Diffusion models have a fundamental flaw: when trained on real-world noisy data, they just learn to perfectly generate that exact noise. We found a way to fix it. Introducing Manifold Attracted Diffusion (MAD), accepted at ICML 2026 🧵

Claude Opus 5.5 writes a fugue in the style of Bach. I called Astra’s fugue the most impressive musical feat I’d ever seen from an LLM, and this is just as good. The circle-of-fifths sequence beginning at 1:13 is beautiful. The interplay of voices is natural and satisfying. LLMs are getting to the point where their music is good enough to listen to for pure enjoyment.

A year ago, these predictions would have seemed unimaginable: - No more conferences devoted to specific open problems. AI solves them before the conference starts. - No more NSF proposals centered on solving open problems. AI solves them before the grant ends. - Most mathematicians shift toward applied mathematics and mathematical modeling. Taking measurements and comparing predictions with reality still require human involvement. - Then humanoid robots enter the picture. They take the measurements and start building more of themselves. What happens after that is unclear. I expect all of this to happen. The uncertainty is the timeline, and it may be shorter than we think.

I am a mathematician but I avoided commenting on this because the problems are (far) outside my domain. Even if I sat down to read the technical details (which I have not), it would be hard to appreciate the context of prior work, etc. But I've gotten enough sense of things through colleagues to be confident about some aspects. First of all, all the mathematics is fundamentally correct. How impressive are the results? There is a spectrum of reactions (as with everything), but the consensus seems to be all the results could realistically land (by prior standards) in the very highest tier of publications, e.g., Inventiones for the math papers and "Best Paper Award" at STOC for the TCS papers. What does this mean practically? Prior to 2026, a Ph.D. student whose only result was one of these 10 would likely land an interview for a tenure line job at a strong university. For some of the results, you could probably replace "tenure line" with "tenured". When Astra comes out, it will clearly be very disruptive to the existing system. I think it's good that the community has the time to react and prepare. Personally I think we should totally overhaul hiring and publishing practices. Are the results "Fields Medal Level"? I have not heard a mathematician answer Yes to this, and the quoted reason is invariably that the solutions are very clever and beautiful but not "deep". This is consistent with what I can see from a cursory glance. However, the same criticisms could be levied at certain human generated works which have won major prizes. Ultimately, comparing results is very subjective and also somewhat political, and I absolutely think that if a human had one of these results, and also the right influential senior advocate, then that advocate could make a strong case for the work to win major prizes. The fact is that most mathematicians, including prize committees, don't have the breadth or time to evaluate all the top results, so they rely on proxies for importance like: Is the problem longstanding? Is it famous? Was there a large community of people actively trying to solve it? For e.g. #3 (existence of non-sofic groups), the answer to each of these questions is undoubtedly Yes. I've always felt that people should pay less attention to these proxies and focus more on the actual mathematics; glad to see that is happening with the AI solutions, but the same standards should then also be applied everywhere.

Mathematicians having Deep Blue (for chess) and AlphaGo (for Go) moment now. Chess hasn't disappeared. Chess players leverage AI chess systems to improve. Same will happen to mathematicians. They'll tacked increasingly ambitious achievements, using AI to assist them.

I suspect math will be like Chess and Go due to verifiability. The period of fruitful collaboration between humans and AI will be short (i.e. a few years or less, not a decade). Progress in math will be jagged, with harder to formalize fields coming last, but I suspect this jaggedness will be compressed in time -- I expect superhuman performance at (nearly?) all areas of math within a few years (a few = 2-3?). AIs will also be better at asking pure math questions than humans, and will quickly develop theories beyond human comprehension. Human theorists will have a recreational comparative advantage over other humans in understanding these theories, but AIs will be better at communicating these theories to applied researchers. Pure mathematicians will need to become applied researchers to do productive work, until applied research is also automated. Confidence level for prediction: 50-65% for gist, 40-50% for all above claims being correct.

Of >105,000 participants with 30-year follow-up, only 9.3% achieved healthy aging (age 70, w/o any chronic diseases). Their diet was significantly associated with this outcome🧵 @NatureMedicine