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AIQuiet 8d · day 9

OpenAI's AI solves Navier–Stokes Millennium Prize Problem

OpenAI claims its AI model proved mathematically that the classic fluid-flow equations break down under extreme conditions.

newest coverage 7d agosummary written 7d ago4 pieces5 likes & upvotes1 comments NewswiresHacker NewsMastodonGoogle News

What to know

  • OpenAI's AI proved the Navier–Stokes equations—foundational 19th-century formulae for fluid dynamics—break down and produce infinite speeds under extreme conditions, solving a Millennium Prize Problem.
  • The singularity appears at 70-nanometer scales where the equations' assumption of continuous fluid fails, as individual molecules become significant.
  • Mathematicians confirm the equations were already known to be insufficient in certain scenarios, and alternative frameworks like the Boltzmann equation may face similar limitations.

“The Navier–Stokes equations make a simplifying assumption that a fluid is a continuous substance, rather than a collection of chaotic molecules. When there are only a couple of molecules across the sample, that assumption is no longer a good approximation of reality, and the equations fail.”

George Karniadakis, Applied mathematician · Nature

OpenAI AI developerGeorge Karniadakis Applied mathematician, Brown UniversityCharles Fefferman Fields Medal-winning mathematician, Princeton UniversityYu Deng Fields Medal mathematician, University of Chicago

OpenAI's AI solves Navier–Stokes Millennium Prize Problem
nature.com

How it unfolded 1 development · click the chart to see its coverage articlesposts

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  1. 1

    Nature examines what the solution means for fluid dynamics

    Nature published analysis placing the breakthrough in context: applied mathematician George Karniadakis calculated the singularity appears at 70 nanometers width for air, where the continuous-fluid assumption of Navier–Stokes breaks down at molecular scale. The piece notes the equations were already known insufficient under certain conditions, and explores alternative frameworks like the Boltzmann equation.

    “Our understanding is very limited.”
    — Yu Deng, mathematician at University of Chicago
  2. background

    OpenAI announces AI solution to Navier–Stokes Millennium Prize Problem — OpenAI claimed its most advanced AI model solved one of the Millennium Prize Problems by proving mathematically that the Navier–Stokes equations produce singularities—predicting physically impossible infinite speeds—in certain instances where a fluid vortex becomes extremely thin.

Also covered reported alongside — the timeline has no entry for these yet

  1. 2 outlets AI cracked the Navier–Stokes challenge. What does that mean for physics?

    first by nature.com, 7d ago · also Nature News