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

OpenAI Buys Orchestra Bio to Put Agents on the Unglamorous Side of Drug Development

OpenAI announced on Tuesday, October 20, that it has acquired Orchestra Bio, a four-year-old biotech software startup whose AI agents handle the operational grind of drug development. Terms were not disclosed. Orchestra had reportedly raised around 20 million dollars as of 2025 from backers including Andreessen Horowitz, Atria, and 8VC, according to TechCrunch. Its platform helps biotech companies track the minutiae of getting a drug through development, from finances to resolving scheduling problems with clinical trials.

  • Read more about OpenAI Buys Orchestra Bio to Put Agents on the Unglamorous Side of Drug Development

OpenAI Races to Raise 30 Billion Dollars Before Anthropic Sets the Market Price

OpenAI CEO Sam Altman speaking on stage at TechCrunch Disrupt.

OpenAI is accelerating a fundraising round of about 30 billion dollars that could value the company at more than 1.4 trillion dollars, Reuters reported on Monday, citing people familiar with the matter. The push is deliberately timed ahead of Anthropic's expected stock market debut in mid-November. Existing backers SoftBank Group and Abu Dhabi-based MGX are in talks to join, and OpenAI met with long-only funds and sovereign wealth funds last week, in the same week Anthropic was holding its own investor day. OpenAI and SoftBank declined to comment to Reuters.

  • Read more about OpenAI Races to Raise 30 Billion Dollars Before Anthropic Sets the Market Price

Another 45 Billion Dollars: Anthropic and Nscale Are Reportedly Talking About Doing It Again

Anthropic and AI infrastructure provider Nscale are reportedly on the verge of announcing a second compute deal worth 45 billion dollars, according to Bloomberg reporting relayed by TechCrunch on October 19. The talks would come a little over a month after the two companies announced a first 45 billion dollar compute deal. Bloomberg's sources, cited by TechCrunch, cautioned that the talks are still underway and the details could change, and TechCrunch said it had reached out to both companies for comment.

  • Read more about Another 45 Billion Dollars: Anthropic and Nscale Are Reportedly Talking About Doing It Again

Pagination

  • First page « First
  • Previous page ‹ Previous
  • …
  • Page 4
  • Page 5
  • Page 6
  • Page 7
  • Current page 8
  • Page 9
  • Page 10
  • Page 11
  • Page 12
  • …
  • Next page Next ›
  • Last page Last »

Copyright © 2026 Rocky Mountain Madman LLC - All rights reserved

Developed and Designed by Rocky Mountain Madman LLC