Birbla

Discussion summary

A recent research claims progress on the Navier–Stokes Millennium Prize Problem, with some skepticism about its validity. Experts discuss the role of internal models and the significance of the proof, including simulations and formal verification.

What the discussion says

  • Some believe the proof is correct, citing formal verification in Lean4.
  • Others are skeptical and question the legitimacy of the proof.
  • There is discussion on whether such research can be done with publicly available models.
  • The importance of the problem for engineering and climate modeling is debated.
“There is a proof in lean4 it's correct by construction”
— keel-control
“Why is no one skeptical that the solution is correct? There's not a _single_ comment asking whether this proof is legit…”
— simianwords

Join the discussion

Write your take first — we'll ask for email only when you're ready to publish.

Sign in
  • Hacker News
  • I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits.

    This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able to until LLMs came along.

    Hard to claim at this point that LLMs aren't capable of novel STEM creativity and genius to a degree that will soon far surpass that of humans.

    If anyone has counterpoints to this I'd love to hear them!

    by intenex
  • From my reading of the announcement:

    - There are at least two versions of a model more powerful than Astra at OpenAI at the moment.

    - The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents.

    - The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents.

    - OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed.

    So the timeline was:

    Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution.

    If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!

    by closetheloopdev
  • Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute.

    The dark forest awaits..

    by recitedropper
  • For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915

    Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees

    by jakevoytko
  • > We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.

    WOW?

    by tiborsaas
  • "we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."

    What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?

    by mewse-hn
  • My take:

    1. It shows what even this wave of AI can actually do.

    2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.

    3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.

    by hdivider
  • Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
    by arctic-true

Explore Birbla archives