Simon Willison
Some thoughts on the Navier–Stokes Millennium Prize Problem
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Simon Willison
Sep 8
On the Navier–Stokes Millennium Prize Problem
Simon Willison reports that OpenAI used an unreleased model to produce a claimed resolution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The claim has been met with controversy, as NYU professor Tristan Buckmaster and mathematician Levent Alpöge—who had been working on related problems with Claude and Codex—accused OpenAI of using their unpublished work. OpenAI has denied accessing their data and has offered to wait for Buckmaster’s publication, but will not include Alpöge as a co‑author due to a competitive relationship with his employer.
Simon Willison
Sep 1
Claude Fable 5.1 made me a really nice animated pelican
The article discusses Anthropic’s Claude Fable 5.1 release, highlighting its claimed improvements in coding, knowledge work, and problem‑solving, particularly a 52.6% score on the new Terminal‑Bench‑Science 0.1 benchmark. The author examines the model’s performance on the pelican benchmark, noting that Fable 5.1’s five reasoning levels (low, medium, high, xhigh, max) sometimes skip reasoning entirely for certain prompts, as evidenced by token counts and cost metrics. The piece provides detailed transcript data for each reasoning level when generating an SVG of a pelican riding a bicycle.
arXiv AI
Oct 15
What the Machine Invented: Mining New Mathematical Instruments from OpenAI's October 2026 Release of AI-Generated Mathematics
arXiv:2610.17090v1 Announce Type: cross Abstract: On 6 October 2026 OpenAI published an initial 722 AI-written mathematical manuscripts, organized into 372 problem families, in the public repository...
Microsoft Research
Oct 21
Solving a 31-year-old grand challenge in mathematics – the KLS conjecture
Microsoft Research reports that a 31‑year‑old mathematical problem, the Kannan–Lovász–Simonovits (KLS) conjecture, has been solved. The conjecture, proposed in 1995, questioned the difficulty of computing in high‑dimensional spaces and had been a major obstacle to understanding the efficiency of randomized algorithms. The new research removes this theoretical barrier, advancing knowledge about algorithmic performance in science and computing.
arXiv Machine Learning
Jul 31
Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration
arXiv:2607. 27705v1 Announce Type: cross Abstract: Large language models can contribute useful ideas to mathematical research, yet long-horizon proof attempts remain difficult to coordinate, evaluate, and reproduce.
Simon Willison
Sep 6
Research acceleration: The view inside OpenAI
The article discusses OpenAI’s focus on Recursive Self‑Improvement (RSI), which the author suggests may represent a new form of AGI. It highlights how OpenAI’s research team is employing coding agents and notes a significant rise in AI spending per researcher in late July, likely linked to internal access to a model later released as GPT‑6 Astra. The piece references related essays and includes a chart illustrating the growth of agentic engineering at OpenAI.