AI Research@Quant Trading | Crypto Trading | Let's build AGI Ex-Engineer@Bytedance, Meta (PyTorch) | Alumni@JHU | Alumni@UMN-Twin Cities
Shanghai, China
Joined March 2014
- Tweets3K
- Following857
- Followers103
- Likes1K
Cuiqing Li retweeted
BREAKING: OpenAI’s solution to Navier–Stokes does not match its Lean verification.
The most important article to read today is not one of OpenAI’s 700 AI-generated math papers.
It is this other paper, making a deep and worrying point:
A Lean-verified proof does not automatically validate the proof written in natural language, nor does it mean that the formal statement captures the intended theorem.
During translation, an AI can change an assumption, weaken a statement, or replace the argument entirely.
It can hallucinate another theorem.
Lean correctly verifies the result.
But the proved result may no longer be what the paper claims.
This is a general problem. Things get spicy when the authors examine OpenAI’s proposed Navier–Stokes solution.
They identify at least two mismatches between the written intermediate results and their Lean counterparts:
One estimate claims that four additional input derivatives suffice. The Lean version requires five: a weaker result.
A pressure-flux estimate is obtained through a different bound, and proved through a different argument.
It is not clear whether these mismatches invalidate the entire proof.
But they raise an important issue.
OpenAI is flooding us with claimed revolutionary breakthroughs. Yet nobody knows whether the proofs are correct or whether they prove what they claim to be proving.
Epistemia at scale.
*
Paper in the first reply
Cuiqing Li retweeted
Harvard math professor Melanie Matchett Wood has joined an independent group of nine mathematicians that will advise OpenAI and other AI companies on how to responsibly release mathematical results. #harvardmath thecrimson.com/article/2026/…
Cuiqing Li retweeted
New on the Science Blog: Yes, Claude can do Nine Loops.
Theoretical physicists predict how particles behave using formulas called scattering amplitudes. These are notoriously hard to compute, so researchers work with layers of increasingly fine corrections called “loops”—each added loop makes the answer more precise but takes exponentially more computation. Most calculations stop at two or three loops. Eight loops was the previous record in a simplified model physicists use as a testing ground (planar N=4 super-Yang-Mills), set by SLAC's Lance Dixon and collaborators.
Last month, physicist and science writer @4gravitons issued a challenge: could an AI push past eight loops in this model, using only the compute budget an academic could reasonably access?
Given a single prompt describing the nine-loop problem, Claude ran largely unsupervised for days in Claude Science and solved it using methods developed by Dixon and his colleagues, at a total cost of a few thousand dollars. Dixon independently verified the result, and von Hippel wrote about the experience for our blog.
Read more: anthropic.com/research/yes-c…
Stable singularity of the Euler equations on R^3 terrytao.wordpress.com/2026/…
Cuiqing Li retweeted
I'm incredibly excited to announce the founding of the Mathematical AI safety Institute (MAISI) maisi.org/. AI safety needs more foundational theoretical development, and mathematicians have the skills and the mindset to help! MAISI is an independent institute with visiting positions ranging from 1 semester to 2 years. Our goal is to get mathematicians up to speed and working on research directions in AI safety as quickly as possible. There is important work to be done, and there is real progress to be made. YOU can help!
Applications are open now! MAISI is aiming to hire 10-30 mathematicians to join us in the Bay Area by January, and scale up to 30-100 for September 2027. If you're a mathematician interested in channeling your skills toward the most important problem of our time, please apply today! maisi.org/apply
Cuiqing Li retweeted
Oops looks like the link was broken. Let's try this again: andrejristeski.github.io/107…
The first set of notes, "PDEs 101" for ML researchers is up: andrejristeski.github.io/107…
Includes a derivation of few "model organism" PDEs (heat eq, advection, Poisson), the strong/weak/variational formulation & basics of numerical methods (finite diffs/elements, exp+imp Euler)
Cuiqing Li retweeted
1/ A major breakthrough on the Riemann Hypothesis recently shocked the world: >67% of zeta zeros lie on the critical line and are simple.
Now Youness Lamzouri has found a strikingly elegant new proof.
And AxiomProver has already formally verified it, in his paper’s appendix.🧵
Cuiqing Li retweeted
I am teaching a new class this semester on "AI for scientific computing". The idea is to cover topics around learned surrogates for scientific computing with applications to PDE solving, forecasting, sampling, and selected downstream applications. andrejristeski.github.io/107…
Cuiqing Li retweeted
This "recurrent depth" is essentially what's in Sec. 5.3 of the 2015 paper: On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models arxiv.org/abs/1511.09249. This paper went beyond the inefficient millisecond by millisecond planning of my 1990 neural world models, addressing planning and reasoning in abstract concept spaces. The 2015 control network C is a prompt engineer that learns to create a chain of thought: to speed up decision making, C learns to query its separate neural world model for abstract reasoning. The prompts and the answers are internal self-generated sequences of vectors that don't have to represent natural language.
OpenAI’s Astra AI uses a new reasoning approach called “recurrent depth.” Though it can help model costs and performance, researchers are concerned bc it obscures a model’s thinking process, making it more difficult to monitor.
w/ @amir @rocketalignment
theinformation.com/articles/…
Cuiqing Li retweeted
Announcing that GPT-6 Astra has pushed the prime gap to 186, with Lean formalization!
I was 9 when I first heard the twin prime conjecture. Its elegance and Yitang Zhang’s legendary story have always stuck with me. A truly surreal night, being the first to see our model make progress, pushing 246 all the way down to 186, on a problem I’ve revered since I was a kid.
For me, it felt like witnessing a new era of intelligence being born, made possible by everyone at @OpenAI!
Cuiqing Li retweeted
I tested GPT-Astra on mathematics. It's a quantum leap. You can talk with the model and prove the statements live in Lean. The feeling is absolutely stunning. You can verify your ideas, compile truth. For a mathematician it feels like finally we arrived in the era where we can focus entirely on the ideation and exploration. Each lemma flows once the logic is set. Before the verification was lagging behind but Astra is very fast and for many tasks the formalization happens as you write your argument in Codex.
If you tell the model to use literate programming + LaTeX you end up with your proof combined with the Lean code, everything explained as you wrote, mixed with small chunks of Lean which are digestible.
I don't want to go back to the era where the only confirmation of the proof was "aha". Now the "aha" is followed by a green tick that indeed tells you that you have captured the essence. Imagine how cool it will be to have all the lemmas of the world combined in one giant database, pointing to people and models who found them. You compose and mix your ideas and build on the shoulders of the giants. But you see much further now and build much faster. And we are just at the beginning of those changes. So much work to do, so much fun!
GPT-6 Astra is here! This is a big moment for our research team - years of work on pretraining, reinforcement learning, and post-training have come together in our most capable and aligned model yet. It can build and test software, work across apps on your computer, and even help you take a crack at open scientific problems!
Capabilities that felt like grand challenges a few years ago have become tools people can actually use. One example is Computer Use - if you’ve tried this before and felt like it was too slow or not good enough, I encourage you to give it another shot. We’ve come a long way since Operator, and it “just works” now.
We’re also asking these systems to act on your behalf for more consequential work. Agents needs to stay aligned with your goals and values, think transparently, and respond to oversight even when tasks become difficult. We’ve made substantial progress on these behaviors in Astra, alongside stronger monitoring that can stop potentially unauthorized actions. That work is part of what makes this release possible.
I think alignment is one of the most important research frontiers in AI, and it remains far from solved. Our ability to understand and align models has to keep pace with model capabilities. We want to give people more room to think, build, and discover with increasingly powerful tools that remain *under their control*.
Huge thanks to the researchers and teams who got us here. There’s a lot more work ahead, and I’m incredibly excited about what we can make possible in the near future!
Cuiqing Li retweeted
FreeToken is fast. Comparing to Ollama, we have 3–4× faster decode, and 6–30× faster prefill
How? We introduce bandwidth-adaptive CPU–GPU execution + semantic-aware caching across agent turns.
More details in the technical report: arxiv.org/abs/2608.16157
Cuiqing Li retweeted
I found this short writing by Peter Sarnak on AI in math an extremely interesting read (even if I don’t completely agree with it). What do you think?
ams.org/journals/notices/202…
Cuiqing Li retweeted
😊 I also just uploaded a new version of the lecture notes. cs229.stanford.edu/main_note… (it's still, and perhaps will always be work-in-progress, given the field is moving fast. Any mistakes are mine :) and any feedback is more than welcome :).
Instead of watching 2 hours of Netflix tonight, watch this Stanford lecture. It’s the clearest end-to-end explanation I’ve seen of how ChatGPT and Claude are actually built.
From tokenization and BPE all the way to the transformer architecture, training pipeline, and next-token decoding.
Whether you’ve never written a line of AI code or you’ve been shipping agents every day, this 2h 34min session will click things into place that most people take years to figure out.
Bookmark it and clear the time this weekend, because this might be the single most valuable thing you learn all month.
Cuiqing Li retweeted
The Grothendieck constant is 1.7...!
We are excited to share this breakthrough on a 70 year-old problem discovered through a year-long human-AI collaboration.
We publish both the math and AI setup because academics should shape AI-assisted research to keep it fundamentally human.
Cuiqing Li retweeted
At 16, a German kid tried to read the most famous proof in modern math. He understood 0% of it. So he taught himself years of university math, backwards, just to decode it. Today he is the most influential mathematician alive.
His name is Peter Scholze.
The proof was Andrew Wiles cracking Fermat's Last Theorem, a puzzle that had stood for over 350 years. A teenager had no business opening it. Scholze opened it anyway. In his own words: "I understood nothing, but it was really fascinating."
Most people would close the book. He did something strange instead. He worked backward. He took what he couldn't understand, found what he needed to learn to understand it, and chased that, over and over, all the way down into the foundations.
He says he never really sat down and learned the basics, not even linear algebra. He just absorbed them while hunting bigger things.
It worked at a level that sounds made up. He became a full professor in Germany at 24, the youngest in the country's history. At 30 he won the Fields Medal, the closest thing math has to a Nobel. His ideas reorganized entire fields in under a decade.
Now he is doing something bolder than solving problems. He is quietly rebuilding the foundations the whole subject stands on.
He recently stood in a German lecture hall and tried to explain that rebuild to a room with no math degrees. The talk is free on YouTube.
A boy who understood nothing at 16 grew up to rewrite the floor under everyone else.
Cuiqing Li retweeted
"The Simple Mathematics of Large Language Models" is a concise free paper if you want to understand the mathematics behind modern LLMs and systems such as ChatGPT and Claude.
I have shared several resources in the past that explain the mathematics behind these systems in detail, but they are often quite long. This paper is only about 20 pages, so I think it is a useful resource if you want a compact introduction without starting from a much larger textbook.
It covers token representations, context, attention as learned weighted averaging, projections and bilinear forms, multi-head attention, normalization, positional information, softmax, maximum likelihood, cross-entropy, and gradient descent. Together, these topics give a concise mathematical picture of how a language model works.
Save it to your bookmarks. It can be useful as a quick reference.
crc.business-school.ed.ac.uk…
Cuiqing Li retweeted
1 of the greatest mathematicians in the world found out his own famous proof was wrong. It had been accepted for years, only because everyone trusted his name.
His name was Vladimir Voevodsky. He had already won the Fields Medal, math's version of the Nobel Prize. He was a legend. When he proved something, people believed it.
So when another mathematician quietly pointed out a serious mistake in one of his big papers, almost nobody listened. Voevodsky himself brushed it off. He was too respected to be wrong.
But years later, he checked again. And the other man was right. His celebrated proof had a hole in it the whole time.
It broke something in him. He later called it the greatest failure of his life. And it forced him to face a scary truth about his entire field.
Math, he realized, runs on trust. Proofs get so long and complex that almost no one fully checks them. People just believe the famous names. And famous names are sometimes wrong.
So he stopped his old research and spent the rest of his life building a new kind of math, one where a computer checks every single step, so no proof can ever hide behind a reputation again.
He died suddenly in 2017, at just 51.
The lesson he left behind is unsettling. A lot of what we call "proven" was really only "trusted."
Cuiqing Li retweeted
We live in a multimodal world. We see, talk, act, and dream.
Yet most LLMs still start with language pretraining. Why not train them natively with multimodal I/O from scratch?
Because it’s SUPER HARD, adding modalities triggers training instability, design complexity, and often modal competition
So what’s the path forward?
Introducing: Towards Physics of Multimodal Pretraining (junlinhan.github.io/projects…)
We unpack the underlying mechanics of multimodal pretraining across 4 aspects: Knowledge Flow, Modality Synergy, Early Unification, and Recipe.
Cuiqing Li retweeted
Fields Medalist Jacob Tsimerman knows MUCH MUCH more about math than I do, or ever will, but I have been studying natural and artificial intelligence for 40 years, and I think his prediction here (“AI systems have already solved many important conjectures on their own, and very soon, I think they'll become robustly better at the rest of what we do too”) will turn out to be wrong.
At least in the near term (“very soon”), I expect that AI math will
- struggle in developing new theories
- struggle in writing clear, understandable proofs
and not be superior to the best human mathematicians in either respect.
If he is willing to commit to what he means by “very soon”, perhaps we can make a public wager about this?
I am willing to abide by any judgments in either direction that Terence Tao renders.
