100% agree on the productivity boost. One just needs patience to correct mistakes, which are more subtle than before imo. I had a nice interaction with GPT-5-pro while proving a convex analysis lemma: arxiv.org/abs/2510.26647 The model didn’t write the full proof, but the interaction was interesting enough for me to write a short report about it. The report illustrates both the productivity gain and the need for careful proof-checking. The model’s contributions are in blue, and the full chat is in the Appendix. You will see my prompts and how I think, so, no judgement please :) The problem itself has an history in optimal transport (see intro) and comes from a question I was discussing with some UCLA math professors last summer. Simpler than @ErnestRyu's recent result imo, but still very useful in optimal transport!

Indeed. But if it was Navier Stokes, the committee would have had to look into it

Okay here is another (certainly less dramatic) "concurrent efforts" story about @icmlconf 2026 outstanding paper awards. Peter’s post below refers to our ICML paper with Khashayar and @sitanch. He raised this point because another ICML paper, “High-accuracy sampling for diffusion models and log-concave distributions” by Chen et al., which independently and concurrently established a result similar to ours, received an Outstanding Paper Award. The story starts on January 15, when we uploaded a paper to arxiv achieving high-accuracy (polylog(1/ε)) complexity for diffusion models. Since Chen et al. are colleagues, they reached out shortly after: "We will soon upload a paper to arXiv with a similar high-accuracy result." We discussed the relationship between the two works and agreed that the papers should be described as concurrent and independent. So they added a section to their paper acknowledging that the two works are indeed concurrent and independent, and then uploaded their paper to arXiv. Then, both papers were submitted to ICML 2026, received identical scores on OpenReview, and were accepted as oral presentations. Chen et al. also received an outstanding paper award for "settling a long-standing conjecture in the theory of score-based sampling" (see the ICML award blog post), namely achieving high-accuracy sampling for diffusion models. Congrats to them! This award is well deserved imo, and their solution is quite elegant. At ICML in Seoul, I was asked several times, "Why didn't your paper also receive the same recognition, since both papers resolved the conjecture independently?" That's why one of the godfathers of our community (not @peter_richtarik) reached out to the committee to ask for the VAR 😂 I will paraphrase the committee's reply because those emails are private. Essentially, they said that it was unfortunate if there had been an omission, but that they could not revisit the decision because the selection process was too complex... Which I understand, since they chose 2 papers out of 6,000+. On the other hand, I hope we can find a way to prevent situations like this from happening again.

yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more. More thoughts here: openai.com/index/ten-advance…

Nesterov wins the Carl Friedrich Gauss Prize 2026 mathunion.org/imu-awards/car… The Gauss Prize is awarded to Yurii Nesterov for his groundbreaking work on mathematical optimization that provided the theoretical foundation and algorithmic backbone for many numerical and data-driven fields, enabling practical computations that were previously too time-consuming to be feasible.

Nice @AdenIshaq!!

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)

Today at #ICML 2026, I'll be presenting our paper on score-based sampling that achieves both high-accuracy and dimension-free guarantees. ORAL Wed, Jul 8, 2026 • 10:30–10:45 AM KST • Hall C POSTER Wed, Jul 8, 2026 • 2:30–4:15 PM KST • Hall A #2507 Please join us if you're around!

Final version of my book (with a new title) Online Learning: A Modern Introduction Using Convex Optimization Especially proud of the Foreword by @NicoloCB! It'll be printed by Cambridge University Press. The end of 7 years of updates :) arxiv.org/pdf/1912.13213

So, I tried ChatGPT. But ChatGPT 5.5 Pro failed, no matter what I tried. So, I used a different strategy: I wrote a pdf with everything I knew about this problem, including results that were not immediately useful, and told ChatGPT to complete the proof. This time it worked!

ChatGPT solved an optimization problem that puzzled me for a very long time. Back in summer 2020, I started to work with coauthors on algorithms for optimal transport. We then invented a very simple and elegant algorithm: Bregman Douglas-Rachford splitting method (BDRS).

😯

Very elegant

🎉 Applications are open for MLSS 2026 — the 50th edition of the Machine Learning Summer School! Join us in Tübingen for world-class lectures, hands-on sessions, and an amazing ML community. 🧠 Apply now 👉 mlss2026.is.tuebingen.mpg.de… #MLSS2026 #MachineLearning #SummerSchool #ML

We'll be organizing the Machine Learning Summer School in Tübingen to be held Aug 31st-Sept 11th, featuring top speakers across academia and industry. If you are a student or ML researcher, save those dates and stay tuned for updates! 🚀

Following my visit last month, I've just arrived to Berkeley again! At 9:30am PT today, I am giving the opening keynote talk at the Simons Institute workshop "Learning from Heterogeneous Sources". simons.berkeley.edu/workshop… Title of my talk: "From the Ball-proximal (Broximal) Point Method to Efficient Training of LLM". Abstract: simons.berkeley.edu/talks/pe… During my February visit, I gave a tutorial on "Federated Optimization" at the "Federated and Collaborative Learning Boot Camp". Recordings of my lectures are available on the Simons Institute YouTube channel: Part 1: piped.video/live/WcHUu08CLcc… Part 2: simons.berkeley.edu/talks/pe… Part 3: piped.video/live/oT02lHX6s7s…

I’ll work to make ChatGPT a better tool for accelerating scientific and mathematical discoveries. If you come across failure cases to improve upon (or exciting success stories) please send them my way!

It's now on the arxiv, enjoy! arxiv.org/abs/2511.16072