether Nash equilibrium is really a universal mechanism that explains how people play games.
Game of Life is the simple case people reach for. A lot of the time the question is how small the rules need to be to get exotic behavior, and the rules can be shockingly small. One of the biggest exports from theoretical computer science is the algorithmic lens. Computation is not only a well-defined problem on a laptop that someone wants to solve. Computation in the natural world teaches what the rules of nature mig
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Why Do Journals Need New Models for AI Proofs?
Ankur Moitra wants new models that ease the load on journals and conferences, including a shared effort to verify AI proofs, while the older publishing models stay in place.
Journals and conferences were already overloaded with review work. Now someone has to review AI-generated papers, and some of them were important, but it is hard to get the community on board. OpenAI results have included improvements on the fast Fourier transform, and tweet streams have carried people improving the idea. He is not on Twitter and wants other ways to track the improvements and organize the ideas. A publication still goes out as the author's own draft: the author posts it on an archive, may add a new vers
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Why Is the Doorman Fallacy Useful for Math and AI?
Ankur Moitra treats the doorman fallacy as a good way to think about mathematics in the age of AI. The fallacy boils a complex job down to the simplest, most visible task and misses the value that is harder to articulate.
A doorman appears to hold the door for people coming and going. In New York, he enjoyed talking with the doorman, and a sliding door that detects arrivals and departures would miss the parts of the job that add a lot of value. The simplest visible part of a mathematician's job is proving theorems, including conjectures left open for hundreds of years, like Fermat's last theorem. A mathematician is someone who thinks deeply. Proving old conjectures is a byproduct. The work
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Does Ankur Moitra Feel More Intellectually Lonely?
Ankur Moitra says he might feel more intellectually lonely than before. He feels very excited. The night OpenAI dropped the results was interesting but not entirely unexpected, because for weeks there had been rumors about the two biggest problems in his areas, the Unique Games conjecture and RL equals L, plus rumors about matrix multiplication. His first reaction was that it was all true, and he was glad the work was finally public so people could go through it, process what happened, and figure out what to do next.
The feeling changes on a daily basis. The biggest feeling is being pulled in two very different directions. His work has always been about asking the right questions, and the t