Math prof. Author of long-form textbooks on proofs (amzn.to/3oZrMNu), real analysis (amzn.to/2kjvMwh) & math history (a.co/d/8pLSo0C).
Sacramento, CA
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🧵 My 3rd book is now out! It is on the fascinating history of math.
How did people throughout history think about math?What problems did they care about? How did they express them? How were they solved?
This book includes a lot of historical math.
a.co/d/gsoNKxP
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Jay Cummings retweeted
I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here:
cmsa.fas.harvard.edu/aimathp…
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Jay Cummings retweeted
I was invited to be an editor to this book and I was happy to contribute to this edition. This is the type of writing that can not be automated, because it has soul in it.
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A few weeks ago I came across this too. I spent a week going through it writing my own version of Astra’s proof.
First takeaway: It was fun! Very cool theorem, and quite enjoyable to wade through Astra’s (imo not great) proof and find a version that I like.
It was also a good exercise in what lots of future math scholarly work might look and feel like.
I plan to put out a YouTube video of it next week.
A few weeks ago Astra gave a stunningly simple proof of the Erdős-Sós conjecture in graph theory (previously thought to be very difficult).
It has been a good example of how the lifecycle of AI proofs should be: after the AI formalisation posted at erdosproblems.com/548
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Jay Cummings retweeted
Look what arrived today. Wanted to read this for a while. @LongFormMath
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Jay Cummings retweeted
Breaking math news: The first-ever 3D Einstein tile, an object that tiles space in a never-repeating pattern, has been found by independent researcher Ioannis Tsiokos using GPT Astra. Resembles a chair. Mathematicians have de-slopped the proof. @kkakaes: quantamagazine.org/updates/t…
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Each paper is converted to a numeric code.
Each paper’s coded text must appear somewhere in the digits of pi.
Just need to know which digit position to start reading.
To learn that position, mathematicians have to solve a sequence of riddles.
This is where MrBeast comes in.
The riddles are hidden inside 100 locked safes scattered across math department libraries around world.
To get into each safe, a top mathematician needs a solve a basic arithmetic problem in less than 10 seconds while standing at the front of a lecture hall being watched by all their colleagues.
Only 20 tries and then you’re locked out forever.
Once inside, you get the riddle, right?
Wrong. This is when Stage 2 begins.
This advisory group created by IAS is advising OpenAI in how to release their math results
Mathematicians can give their opinion in this link
agmai.org
I share publicly my opinion below (more than happy to have debate / disagreements in the responses!)
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Decades worth of “progress” can now be accomplished in 3 weeks using a single model.
The era of theorem abundance is here.
We’re working with an independent advisory group of mathematicians to help OpenAI responsibly share advances in AI and mathematics.
The group will advise on how we assess and communicate new mathematical results, uphold academic and professional standards, and build tools that support mathematical research and learning.
Through this work, we want mathematicians to be at the center of shaping how AI supports mathematical understanding and how its benefits reach the wider community.
openai.com/index/advisory-gr…
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Jay Cummings retweeted
Proof of Sylvesters conjecture (every prime number that leaves a remainder of 4, 7, or 8 when divided by 9 is the sum of two cubes) by my brilliant colleague Ashay Burungale. Unsolved since the 1870s...
arxiv.org/abs/2609.14893
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The Bernoullis were more than a family of mathematicians; they formed a remarkable mathematical dynasty.
Across several generations, Jacob, Johann, Daniel, and others made important contributions to mathematics and mathematical physics during the 17th and 18th centuries, alongside figures such as Newton, Leibniz, and Euler.
Their story also includes one of the most famous rivalries in mathematical history. Jacob and Johann initially collaborated in studying Leibniz’s calculus, but their relationship gradually deteriorated into a bitter and very public competition, with the brothers challenging and criticizing each other over mathematical problems and priority.
Whether this rivalry actually fueled their achievements is difficult to establish. What is clear is that their intense competition existed alongside work of lasting importance, and their family became one of the most influential mathematical lineages in early modern Europe.
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Don’t pick Newton.
As a professor at Cambridge he was required to give periodic lectures but he was so bad at it that often not a single person would show up.
(Being a man of honor, he would lecture anyways—to an empty room.)
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Jay Cummings retweeted
I've written an essay on how I think the mathematics profession should adapt to highly capable AI systems. It's hosted here on "Proofs and Prompts": proofsandprompts.com/2026/09…
though you should also feel free to complain/comment on my website here: daniellitt.com/blog/2026/9/1…
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Around 12 years ago I asked Ron Graham who he thought was the greatest living mathematician. He said, "Well most people would say Tao, and he very well might be, but I'll say Serre."
Jean-Pierre Serre turns 100.
Youngest Fields Medalist ever: 27.
First Abel Prize laureate: 2003.
and still editing Wikipedia.
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If the math profession collapses, I would be depressed enough that I might actually read his novels
JUST IN: Chinese Fields Medal winner Deng Yu announces he’ll retire from mathematics & write romance novels if AI becomes capable of solving all math problems.
Community note
Deng Yu joked on social media that he would write his yuri novel if AI solved all math problems and clarified it was not serious; the post inaccurately frames this as an announcement of retirement and uses "romance novels" for the specific yuri genre of lesbian fiction.
scmp.com/news/china/sci…
en.wikipedia.org/wiki/Yu_Deng
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Jay Cummings retweeted
24 Fields Medalists speak out against "A Severe Misalignment of AI in Mathematics"
mathandai.org/
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“Whew. Big day of math news. But that’s enough math twitter for today. Let’s just flip over to my politics twitter account and see what everyone’s talking about over there—”
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Jay Cummings retweeted
Two heroes of today's Navier-Stokes story are not getting enough credit. Córdoba and Martínez-Zoroa came up with the crucial strategy. Others built on it and, with the help of AI, provided the computations that finished the problem. Thankfully @QuantaMagazine gets this right:
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I...worked on this proof for a year...and...they just…tweeted it out.
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
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Hey check out my SoundCloud
amazon.com/dp/B08TCGLSXM?bin…
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Pretty rare and special to be able to teach my math history class on the same day that math history is made. But here we go!
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
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