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Controversy over OpenAI's Maths Breakthrough
OpenAI claims its internal model proved the Navier-Stokes equations 'blow up' — a Millennium Prize Problem — amid allegations it borrowed mathematicians' methods.
OpenAI announced that an internal model produced a proof, certified in the Lean proof assistant, showing the Navier-Stokes equations can 'blow up,' implying infinite fluid speeds — a claimed solution to one of the seven $1-million Millennium Prize Problems. Mathematician Tristan Buckmaster alleged OpenAI, after learning of progress by him and Anthropic employee Levent Alpöge on 'blowing up' the related Euler equations, adopted a similar 'forcing' method; OpenAI's Sébastien Bubeck denied this, saying the model independently solved Euler by different means and produced the full Navier-Stokes proof over one weekend. Mathematicians including Diego Córdoba, co-developer of the forcing approach, remain cautious, and the community is still evaluating the competing proofs.
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The Frontier AEO Tracker: What Astra Chooses (and every other frontier model, and what you can do about it)
Latent Space launches an AEO tracker scoring 7 frontier models' product recommendations across 161 categories, revealing generational bias flips.
Latent Space built a tracker measuring Answer Engine Optimization by running 6 prompt variations across 7 frontier models with search enabled over 161 product categories, scoring first choices, alternatives, mentions, and anti-recommendations. It found 28 categories with a universally dominant primary choice and observed soft biases, such as models favoring their own lab's coding agents. Analysis of Anthropic's Sol→Astra and Opus→Fable generations showed newer models consulting fewer sources and being less likely to change answers when questions are paraphrased.
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The AI ‘Ghosts’ Contaminating Academic Publishing
Samsung and University of Warsaw researchers find LLMs repeatedly generate the same fake author names, contaminating academic records with 1,655 ghost-authored DOIs.
A preprint from Samsung and the University of Warsaw, "The Ghost Couple: Correlated LLM Name Priors and Their Haunting of the Web and Academic Publishing," shows that LLMs such as Claude, ChatGPT, and Gemini repeatedly generate the same fictional names like Elena Vasquez, Marcus Chen, and Aris Thorne as experts and co-authors. Researchers identified 1,655 ghost-authored records on CERN-operated Zenodo carrying real DataCite DOIs, fabricated journals, and backdated publication dates. Ghost names also form synthetic research groups on ResearchGate and are indexed without verification by Google Scholar and Semantic Scholar. The researchers suggest correlated name priors could serve as provenance signals for detecting AI-generated content.
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🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing
Caltech professor Anima Anandkumar discusses Neural Operators and FourCastNet for physics modeling, arguing inductive biases beat pure token scaling.
Anima Anandkumar, Bren Professor at Caltech and co-founder of Accelerated Understanding, describes Fourier Neural Operators that learn in frequency and spherical-harmonic domains to model weather, fusion, and fluid or heat flow. Her team built FourCastNet 3, a global weather model competitive with physics-based simulations that runs on consumer-grade GPUs. She also introduced TorchLean, a framework for writing PyTorch-style networks inside the Lean proof assistant for formal verification, and was appointed to the United Nations Scientific Advisory Board. She argues physical domains resist scaling due to tiny datasets and context lengths in the hundreds of billions, so progress comes from built-in structure and physical priors.
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I wrote an AI textbook — how long until AI can do it better?
AI researcher Nathan Lambert argues LLMs remain weak at long-form technical writing, questioning whether models can autonomously organize scientific knowledge for breakthroughs.
Nathan Lambert describes writing a post-training textbook, Reinforcement Learning from Human Feedback, and finds today's LLMs weak at organizing long-form technical content despite becoming superhuman at coding and math. He notes GPT 5.5 Pro found deep typos across a 200-300 page manuscript while Claude models proved more useful as editors. He argues that compressing knowledge through writing is a prerequisite for autonomous scientific insight and tempers expectations for near-term AI-driven open science.
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