#Reasoning

AIOpenAI released GPT-6 Sol and Luna, priced 50 percent below GPT-5.6 promo API pricing, and rolling out in ChatGPT Work, Codex and the API, not yet in regular Chat. Anthropic released Claude Opus 5.5, described as roughly Claude Fable 5.1 level for 40 percent less than Opus 5 and over 30 percent faster, with Sonnet 5.5 and Haiku 5.5 due in coming weeks.

Why it matters: The recap puts OpenAI and Anthropic releases side by side, with pricing and capability claims that help compare the two launches.

AIAnthropic reports that Claude solved a nine-loop calculation in the planar N=4 super-Yang-Mills model, surpassing the previous eight-loop record set by Lance Dixon and collaborators. The quoted post says Claude ran largely unsupervised for days in Claude Science using a single prompt, at a total cost of a few thousand dollars, and Dixon independently verified the result. Kevin Weil's own text praises the achievement and expects AI to advance high energy physics over the coming 12 months.

Why it matters: The quoted Anthropic post gives a concrete benchmark: Claude ran for days to reach nine loops, extending the previous eight-loop record in a physics model.

AIOpenAI announced that a swarm of 10,000 agents produced a solution to the Navier-Stokes Millennium Problem, a result that angered mathematicians. NYU mathematician Tristan Buckmaster and Anthropic-employed collaborator Levent Alpöge had been working on related problems and released three draft papers of about 245 pages. Buckmaster said OpenAI's offer to merge efforts required acknowledging an OpenAI model and excluded Alpöge as co-author.

Why it matters: The piece separates the mathematical result from the collaboration dispute, showing how AI labs' compute spending is straining academic norms around credit and openness.

AIMark Chen announced that a group of agents produced a solution to the Navier-Stokes Millennium Prize Problem, using an unnamed OpenAI next-generation model. The post says the problem concerns whether smooth three-dimensional fluid motion described by the Navier-Stokes equations can break down, and that it had been open for roughly 90 years. The quoted OpenAI post and the attached illustration of inward spiral and axial stretching are cited as context, but the source provides no proof details.

Why it matters: The post claims an AI-produced proof of a famous open problem, but the source gives no proof details or independent verification, so the claim itself is the main point.

AIAn OpenAI model disproved Erdős's longstanding planar unit distance conjecture, which Paul Erdős posed in 1946, by discovering a new family of constructions that performs better than the square grids mathematicians had long assumed. Mark Chen says the proof draws on algebraic number theory and describes it as the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

Why it matters: The post names the specific open problem and the approach used, giving readers a concrete case of AI producing a research proof in mathematics.

AIARC Prize reports that the top Kaggle entry reached 24% on the ARC-AGI-2 private dataset at $0.20 per task, and that all winning solutions and papers are open source. The top verified commercial model, Opus 4.5 (Thinking, 64k), scored 37.6% at $2.20 per task, while a Poetiq refinement on Gemini 3 Pro reached 54% at $30 per task. The author argues that refinement loops are the main driver of 2025 progress, and says ARC-AGI-3 is planned for early 2026.

Why it matters: The post links 2025 competition results to a broader argument about refinement loops, showing how benchmark outcomes are being read as evidence of AI reasoning progress.