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Navier-Stokes Equations

19th-century partial differential equations describing viscous fluid motion, foundational to fluid dynamics and a famous unsolved math problem.

Known aliases

  • Navier-Stokes
  • Navier–Stokes
  • Navier–Stokes equations

Current stories

leadershipConfirmed3 publishers

OpenAI's 372 math results outrun the people who must check them

OpenAI published 372 families of math results from an unreleased model on Oct. 6, more than mathematicians have yet been able to check or understand. Each claim now waits on human readers, who must work without the prompts OpenAI chose not to publish.

Perspective Coverage

3 publishers
Builder
Builder 32%
Operator
Operator 38%
Investor
Investor 30%

Reality

Evidence50
Adoption
Not scored
Hype gap+45
Incentives65
Confidence60
productConfirmed3 publishers

OpenAI's math proofs fall short of a Princeton panel's verification standards

OpenAI released 719 manuscripts of claimed solutions to hard math problems this week and included the model's chain of thought for only ten of them. The advisory group of mathematicians OpenAI consulted had set verification standards the lab's release misses on several counts.

Perspective Coverage

3 publishers
Builder
Builder 44%
Operator
Operator 38%
Investor
Investor 18%

Reality

Evidence58
Adoption
Not scored
Hype gap+40
Incentives55
Confidence60
buildOne report1 publisher

Researchers curb unpublished uploads to AI models after two discovery disputes

OpenAI announced an agent-generated Navier-Stokes solution a day after Tristan Buckmaster and Levent Alpöge shared a year of work, Nature reported. No independent check shows OpenAI or Anthropic misused data, so researchers' practical exposure depends on account settings and on who publishes first.

Publishers:theneuron.ai

Reality

Evidence40
Adoption
Not scored
Hype gap+10
Incentives
Not scored
Confidence45
scienceConfirmed7 publishers

Terence Tao says automated proof checking is why the AI labs stopped consulting mathematicians

A proof checker confirmed the steps of OpenAI's Navier-Stokes result within days. The argument now running through mathematics is over who explains the 166 pages and who gets the credit for them.

Perspective Coverage

7 publishers
Builder
Builder 46%
Operator
Operator 33%
Investor
Investor 21%

Reality

Evidence60
Adoption
Not scored
Hype gap+40
Incentives70
Confidence58
productOne report1 publisher

OpenAI denies reading two mathematicians' Codex logs before racing them to Navier-Stokes

Tristan Buckmaster says OpenAI accelerated onto Navier-Stokes after learning of his work with Anthropic's Levent Alpoge, and that the answer he got about his prompt history addressed lookup rather than training.

Publishers:wired.com

Reality

Evidence40
Adoption30
Hype gap+45
Incentives88
Confidence50
scienceOne report1 publisher

Navier-Stokes, Rederived: Fluid Theory Gets a Reason Instead of a Fit

A 20-year rebuild defines a fluid by its symmetries and recovers the classical equations as a consequence, which is what tells you where they stop working.

Reality

Evidence38
Adoption
Not scored
Hype gap+24
Incentives22
Confidence36