On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, o...
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.
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.
By Xinzhi Zhang
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...
By Ying Xie
Simon Willison discusses how the current trend of mining open mathematical problems in a non-renewable way could make these problems scarce. He notes that rumors of a problem can trigger large AI-driven efforts to solve it before original researchers can fully develop their work. This shift may discourage sharing promising research, potentially reversing centuries of open science and harming the field’s future.
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.