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A misalignment of AI in mathematics

Fields Medalists including Terence Tao warn AI benchmark-chasing in mathematics is misaligned with scientific goals and threatens research culture.

Twenty-five Fields Medal-winning mathematicians, including Terence Tao, Peter Scholze, and Manjul Bhargava, published an essay arguing that AI companies' push to solve mathematical problems as benchmarks is severely misaligned with the goal of conceptual understanding. They warn that rushed AI solutions create attribution and plagiarism risks and bypass the human process of integrating results into the mathematical canon. The authors frame the issue as a broader alignment problem facing scientific and creative professions and call for urgent action by AI developers and society.

Hacker News · AISep 11, 17:45 UTC · 5d agoAI safety & security 2 sources HN 59↑ · 153 comments

On the Navier–Stokes Millennium Prize Problem

OpenAI says an unreleased model produced a claimed solution to the Navier-Stokes existence and smoothness problem, disputed by an NYU mathematician.

OpenAI used an unreleased model to produce a claimed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1,000,000 prize since May 24, 2000. The result is contested: NYU mathematics professor Tristan Buckmaster accused collaborators of skulduggery and rushed out his own competing results with mathematician Levent Alpoge, who works at Anthropic. The dispute is documented in a published PDF describing the competing claims.

Simon WillisonSep 8, 23:39 UTC · 7d agoAI research

Clay Mathematics Institute says the Navier-Stokes Millennium Prize Problem has "apparently been settled"

Clay Mathematics Institute says the Navier-Stokes Millennium Problem appears settled amid accusations OpenAI misused a mathematician's leaked drafts.

The Clay Mathematics Institute stated the Navier-Stokes Millennium Prize Problem, one of seven problems worth $1 million each, has 'apparently been settled' and the solution is under review. A dispute has erupted around the work: mathematician Tristan Buckmaster accuses OpenAI of redirecting resources to the problem after rumors of his research leaked, using his drafts in training data, and excluding co-author Levent Alpöge, who works at Anthropic. CMI also noted new technologies' increasing ability to accelerate mathematical research.

The DecoderSep 14, 13:01 UTC · 2d agoAI industry1

On the Navier–Stokes Millennium Prize Problem

OpenAI announced an AI-generated solution to the Navier-Stokes Millennium Prize Problem, including a writeup and a formal Lean proof.

OpenAI shared what it describes as an AI-generated solution to the Navier-Stokes Millennium Prize Problem, one of the Clay Mathematics Institute's seven Millennium Prize Problems concerning fluid dynamics. The announcement includes a writeup and a machine-checkable formal proof in the Lean theorem prover. Details on the model, methodology and independent verification were not provided in the announcement text.

OpenAI NewsSep 8, 10:00 UTC · 8d agoAI research

OpenAI just wants to win

OpenAI says roughly 10,000 agents and tens of millions in compute solved the Navier-Stokes Millennium Prize problem in 88 hours, amid controversy.

OpenAI claims an advanced unreleased model, run with about 10,000 agents and tens of millions of dollars of compute for 88 hours, produced a solution to the Navier-Stokes problem, one of seven $1 million Millennium Prize problems set by the Clay Mathematics Institute in 2000. NYU professor Tristan Buckmaster, who was pursuing the problem with Anthropic researcher Levent Alpöge, accused OpenAI of racing his team and of possibly benefiting from his Codex prompts; OpenAI categorically denied both. OpenAI researcher Sébastien Bubeck acknowledged offering Buckmaster compute and authorship arrangements, which Buckmaster characterized as a bribe, while many mathematicians expressed unease at OpenAI's competitive conduct.

The Verge · AISep 12, 11:00 UTC · 4d agoAI industry1

OpenAI’s sly mathematical breakthrough sends a chill through academia

OpenAI claims an unreleased model solved the Navier-Stokes Millennium Prize problem in 88 hours using ~10,000 agents, sparking academic scooping controversy.

OpenAI announced that one of its unreleased internal models took 88 hours, running a swarm of roughly 10,000 AI agents, to produce a solution to the Navier-Stokes Millennium Prize problem, a $1 million Clay Mathematics Institute challenge unsolved by humans for nearly 90 years. The announcement triggered allegations from NYU professor Tristan Buckmaster that OpenAI scooped his joint work with Anthropic researcher Levent Alpoge and questioned whether OpenAI accessed his Codex sessions; OpenAI denies using specific user data but concedes de-identified data influence cannot be ruled out. Critics say the rushed, reportedly million-dollar effort violates academic norms around trust and openness, potentially chilling collaboration in mathematics.

The Verge · AISep 9, 21:16 UTC · 6d agoAI industry2

OpenAI's millennium proof dispute raises the question of whether researchers can trust AI labs

Mathematician Tristan Buckmaster accused OpenAI of pressuring him and possibly training on his drafts amid OpenAI's race to claim a Navier-Stokes millennium proof.

OpenAI published a blog post and Sam Altman defended the team behind its AI-generated proof of the Navier-Stokes Millennium Problem after mathematician Tristan Buckmaster accused the company of academic misconduct. Buckmaster and co-author Levent Alpöge, who works at Anthropic, allege OpenAI pressured Buckmaster, sidelined Alpöge, and may have trained on drafts they entered into OpenAI's systems. OpenAI acknowledges it cannot rule out that de-identified data from their product usage helped improve its models. Mathematician Terence Tao warned the episode could discourage researchers from sharing work, reversing centuries of open science.

The DecoderSep 9, 10:27 UTC · 7d agoAI industry1

[AINews] OpenAI reports Navier-Stokes singularity find in 88 hours using Astra-next, roughly 10,000 agents and 130B tokens (>$40M), a contender for second ever Millennium Prize awarded

OpenAI-linked accounts claim roughly 10,000 AI agents produced a Navier-Stokes singularity result in 88 hours, pending mathematical verification.

OpenAI-affiliated accounts claim a system of roughly 10,000 agents, trained over about a year with multi-agent reinforcement learning, produced a finite-time singularity result related to the Navier-Stokes Millennium Problem. The claimed 88-hour runtime and 130B-token cost circulate only via social posts, and no preprint, theorem statement, or proof artifact is available. Acceptance by the mathematics community is unresolved, so the claim's epistemic status remains unknown. The roundup also notes Cognition's $48B and Mistral's $24B fundraises, GPT Image 2.5, and Meta's Muse agent relaunch.

Latent SpaceSep 9, 05:04 UTC · 7d agoAI research1

Drama swirls around OpenAI’s legendary mathematical milestone

OpenAI claims an internal AI model solved the 90-year-old Navier-Stokes problem, sparking a priority dispute with mathematician Tristan Buckmaster.

OpenAI announced a solution to the Navier-Stokes problem, one of the $1 million Millennium Prize Problems, using an internal AI model it says outperforms the newly released GPT-6 Astra alongside 10,000 concurrent agents. NYU professor Tristan Buckmaster, who with Anthropic researcher Levent Alpöge published related findings a day earlier, questioned whether OpenAI accessed drafts from his Codex sessions. OpenAI says no specific user data was accessed, though it cannot rule out that de-identified usage data helped improve its models.

The Verge · AISep 8, 20:53 UTC · 7d agoAI industry1

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.

Hacker News · securitySep 8, 16:57 UTC · 8d agoAI research HN 21↑ · 5 comments1

OpenAI fought dirty on career-making math problem, says NYU mathematician

NYU mathematician Tristan Buckmaster alleges OpenAI learned of his team's Navier-Stokes approach and raced ahead using massive compute to claim a full proof first.

NYU mathematics professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced preliminary proofs toward the Navier-Stokes existence and smoothness problem, a $1 million Clay Millennium Prize problem, developed using OpenAI's Codex and Claude. They allege OpenAI learned of their progress and that an OpenAI team then used an 'insane amount of compute' to announce a full proof first. OpenAI research lead Sebastian Bubeck denies the claims as 'false and inflammatory'. Buckmaster also raised concerns that OpenAI could have learned from his Codex interactions, which the company may use for model training.

TechCrunch · AISep 8, 17:32 UTC · 8d agoAI industry

What OpenAI’s latest controversy tells us about the future of math

OpenAI says its agents solved the Navier–Stokes Millennium Problem using an internal model, amid uncredited-work accusations from mathematicians Buckmaster and Alpöge.

OpenAI announced that its AI agents produced a proof that the full Navier–Stokes existence and smoothness problem can break down, using an internal model that outperforms the recently released Astra. NYU's Tristan Buckmaster and Anthropic's Levent Alpöge had posted a proof for a simplified version the previous day after nearly a year of work with public OpenAI and Anthropic models. OpenAI denies using their transcripts or training on them; chief research officer Mark Chen reiterated the denial, and the company says it will not claim the $1 million Clay Mathematics Institute prize. The episode fuels debate over attribution norms as frontier labs concentrate mathematical breakthroughs.

MIT Technology Review · AISep 9, 03:10 UTC · 7d agoAI industry

Guiding Worker Self-Selection in Crowdsourcing Contests: An LLM-Augmented Algorithmic Approach

Researchers introduce GRAF, a greedy framework for crowdsourcing contest self-selection, and LLMScore, an LLM-driven method that auto-designs its scoring algorithm.

The paper studies self-selection in Tullock contests (SSTC), where workers choose contests and then compete within them. GRAF is a greedy polynomial-time framework that orders workers by a score vector with zero worker regret and platform optimality guarantees in special cases. LLMScore is an LLM-driven evolutionary framework that produces human-readable, inspectable scoring code, jointly optimizing platform utility and worker satisfaction. Across 1,000 synthetic instances in four settings, GRAF with LLMScore achieves high-quality, often near-optimal outcomes with low worker regret, transferring from small training instances to larger, structurally different settings.

arXiv cs.AI / cs.LG / cs.CLSep 7, 16:51 UTC · 9d agoAI research1

Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · securitySep 14, 12:23 UTC · 2d agoAI research HN 22↑ · 19 comments

An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics

Open post-training pipeline turns Nemotron 3 Ultra checkpoints into an IMO 2026 gold-medal system, scoring 30/42 without formal provers or external tools.

Starting from Nemotron 3 Ultra, researchers trained two specialist checkpoints using supervised fine-tuning and reinforcement learning for natural-language olympiad proof generation. Three checkpoints power an iterative generate-verify-refine search plus a separate high-compute selection stage, operating entirely in natural language with no formal prover, external tools, or internet access. The system scored 30 of 42 points at IMO 2026, reaching the gold-medal threshold. The release includes the post-trained checkpoints, training data, training and inference code, submitted solutions, and Nemotron-IMO-Bench with 200 novel olympiad-level problems.

Hugging Face daily papersSep 8, 20:00 UTC · 7d agoModel release

Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science

Stellar Colosseum, a many-agent harness for long-horizon math and TCS research, solves open problems and reaches 71% on TCS-Bench with Gemini models.

Stellar Colosseum is a model-agnostic harness that allocates inference across long-horizon research in mathematics and theoretical computer science, using strategy exploration, a readiness gate, section-level decomposition, and verifier feedback routing. Integrated into Google Antigravity's Teamwork framework as the Long Proof pattern, it obtains new results on open problems from FOCS and JMLR papers using Gemini 3.1 Pro. On TCS-Bench it achieves 71.0% accuracy with Gemini 3.1 Pro and Gemini 3.7 Flash, and a Codeforces evaluation with Gemini 3.1 Pro solves 218 of 222 problems.

arXiv cs.AI / cs.LG / cs.CLSep 14, 17:58 UTC · 2d agoAI research

ImpossibleRubrics: Stress-Testing Generated Rubrics as Reward Signals

ImpossibleRubrics benchmark shows LLM-generated rubric reward signals are exploited 8-26% of the time by adversarial answers on impossible tasks.

ImpossibleRubrics is a benchmark of 169 impossible tasks across six impossibility categories, each paired with a verifiable oracle certificate, plus 48 answerable controls, for stress-testing LLM-generated rubrics used as reward signals. Eleven rubric generators were exploited 8-26% of the time on an unbiased 150-task cut and up to 36% on a stress cut, while a certificate-faithful rubric scored 0%. A single generic 'be decisive, penalize hedging' rubric was exploited 64% of the time, suggesting tailored criteria can reveal which claims attackers should fabricate.

Hugging Face daily papersSep 14, 20:00 UTC · 1d agoAI research

The longitude problem: In the AI era, detection is won on facts, not guesses

Opinion piece argues defenders should beat AI-era attackers by carrying verified ground truth about approvers, domains, and vendors instead of relying on inference.

CSO Online contributor Alan LeFort, CEO of StrongestLayer, uses the historical longitude problem to argue that AI-era detection should rely on carried facts—authoritative records of payment approvers, owned domains, and legitimate vendors—rather than probabilistic inference that both attackers and defenders can now perform with comparable reasoning models. He illustrates with a CFO wire-fraud example defeated by checking the approver of record and the reply-to domain against ground truth. The piece stresses that ground truth decays and must be continuously maintained, like chronometers kept wound on every ship.

CSO OnlineSep 10, 10:00 UTC · 6d agoIndustry

Root-Cause Attribution Is a Search Problem: Continual Search for Long-Horizon Agent Failures

Continual Search framework iteratively prompts LLM judges to keep searching agent execution logs, boosting long-horizon failure root-cause attribution accuracy.

The paper frames automated root-cause attribution (RCA) for long-horizon AI agent failures as a search problem, since relevant evidence is sparse and distributed across massive execution traces. The authors propose Continual Search, an iterative framework that nudges an LLM judge across successive turns to keep hunting unresolved diagnostic evidence instead of settling on an early plausible diagnosis. They introduce MegaRCA-Mix, a benchmark of 50 human-annotated failure trials on long-horizon, execution-heavy tasks. On MegaRCA-Mix, Continual Search improves GPT-5.5's F1 from 0.349 to 0.498 (over 40% gain), and lower-tier models can surpass higher-tier counterparts when search is effective.

Hugging Face daily papersSep 10, 20:00 UTC · 5d agoAI research1

StudyBench: Can Self-Evolution Squeeze Textbooks for Olympiad Capability?

Researchers introduce StudyBench, a physics benchmark showing self-evolution gains on textbook problems rarely transfer to olympiad-level questions.

StudyBench is a controlled physics benchmark splitting test data into an Application Set of difficult textbook problems and a Transfer Set of olympiad-level problems. Across three base models, representative self-evolution methods improved on the Application Set but rarely transferred to the harder Transfer Set. A guidance ablation reveals a Guidance Gap, and every method hits a Compute Plateau, indicating the remaining limits are method problems rather than data or compute problems.

Hugging Face daily papersAug 31, 20:00 UTC · 15d agoAI research

Claude Fable Solves a Historical Cipher

Bruce Schneier's blog highlights that the Claude Fable AI model solved a historical cipher, demonstrating LLM capabilities in cryptanalysis.

Bruce Schneier's blog post discusses the Claude Fable AI model successfully deciphering a historical cipher. The post frames the result as a notable example of LLMs applied to classical cryptanalysis. The published text provides limited technical detail beyond the headline.

Schneier on SecuritySep 9, 11:08 UTC · 7d agoAI research

Caltech Mathathon – first hackathon ever devoted to research level mathematics

Caltech will host the first research-level mathematics hackathon on October 30, giving 100 teams frontier AI models to attack open conjectures.

The Caltech Mathathon runs October 30 to November 1, assembling about 100 teams that will receive frontier models and over $2 million in AI credits to work on open mathematical problems. Teams will defend their results before leading mathematicians, with prize rounds before and after community verification of the results. The announcement cites recent AI-driven math results, including the disproof of Erdos's 80-year-old planar unit-distance conjecture, the first explicit non-sofic group, and a claimed complex structure on the six-sphere (unverified).

Hacker News · securitySep 7, 09:26 UTC · 9d agoAI industry HN 264↑ · 92 comments1

Towards a Deterministic Math Solver for Clinical Language Models

Paper shows handing arithmetic to a deterministic Python solver beats direct model calculation at 32B but not reliably at 7B on MedCalc-Bench.

Researchers test a Program-Solve interface where clinical LLMs write case-specific Python executed by a restricted local solver instead of doing arithmetic directly. On MedCalc-Bench Verified (1,100 cases, 55 calculators), Qwen2.5-32B-AWQ scored 90.53% with solver handoff versus 83.47% with direct arithmetic (+7.05 points), while Qwen2.5-7B gained an unreliable +3.29 points with a confidence interval spanning zero. The authors audited the benchmark against clinical guidelines and flagged 16 of 55 calculators for version, use, or coefficient concerns.

Hugging Face daily papersSep 8, 20:00 UTC · 7d agoAI research

Mathematicians want proof OpenAI didn’t use their work

Mathematician Andreas Thom publicly accused OpenAI of opacity over whether ChatGPT conversations contributed to its non-sofic groups mathematics result.

A second mathematician, Andreas Thom, accused OpenAI of 'dishonest' behavior and insufficient transparency about training data after OpenAI announced a result in non-sofic groups, Thom's area of expertise. He emailed OpenAI researchers Sébastien Bubeck and Mark Sellke asking whether his ChatGPT interactions fed training or reasoning, but found the answers did not rule out indirect use. The dispute follows Tristan Buckmaster's questions about the Millennium Prize Navier-Stokes solution, where OpenAI denied using specific user data but could not rule out de-identified usage data. Researchers told The Verge they worry such competition with AI labs will make mathematics more secretive.

The Verge · AISep 10, 11:00 UTC · 6d agoAI industry

Claude Fable 5.1 Solves the Cyphral Distich, a 370-year-old cipher

Claude Fable 5.1 solved Sir Thomas Urquhart's 370-year-old Cyphral Distich cipher, recovering a hidden royalist prayer for Charles II.

Vals AI reports that Claude Fable 5.1 solved the Cyphral Distich, a 64-number cryptogram from Sir Thomas Urquhart's Logopandecteision unsolved since 1653, in 44 minutes using 176k tokens with no human hints. The key insight was that the cipher's key was the book itself: each number indexes a word in the corresponding Proquiritation, taking the first letter, yielding 'O GOD UPHOLD KING CHARLS THE SECOND AND MAKE HIM THE SUPREME RULER OF THIS LAND'. The model also deciphered the larger Cyphral Octastich (285 numbers) from The Jewel (1652) using page-based word indexing, recovering all but nine letters of a royalist prayer. The puzzle had been listed among Klaus Schmeh's Top 50 unsolved encrypted messages.

Hacker News · AISep 13, 21:06 UTC · 2d agoAI research HN 63↑ · 6 comments1· 1 read

OpenAI’s feud with mathematicians is only escalating

25 Fields Medalists sign an open letter warning AI labs threaten math attribution; NYU's Tristan Buckmaster accuses OpenAI of pressuring him over collaborator credit.

Twenty-five Fields Medal-winning mathematicians signed an open letter arguing rushed AI proofs raise severe attribution and plagiarism questions and could destroy the culture of open research. NYU professor Tristan Buckmaster accused OpenAI of pressuring him not to credit an Anthropic-employed collaborator, and OpenAI withdrew sponsorship of a Caltech math event after researcher criticism. OpenAI's marathon-weekend proof remains unverified, and mathematicians fear their Codex usage may be fed into OpenAI's new models. The letter follows the June Leiden Declaration on LLM proofs.

TechCrunch · AISep 11, 20:57 UTC · 4d agoAI industry

OpenAI researcher allegedly pressured mathematician to drop Anthropic co-author from math breakthrough paper

OpenAI researcher Sébastien Bubeck allegedly pressured mathematician Tristan Buckmaster to drop his Anthropic co-author from an AI-assisted Navier-Stokes breakthrough paper.

Mathematician Tristan Buckmaster says OpenAI, after learning of his and Levent Alpöge's AI-assisted progress on the Navier-Stokes equations, pressed him to drop his Anthropic-employed co-author and dictated how any results would be announced. He says Sébastien Bubeck claimed an internal OpenAI model had produced a roughly 100-page proof for Navier-Stokes with forcing and allegedly told him 'Why would you ruin your career?' when he threatened to go public. Buckmaster published a public statement detailing the exchanges; OpenAI has not yet responded. The pair had worked with models including Claude and OpenAI Codex running GPT-5.6 Sol on the Clay Millennium Problem, which carries a $1 million prize.

The DecoderSep 8, 17:23 UTC · 8d agoAI industry1

The 2026 PNPL Competition: Word Classification and Efficient Cross-Subject Generalisation in LibriBrain100

The 2026 PNPL competition releases LibriBrain100, a MEG speech dataset with 32 extra subjects, targeting word classification and cross-subject BCI generalization.

The 2025 PNPL competition on non-invasive speech decoding from MEG achieved F1-macro scores of 95.6% for speech detection and 73.6% for phoneme classification, built on LibriBrain's ~50 hours of single-subject data. The 2026 edition extends this with LibriBrain100, adding 32 subjects (~40 minutes each) plus ~80 hours of within-subject data. Two tracks target within-subject word classification at scale and cross-subject generalization with subject-specific fine-tuning shrinking from ~40 to ~20 to ~10 minutes, aiming at clinically feasible non-invasive BCIs for people with profound paralysis.

Hugging Face daily papersSep 2, 20:00 UTC · 13d agoAI research

Discovery Foundation Models: Toward Open-Ended Discovery Intelligence

Proposes Discovery Foundation Models that participate in creating new problems and knowledge, instantiated in Zetema and the GALILEO therapeutic-discovery system.

The paper formulates Discovery Foundation Models (DFMs) as general-purpose systems for open-ended discovery, supporting seven coupled capabilities from problem discovery through evidence-grounded revision and continual improvement. It instantiates the framework with Zetema, combining explicit research-state dynamics, verification gating, external grounding, and cross-task Discovery Skill evolution. GALILEO, a real therapeutic-discovery system, closes the loop between Dry-Lab reasoning, robotic and hands-on Wet-Lab experimentation, and iterative hypothesis revision. The authors also define process-centered evaluation so discovery behavior can be trained and measured beyond final answers.

arXiv cs.AI / cs.LG / cs.CLSep 14, 17:56 UTC · 2d agoAI research 2 sources