number theorist, szegő assistant professor of mathematics at @Stanford
Joined July 2024
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Update on Erdős Problem 1196:
In joint work, we refined and adapted the proof method from GPT-5.4 Pro to give proofs of several additional problems. This includes another 60 year old conjecture by Erdős, Sárközy, and Szemerédi.
A proof is valued not just by the problem it solves, but by what new avenues it opens up. This is perhaps one of the first examples of an AI-generated proof having downstream impacts, which we are still exploring.
We are announcing the result today at the Future of Mathematics Symposium (see links below)
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Jared Duker Lichtman retweeted
May 28
It's really important here that one is working in a number field of arbitrarily large degree.
I personally still believe in the original sum-product conjecture over the integers.
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Jared Duker Lichtman retweeted
AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried.
openai.com/index/model-dispr…
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May 19
All Future of Mathematics Symposium talks are now available on Youtube, linked below.
Panels:
Formal and Informal Methods - Freedman, Barrett, Abouzaid, Haskell
AI for Mathematics - Arora, Brown, Luong, Vakil
Fields & Roundtable - Tao, Viazovska, Vakil, Haskell
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May 19
Formal and Informal Methods - Freedman, Barrett, Abouzaid, Haskell
youtu.be/SNKlwARCtkk.
AI for Mathematics - Arora, Brown, Luong, Vakil
youtu.be/hjh4IfJDeN4.
Fields & Roundtable - Tao, Viazovska, Vakil, Haskell
youtu.be/78Rjdz1SPYM.
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May 19
All Future of Mathematics Symposium talks are now available on Youtube, linked below.
Day 2 talks:
Sébastien Bubeck, OpenAI
Sanjeev Arora, Princeton
Terence Tao, UCLA
Thang Luong, DeepMind
Maryna Viazovska, EPFL
Sergei Gukov, Caltech
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May 19
Sébastien Bubeck: Probability, combinatorics and optimization from GPT-5 to GPT-5.5
youtu.be/YlFV45lsPoU.
Sanjeev Arora: Rethinking thoughts - Power of self-reflection for AI (and humans)
youtu.be/j22Iz0ked-4.
Terence Tao: New mathematical workflows
youtu.be/Uc2zt198U_U.
Thang Luong: Towards AI Superhuman Reasoning- from neuro-symbolic to foundational models
youtu.be/MNVo14pIMo8.
Maryna Viazovska: Formalizing the sphere packing problem
youtu.be/lcgPj7hge-E.
Sergei Gukov: AI tools for long-horizon, sparse-reward tasks
youtu.be/jJOMZ3LPbVs.
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May 19
All Future of Mathematics Symposium talks are now available on Youtube, linked below.
Day 1 talks:
Leonardo de Moura, Amazon
Clark Barrett, Stanford
Michael Freedman, Harvard
Kevin Buzzard, Imperial
Andrea Bertozzi, UCLA
Adam Brown, DeepMind
Deirdre Haskell, Fields Institute
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May 19
Leonardo de Moura: Machine-Checked Mathematics in the Age of AI
youtu.be/objFfoJRH_U.
Clark Barrett: CSLib - Building a Platform for AI-assisted Formal Verification in Lean
youtu.be/txRvy9hv52M.
Michael Freedman: Compression Is All You Need - Modeling Mathematics
youtu.be/4nM82nZzIxU.
Kevin Buzzard: On Autoformalisation
youtu.be/etZzn1Q7is0.
Andrea Bertozzi: A foray into AI for Mathematics
youtu.be/bx4BfuVFaPg.
Adam Brown: A.G.I. and the Future of Reasoning
youtu.be/gf1uwCH0HUU.
Deirdre Haskell: Mathematical AI at the Fields Institute
youtu.be/8lcHpsuIsOM.
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May 13
The Future of Mathematics Symposium keynotes from Fields Medalists:
Terence Tao, Maryna Viazovska, and Michael Freedman
Now available on Youtube, links below.
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Agree completely:
Regardless of what actually transpires in the coming years, there is already sufficient evidence that the mathematical community must start planning now on how to adapt to potential futures.
But if AI mathematics continues to progress at anything like its current rate -- which is what I expect to happen -- then we will face a crisis very soon, and mathematics departments, who owe a duty of care to their students, should be urgently preparing for it.
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Jared Duker Lichtman retweeted
May 3
This symposium was historically significant. I enjoyed listening in.
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Jared Duker Lichtman retweeted
May 3
Thanks for organizing, Jared! Great event!
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Thank you to everyone coming out to attend the Stanford Future of Mathematics Symposium, along with those watching the livestream!
The event was announced at the last minute two weeks ago, yet we received over one thousand registrants, and three thousand viewed the talks on YouTube.
The Symposium was absolutely buzzing with excitement. To our excellent group of speakers and panelists, you made it a truly remarkable event. These discussions are of vital importance to the mathematical community.
Finally, thank you to the staff and donations that made it all possible.
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The full livestream is available for the public on Youtube:
youtube.com/@FoMathematics
Videos of the individual talks coming out in the next couple weeks!
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Update on Erdős Problem 1196:
In joint work, we refined and adapted the proof method from GPT-5.4 Pro to give proofs of several additional problems. This includes another 60 year old conjecture by Erdős, Sárközy, and Szemerédi.
A proof is valued not just by the problem it solves, but by what new avenues it opens up. This is perhaps one of the first examples of an AI-generated proof having downstream impacts, which we are still exploring.
We are announcing the result today at the Future of Mathematics Symposium (see links below)
25
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201,906
The paper will appear on arXiv next week.
Watch the talks here: youtube.com/@FoMathematics
Symposium further information: events.stanford.edu/event/fu…
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The Future of Mathematics Symposium is being held on May 1st-2nd!
We have a truly exceptional group of speakers, with multiple Fields Medalists including Terence Tao.
Tune in for livestream 9am-5pm PST (link below)
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Watch the talks here:
youtube.com/@FoMathematics
Symposium further information:
events.stanford.edu/event/fu…
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