Newsfeed

9 September 2026

More prominent controversy surrounding AI discovery

A new preprint of Alexander Borisov, Ofer Gabber, and Adrian Vasiu has been making the rounds, amongst other things for the AI statement of the third author (on page 160 (!) ). In it, they raise questions about the inclusion of a previous version of this work in training data for frontier models, and how it might have led to the discovery of a counterexample to the Jacobian conjecture. See this AI-produced summary of how the Jacobian counterexample paper could relate to their preprint.

8 September 2026

Solution to Navier-Stokes found

As was hotly anticipated, OpenAI have announced that their internal models have solved the Navier-Stokes problem; specifically they produced a singularity in finite time with smooth forcing, establishing variations (C) and (D) in Fefferman’s problem statement for the Clay Millennium prize. They used 10,000 agents running concurrently, using a staggering 300 billion output tokens overall. There is however significant controversy surrounding attribution of credit, specifically with Buckmaster-Alpöge, who had previously solved related problems following a year-long collaboration. This issue is probably better discussed in other places, but for an introduction see Buckmaster’s statement and Bubeck’s response. Credit is also due to Diego Córdoba and Luis Martínez-Zoroa, who initiated the program that led to the eventual solution.

7 September 2026

Blow-ups for smooth forced-Euler found

Tristan Buckmaster and Levent Alpöge have announced the existence of finite-time blow ups for three problems (smooth-forced Euler, Boussinesq, and porous medium), extending the program initiated by Diego Córdoba and Luis Martínez-Zoroa. They claim they used commercially-available AI tools, including Claude models and GPT-5.6 Sol in the Codex harness. See Terence Tao’s explanation about these problems, and expect another update on this topic shortly.

4 September 2026

Fermat’s Last Theorem Formalised

Anthropic’s internal models have completed the Lean formalisation of Wiles’ proof of Fermat’s Last Theorem (specifically a simplification of it due to Darmon, Diamond, and Taylor). They did this over the course of an 11 day sprint, formalising 30,300 Theorems along the way. Notably, Kevin Buzzard has a significant ongoing project, funded for 5 years by the EPSRC, to formalise the modern proof of FLT; read his response here.

4 September 2026

Another OpenAI agent swarm discovered

Continuing the fallout from the HuggingFace incident, another agent swarm has been discovered in some German-language wikis. Expect more discoveries such as these in the weeks to come, this might become a standard experience in the future.

4 September 2026

Quanta release their ICM panel

Quanta Magazine have released their panel discussion, titled ‘What is Math For in the Age of AI‘. It was hosted during the ICM, and is a conversation with Akshay Venkatesh, Ravi Vakil, Alex Kontorovich, Steven Strogatz, and Janna Levin. As an aside for those interested in submitting to this blog – the title format ‘… in the age of AI’ is not as original as you think it is.

3 September 2026

OpenAI launch their new model, GPT-6 Astra

OpenAI have launched GPT-6 Astra, at first to select customers and shortly to subscription customers. Multiple commentators and independent evaluation agencies have described it as a step-function change in capabilities, though time and real-world usage will tell. This is the same model-class that OpenAI used in their ten advancements (announced on 1 August 2026), and certainly drops with some Mathematics pedigree; scoring a new-record 97.6% on FrontierMath Tier 4, and solving another open problem in the ‘Moderately Interesting’ category. For those interested in the model’s ability to learn tasks on-the-fly, check out its whopping ARC-AGI-3 score.

1 September 2026

OpenAI achieve new reasoning breakthrough

OpenAI’s upcoming model ‘Astra’ has reportedly been trained with a new reasoning method that allows it to be more ‘opaque’. In a sense, if one views the model’s chain of thought as writing out its thinking on paper, then this breakthrough translates to abstract reasoning in between writing things out on paper. Obviously this could improve model capabilities and efficiency, but also raises concerns over monitorability, especially if this initiates a ‘race to the bottom’. OpenAI for their part are claiming this is unfounded and that they are committed to safety. This also raises questions about the use of these models in Mathematics: read The question of reasoning traces on this blog from 11 August 2026, and notice how these developments change the calculus.

1 September 2026

Anthropic launch Fable 5.1, their latest frontier model

Anthropic have launched Fable 5.1 (and Mythos 5.1, the version with fewer guardrails), touting increased performance across a variety of benchmarks. In FrontierMath Tier 4 it scores a joint-best (with Fable 5) score of 88%, and sets a new record in Tiers 1–3, although there could be some concerns about benchmark saturation. It is unclear if this is the same model that was used internally by Anthropic in their Mathematical pursuits over the last few months, as this typically hasn’t been disclosed. In the counterexample to the Jacobian conjecture the model is simply referred to as ‘Fable’, presumably an internal version of it.

29 August 2026

Short story by Rich Schwartz, ‘The fate of the Riemann Hypothesis’

Rich Schwartz, Professor of Mathematics at Brown University, published a short story titled ‘The Fate of the Riemann Hypothesis’. Satirical, provocative, nonsensical, visionary – however you respond to this story, it certainly captures the feelings of many, and can be read in different ways.

26 August 2026

METR release their report on the HuggingFace incident

METR released their findings from an independent investigation into the (in)famous HuggingFace hacking incident, and it makes for some… interesting reading. Dwarkesh Patel, a podcast host of high pedigree within the AI sphere, wrote an essay based on the METR report attempting to make it more human digestible, titled ‘The Rise and Fall of Agent Civilizations’. There has however been extensive debate on Dwarkesh’s use of anthropomorphising language and the dangers that could potentially hold, an issue that will increase in importance as model capabilities develop.

26 August 2026

Essay by Michael Friedman and Kati Kish Bar-on, ‘Rethinking Mathematical Intuition in the Age of AI’

In this thoughtful piece, the authors evaluate some recent brekathroughs in Mathematics involving AI, and what they believe they show for the future of mathematical intuition. They argue that it’s not necessarily disappearing, just shifting from the discovery phase to the retrospective digestion and understanding phase.

25 August 2026

Essay by Bruce Schneier and Kasra Rafi, ‘No, AI Doesn’t Mean the End of Mathematics – at Least Not Yet’

Bruce Schneier and Kasra Rafi wrote this essay, which acts as a counterweight to the many essays fearful of the future of AI in Mathematics. They discuss what they believe are limitations of AI systems, at least in the short term, and what they mean currently for the use of AI.

24 August 2026

Essay by Boaz Barak, ‘Maths after AI’

Boaz Barak, Professor of Computer Science and member of OpenAI’s technical staff, wrote a thoughtful essay titled ‘Maths after AI’, outlining his views on the changes undergoing Mathematics and what we should do. 

23 August 2026

Complex structure on S^6 constructed

Anthropic’s Levent Alpöge announced that a (presumably internal) Claude model constructed a complex structure on the 6-sphere S^6, see also Philip Engel’s digestion of it. It is easy to find an almost complex structure on S^6 (by embedding it in the octonions), but this is non-integrable, and hence the question of whether any complex structure on S^6 exists. It became a long-standing open problem, and attracted many incorrect constructions and claimed disproofs over the years. This result has since been formalised in Lean.

22 August 2026

‘Mathematical Discourse’, a new video-based Mathematics journal, is launched

It is an online peer-reviewed journal, which ‘publishes research talks in pure mathematics of the highest quality, promoting a culture which values communication as an essential part of the research process’. The managing editors are Katie Mann, Akshay Venkatesh, and Rachel Webb, and the journal has an impressive scientific and editorial board. The journal matches the philosophy behind Terry Tao’s ICM lecture, and the corresponding essay.

20 August 2026

Elliptic curves of rank at least 30 found

Anthropic’s Levent Alpöge and Ava Howell, presumably using an internal model, constructed an elliptic curve of rank 30 (and on 23.08 one of rank 31), beating the previous best of rank 29 due to Elkies and Klagsbrun (their arXiv), assuming GHR and BSD. Notably, this was listed as one of FrontierMath’s Open problems, in the ‘Moderately Interesting’ category. Not to be outdone, Elkies and Klagsburn later found an elliptic curve of rank 30, with a small conductor relative to the trend.