szegő assistant professor of mathematics @Stanford
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This recent interview with @scottnarmstrong is well worth a watch:
piped.video/watch?v=NaAkLIrQ…
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I have been waiting for this moment since 2019 as a grad student. It took me a much longer time to realize that most mathematicians didn't see what I see ahead for us.
Disruption without a replacement leaves a vacuum. But a definite vision for the future breathes in fresh life, and the next step is clear:
We are poised to translate all known math into formal code.
x.lingyaoai.com/jdlichtman/status/2097…
Reading all those recent beautiful essays by Terry Tao, Kevin Buzzard and @wtgowers, I could not resist, but write up my deeply personal perspective on how I perceive and see things:
docs.google.com/document/d/e…
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Jared Duker Lichtman retweeted
Reading all those recent beautiful essays by Terry Tao, Kevin Buzzard and @wtgowers, I could not resist, but write up my deeply personal perspective on how I perceive and see things:
docs.google.com/document/d/e…
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Jared Duker Lichtman retweeted
Another interesting perspective, from someone whose predictions about maths and AI have aged better than pretty well everyone else's.
Reading all those recent beautiful essays by Terry Tao, Kevin Buzzard and @wtgowers, I could not resist, but write up my deeply personal perspective on how I perceive and see things:
docs.google.com/document/d/e…
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This is also what I was expecting, but this term I've had students at all my office hours so far!
Talked to a Stanford prof last night who told me that AI has led to students all acing all the homeworks, never showing up to office hours, and then failing the final exams in-person.
So in response the department is changing the TA's purpose, by eliminating office hours and requiring students meet with TAs 1:1 and walking them through each coding assignment to demonstrate they actually understand what's going on in the code.
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Jared Duker Lichtman retweeted
I used GPT-6 Astra to break an unsolved cipher to one of Napoleon's generals that had gone unread for 217 years.
What makes this impressive isn't actually the codebreaking, but that Astra completed the entire multi-modal workflow in ~6 hours from a single image and goal.
1/6🧵
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The people want to see @JensenHuang debate @BillGates on AI
I appreciated the opportunity to speak with @ezraklein at length about the state of AI. I believe the world isn't awake to the dangers of this technology and the choices humanity has to make. AI will either be the greatest tool for opportunity and equality we've ever seen—or the cause of immense, unprecedented harm. Which way things go is up to us. b-gat.es/4AFZZqC
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The people want to see @JensenHuang debate @BillGates on AI
Tomorrow on the show: @JensenHuang, the CEO of NVIDIA, who thinks A.I. fear is getting way out of hand.
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New Numberphile video on Navier-Stokes:
I find Brady here a breath of fresh air
piped.video/watch?v=Mzbtj5nk…
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We are entering the era of hardening our systems,
in this case the mathematical literature!
A touching development!
A 1989 landmark paper Wilczek, Witten and Halperin with PhD student Yi-Hong Chen featured what they called “something of an embarrassment": a violation of current conservation.
Claude has now found the source of the error--a dropped factor of 2!
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It's happening
Two years ago I argued we needed an autoformalizer.
Now the time has come to formalize all of mathematics.
We need to unite behind a single Mathematics Autoformalization Project that turns all known mathematics into one Lean library.
@jdlichtman @patrickshafto
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Jared Duker Lichtman retweeted
Two years ago I argued we needed an autoformalizer.
Now the time has come to formalize all of mathematics.
We need to unite behind a single Mathematics Autoformalization Project that turns all known mathematics into one Lean library.
@jdlichtman @patrickshafto
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Jared Duker Lichtman retweeted
Sept 4 (Friday of Labor Day weekend): FLT formalization announced by Anthropic
Sept 7/8: Tristan+Levent -> OpenAI announce Navier-Stokes
But somehow amidst all the commotion, we all seemed to have missed the following (!!!).
Sept 6: Lech Mazur claims an AI-generated proof that a positive proportion of numbers go back to 1 under Collatz!! And it's Lean-formalized. I went through the Lean (or rather, had my AI do it) and I think it's right. Now I'm trying to make sense of the math (doesn't look like anything is too hard, just a lot of arguments, building on top of Terry's earlier work).
Naoufal El Jaouhari, an Applied Maths Engineer based in Paris, wrote to me a few days ago that he'd gotten his AI to formalize the same proof for 3x-1 building on Mazur, which led me to look at Mazur.
Now I'm working on a "digestion" of all of this. Weird wild stuff!!
ANNOUNCEMENT: An AI milestone on one of maths' most famous unsolved problems: COLLATZ.
For every sufficiently large X, at least cX positive integers n < X reach 1 within 10.46 ln(n) ordinary Collatz steps, for one fixed c > 0.
Previously, lower bounds such as X^0.84 and X^0.90 left open whether the proportion of starting values reaching 1 could tend to zero.
Lean-formalized (42k additional lines), building on earlier formalizations of almost-boundedness (Tao) and its natural-density extension.
Developed primarily by AI agents using the ProofAtlas.ai harness and Codex, with some high-level guidance from me (which may or may not have helped).
Paper: proofatlas.ai/papers/positiv…
Formalization: proofatlas.ai/formalizations…
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The fact of our current moment is:
remarkable AI capabilities, along with modest job & economic impact
Graeber vindicated?
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Jared Duker Lichtman retweeted
Claude corrects puzzle from famous Witten, Wilczek, and Halperin 1989 paper on high-Tc superconductors.
In my experience, GPT and Claude have superhuman capability in theoretical physics as well as math now. 🦾🧠😱
An extremely instructive development in the use of AI in theoretical physics just emerged from the University of Chicago, thanks to Dam Son-- everybody and anybody seriously interested in theoretical physics should read this and ponder its implications
home.uchicago.edu/dtson/pape…
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Jared Duker Lichtman retweeted
home.uchicago.edu/dtson/pape…
Really awesome result from Son+Claude. I could not find the error during my PhD. Turns out they lost a factor of 1/2 🫠
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I remember having a deep discussion with Ben Chow last year:
He was worried he wouldn't complete the Poincaré project in his *lifetime*.
I told him it would all be in range in a year, but he didn't believe me. Now he's led a team to complete the project in a 2-week sprint
Congrats!!
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Amazing result!!
The Poincaré conjecture is now formalized in Lean
With Ben Chow, Yuan Liao and Ziyang Qin, we have completed a full Lean formalization of the Hamilton-Perelman proof of the Poincaré conjecture!
The proof is around 4.7 million lines of code, written in roughly two weeks. Grateful to the @DARPA expMath program for its support!
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