Machine learning researcher at @GoogleDeepMind & mathematician. Host of The Cartesian Cafe podcast. All opinions are my own.
London, England
Joined May 2017
- Tweets1.8K
- Following478
- Followers12.5K
- Likes1.9K
Pinned Tweet
Quantum field theory textbooks have been lying to you or have left you confused. For a typical passage like the following from Peskin&Schroeder - what does it mean to do a change of variables on an ill-defined path integral? For perturbative QFT, my paper resolves this issue: 🧵
Extraordinary to see the validity of the largest mathematical result finally certified. The classification of finite simple groups, whose proof spans tens of thousands of pages, is not something you want left to the authority of experts that will not be around forever. Michael Ashbacher was my first math mentor when I was an undergrad at Caltech. Glad that he and others are able to witness today's achievement!
This is jaw droppingly insane. Three new breakthrough results across the board:
1) Harmonic analysis results superceding that of this year's Fields medal (in particular, Kakeya conjecture in every dimension, not just three)
2) Existence of pure Yang-Mills in dimension four. A large part of the Millenium problem (though mass gap still needed).
3) And finally, a subexponential algorithm for 3-SAT upends hundreds of conditional hardness bounds in fine-grained complexity. (However, it doesn't settle P vs NP and because general polynomial reductions blow up instance sizes, the current bound does not make all NP complete problems subexponetial.)
What an insane time for the mathematical sciences.
We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
openai.com/index/building-sc…
Timothy Nguyen retweeted
We're also hiring Student Researchers in the Frontier Computation team @GoogleDeepMind, to work with @re_rayne & @IAmTimNguyen!
Areas of interest: agentic optimisation, learning algorithms/simulations, OOD generalisation, AI4Physics, CFD, numerical math.
Applying details below!
Come join my team at @GoogleDeepMind, where we are working on a variety of open-ended problems related to security, sparse computation, agent-guided optimization, and more! We are targeting hires at the L4 level so yes, junior researcher roles still exist. Details:
My team @GoogleDeepMind is hiring! We are seeking a Research Scientist to rigorously study the internals and generalisation of frontier AI systems, w/ a particular view to AI security.
This is an in-person role at our Platform 37 office in London 🎡
Link to apply in thread 👇
Would love to know how the @arxiv moderators let this one through: arxiv.org/abs/2209.01890
Timothy Nguyen retweeted
I’m excited to announce that I will be working at the Mathematical AI Safety Institute (MAISI) full-time as its founding Scientific Director! This means I will not be joining OpenAI as an employee, though I will still be collaborating with them, and I’m happy to announce that OpenAI will be supporting MAISI. They have offered us $10MM in API credits, and access to their latest models for our research use. Moreover, they will be participating in a multi-lab AI safety workshop we are organizing for next year with other frontier AI labs.
As an independent research institute, we are also in conversations with other labs and AI safety orgs about how MAISI can collaborate with them and contribute quickly to AI safety research across the industry. As we’ve seen over the past few weeks, the need for action on AI safety is extremely urgent. Research is an important part of that, and mathematicians have an important role to play!
Are there any public confessions by senior mathematicians of the form “Had I known during my student days that AI was gonna drop on math like it did on October 6, 2026 I would have become X instead.”? Curious what the values of X are.
I don’t know who it’s from but there’s an adage that goes “you should only do math if you can’t see yourself doing anything else.”
Timothy Nguyen retweeted
While we wait for the OpenAI slop storm, here is some open-source Yang-Mills slop!
github.com/ethanwsussman/Yan…
Ethan Sussman and @__alpoge__ are completing/clarifying Balaban's existence program for 4d Yang-Mills.
For now they have Levent-style slop. The goal is to get a readable PDF and I'm told everyone is welcome to participate. The repo is public.
I'm really enjoying looking at the list of problems openai has solved. What a rare panoramic view of math. It's like a new planet was discovered and all its artifacts got curated and put into a museum. Exciting times! Though personally, I'm still waiting for the day AI can do something open-ended like find a mathematical rigorous unification of quantum field theory and general relativity.
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
Timothy Nguyen retweeted
Amélie Loher and I are releasing skill files for writing math research articles.
The purpose of these skills is to take LLM slop-written papers and de-slop them while at the same time checking for mistakes and improving exposition.
You can start either from (i) a proof outline in some format (but no paper), or (ii) an existing draft of a paper.
There is also a separate set of skills for writing a "visual paper" (a webpage for the paper with extra explanations, illustrations and animations). It takes a paper and builds a webpage for you.
Timothy Nguyen retweeted
I wonder what @GaryMarcus thinks of this bet now. It was in a thread originated by @MCHammer that seems to be deleted, but I saved the screenshots back then.
A beautiful and poetic take on why you should be excited about the AI disruption in math:
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…
A sober reflection on how the math community ought to be responding to the impact of AI:
"We face the daunting task of continuously recreating our institutions as capabilities evolve.... Above all, we need to reevaluate our identity. What is it that makes mathematical knowledge and research valuable? ... What are we offering society, and how much of it survives in a world where models match or exceed humans in some or all relevant mathematical skills? ... Now that the deal needs to be renegotiated, we should approach it with humility rather than entitlement."
theorydish.blog/2026/09/29/s…
Timothy Nguyen retweeted
My utility as an individual AI researcher will be gone in a year.
Writing math proofs will be automated even sooner.
It was never about proofs.
Science is about curiosity, creativity, and compression - via @SchmidhuberAI
*Mathematicians Should Become Formal Theory Influencers*
Mathematicians were the original influencers: they created conjectures and theories that others understood, cited, and built on.
Difficult proofs often reflected deep understanding. But the proof itself was rarely the point.
Frontier AI can already generate informal proofs much faster than humans can carefully inspect them. The scalable response is machine-checkable mathematics in systems such as Lean.
AI-generated formal proofs may increasingly resemble compiler-generated machine code: essential, but rarely worth reading or writing by hand.
That shifts mathematical work up the abstraction stack.
Mathematicians become formal-math software engineers, working with AI on clean definitions, interfaces, key theorems, and reusable libraries rather than low-level proof details.
Call everything derivable from a formal library within a fixed compute budget its mathematical halo.
Humans and AIs should compress clusters of results into insightful, useful theories that expand the halo further.
A great theory compresses many results, makes future results cheaper to derive, and exposes structure that humans and machines can understand and build on.
That is why minimum description length is a useful lens on mathematical insight.
Frontier math will eventually require huge compute budgets.
At that point mathematics starts to resemble experimental science: scarce computational instruments, with researchers deciding which problems deserve them.
Mathematicians and AIs should create conjectures and theories that expand the mathematical halo.
Mathematics should become an enormous machine-checkable software project.
*Become a Formal Theory Influencer*
Inspired since 2010 by:
people.idsia.ch/~juergen/art…
Timothy Nguyen retweeted
Karthik Viswanathan -- a theoretical physics PhD from the university of amsterdam, and now an AI safety researcher -- has prepared a super useful list of resources for anyone who is considering a similar transition:
karthikviswanathn.github.io/…
Timothy Nguyen retweeted
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…
Timothy Nguyen retweeted
In light of the progress in mathematics, we at Edison Scientific and FutureHouse have assembled a set of Millennium Problems for Biology. They are chosen to be very hard to solve but very easy to validate in a simple laboratory environment. Any of these, if solved, would mark a major advance in biotechnology, and most of them would contribute materially towards curing disease. These are, in some sense, the “last reasonable eval” for AI in biology. This was work primarily by @MichaelaThinks and myself, with contributions from many others.
Short descriptions below. The full descriptions of the problems with acceptance criteria are at the Bio Millennium Problems website, linked in the next post. Share more if you have ideas. If they meet our criteria, we’ll add them to our list (with attribution and permission).
