Skip to header Skip to main navigation Skip to main content Skip to footer

OpenAI Says Its Models Disproved a Core Complexity Conjecture. Now Experts Have to Check the Proof

Breadcrumb

  • Home
  • OpenAI Says Its Models Disproved a Core Complexity Conjecture. Now Experts Have to Check the Proof
A mathematician writing a proof in chalk on a blackboard covered with equations.

OpenAI announced on October 26 that its internal models have produced three new scientific results: a proof of Sogge's local smoothing conjecture in harmonic analysis, a disproof of the Exponential Time Hypothesis in computer science, and a rigorous existence proof for quantum chromodynamics and related quantum field theories in physics. None of the three has been peer reviewed. OpenAI is unusually candid about that, calling the manuscripts raw research data and handing them to outside experts to examine, explain, and, if they hold up, turn into actual scientific understanding.

The computer science claim is the one with the widest blast radius. The Exponential Time Hypothesis, proposed by Russell Impagliazzo, Ramamohan Paturi, and Francis Zane, holds that 3-SAT cannot be solved in subexponential time, and hundreds of papers have used it to derive conditional hardness results across graph theory, databases, computational biology, and geometry. OpenAI says its system found a natural-language disproof on October 16 and formalized it in the Lean proof assistant the next day. Both the writeup and the Lean proof are public on GitHub. Fittingly, the examination will be led by Impagliazzo and Paturi themselves, alongside MIT's Ryan Williams, and OpenAI has agreed to fund a conference on the implications. If the result stands, it does not make hard problems fast overnight; OpenAI itself notes that turning it into practical algorithms will take significant further research.

In mathematics, the claimed proof of Christopher Sogge's 1991 local smoothing conjecture covers every spatial dimension, which would also resolve the Kakeya conjecture and Stein's restriction conjecture in all dimensions; human mathematicians had settled local smoothing in two dimensions in 2019 and Kakeya in three dimensions in 2025. The AI output arrived on October 18 and was formalized in Lean a day later. The physics claim is the most closely held: existence proofs for four-dimensional quantum field theories including QCD, built on Balaban's approach to constructive quantum field theory, with pure Yang-Mills existence, part of a Clay Millennium Prize problem, as a subproblem. A group led by Nobel laureate David Gross will shepherd that work, and unlike the other two, its materials are being withheld until that group writes them up.

The release model may matter as much as the results. OpenAI says it seeks no academic credit, set no nondisclosure agreements, and made participation voluntary and unpaid, with three different strategies chosen by the experts: open release for the mathematics, public release plus an external group for computer science, and expert-led delay for physics. That is a more honest template than a victory-lap announcement, and it acknowledges the asymmetry baked in: the lab still chooses who sees extraordinary claims first.

For people building with AI, the lesson is not that conjectures are falling like dominoes. It is that generation has outrun verification, again. A Lean formalization is a real check on the argument as formalized, but experts still have to confirm the formal statement matches the conjecture mathematicians actually care about, which is why none of this counts as settled until the examiners report. The same trust gap showed up in miniature on October 27, when TechCrunch reported Bank of America emailing customers not to share their banking passwords with AI assistants. Whether the claim is a disproved hypothesis or an agent asking for your login, the productive question is the same: what, exactly, has been verified, and by whom?

Rocky Mountain Madman LLC
OpenAI
AI Research
Mathematics
Frontier Models
Large Language Models

Ai Industry News

Nvidia's Flora Labels Robot Video for 72 Cents an Hour, Not 88 Dollars

Photograph of two humanoid robots, one working alongside a woman in a kitchen and another wearing a white Nvidia hard hat at a work station

Nvidia's GEAR robotics lab has open-sourced Flora, the data engine it uses to train its GR00T humanoid robot models, and the headline number is hard to ignore. Reporting by The Decoder on October 25, drawing on Nvidia's research paper, puts Flora's cost at about 72 cents to label one hour of robot video, compared with roughly 88.49 dollars for OpenAI's GPT-6 Astra. The models are available on Hugging Face, and Nvidia says the system already annotates up to 200,000 hours of video a day across 512 GB300 GPUs in its own training pipeline.

  • Read more about Nvidia's Flora Labels Robot Video for 72 Cents an Hour, Not 88 Dollars

Apollo Says AI Has Paid Off Nowhere Outside Tech: The S&P 493 Are Still Flat

Photograph of the carved stone facade of the New York Stock Exchange building with its gold Stock Exchange lettering.

Apollo Global Management's chief economist has put a number on the suspicion many finance chiefs have been voicing privately. In a note published October 24, Torsten Slok argued that artificial intelligence has delivered, in his words, zero financial payoff to corporate America outside of tech. TechCrunch reported the note on October 25. His test is deliberately plain: strip the Magnificent Seven out of the S&P 500, and the remaining 493 companies show flat profit margins, flat revenue per worker, and no sign in the productivity data that AI is moving the needle yet.

  • Read more about Apollo Says AI Has Paid Off Nowhere Outside Tech: The S&P 493 Are Still Flat

Anthropic Says One Agent Beats Many: Fold Your Subagents Back Into the Loop

Photograph of Dario Amodei.

Anthropic is telling enterprise builders to do the unfashionable thing: use fewer agents. In guidance published October 22 from its Applied AI team, and reported widely on October 25, the company said that across several enterprise deployments a single agent that loads skills and tools only when needed frequently beat both a one-prompt-for-everything design and a fleet of specialised subagents on quality, and often cost less and ran faster. In one comparison the single-agent setup ran about twice as fast as the multi-agent version it replaced.

  • Read more about Anthropic Says One Agent Beats Many: Fold Your Subagents Back Into the Loop

Pagination

  • First page « First
  • Previous page ‹ Previous
  • Page 1
  • Page 2
  • Current page 3
  • Page 4
  • Page 5
  • Page 6
  • Page 7
  • Page 8
  • Page 9
  • …
  • Next page Next ›
  • Last page Last »

Copyright © 2026 Rocky Mountain Madman LLC - All rights reserved

Developed and Designed by Rocky Mountain Madman LLC