Math prof. Author of long-form textbooks on proofs (https://xitter.cf/t.co/YqXnxDmOe0), real analysis (https://xitter.cf/t.co/3IGQ6BIx5Z) & math history (https://xitter.cf/t.co/KkXMGTxCDK).
Sacramento, CA
Joined July 2019
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Jay Cummings retweeted
We want to support the mathematics community in turning progress in AI into deeper human understanding and new discoveries. To support that goal, we are contributing $5 million to a new Simons Foundation initiative to help mathematicians examine, understand, and build on results produced by AI, including the results we recently published.
The funding, managed and awarded by the @SimonsFdn will support workshops, conferences, and special programs. We will also provide access to our models and computing resources to Simons Foundation-supported researchers.
How can the math community forge the best path forward in the AI age? We're committing $15M to workshops and initiatives — plus free AI computing resources for foundation-supported researchers — through new partnerships with @AnthropicAI and @OpenAI: bit.ly/4zpfIbW
#math #science #AI
Jay Cummings retweeted
you could be living in sacramento
you could be sacramentomaxxing
we have the the kings, old sac, the waterfront
you will build your life in sacramento, california
America’s most livable cities, at local median salary and local tax rate.
New York: this is probably the reason why Mamdani won
Readers added context they thought people might want to know
The chart's "most livable cities" rankings and quality-of-life data rely on Numbeo, a crowdsourced site where anyone can submit or alter entries; it carries explicit disclaimers on accuracy and has been widely criticized by experts and media as unreliable.
numbeo.com/common/terms_o…
en.wikipedia.org/wiki/Numbeo
tf1info.fr/international/…
Jay Cummings retweeted
Just getting started on @LongFormMath’s Proofs, already much more lively than how proofs were taught in high school. Looking forward to the rest of it!
Jay Cummings retweeted
10 remarks on AI and math that can be true all at once:
1. The recent progress is stunning and exciting.
2. The Quasi-Riemann Hypothesis is arguably Fields-medal level.
3. Mathematics is being transformed and there is no way back.
4. OpenAI doesn't give a fuck about the future of mathematics.
5. Half-baked unreadable preprints claiming major results can effectively stall mathematical progress.
6. Some mathematicians are responding with naive, overly defensive comments.
7. The social-media wankers framing this as "OpenAI tramples gatekeeping" have no experience of mathematical research.
8. The product of mathematics is clarity and understanding. Not theorems, by themselves.
9. Mathematics is a critical infrastructure of human cognition. The human need for understanding isn't obsolete and it can't be offloaded to machines.
10. We haven't "solved" mathematics and we won't get there before the Sun burns out.
Jay Cummings retweeted
Based on a hot tip: I had Astra check the OpenAI paper "Algebraicity of Weil classes on split abelian eightfolds", and it seems to be flawed. This is one of the nonformalized results. Concerning.
Jay Cummings retweeted
Many staggering results here. But this is a particularly amazing one: the exponent for matrix multiplication is no more than 2.25. The previous world record had been something like 2.37. This leap in progress is like Bob Beamon's long jump.
github.com/openai/math/blob/…
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
github.com/openai/math
Jay Cummings retweeted
Quasi-RH?!?!???! Are you kidding me? If a human did this, it would be an instant Fields Medal, no questions asked.
RH says zeta has no zeros in Re(s)>1/2. The best we had until a second ago was a region that got thinner and thinner the higher up the imaginary axis you go. I thought maybe they’d fatten that up a bit, that’d be a massive breakthrough. But no. They got a zero free strip!!!! Insane
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
github.com/openai/math
Jay Cummings 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…
Jay Cummings retweeted
Junior scholars: "I feel awkward citing myself"
Senior scholars: "as I cleverly argued (1988; 1991), admirably reiterated (1993; 1995; 1996); and handsomely concluded (2001; 2004; 2007)..."
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…
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.
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…
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
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…
Jay Cummings retweeted
24 Fields Medalists speak out against "A Severe Misalignment of AI in Mathematics"
mathandai.org/
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:
Jay Cummings retweeted
Here's Tristan Buckmaster's statement. (You've probably seen bits of it quoted here today, but the whole thing is worth reading.)
cims.nyu.edu/~tristanb/state…
