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On the Navier–Stokes Millennium Prize Problem

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On the Navier–Stokes Millennium Prize Problem

#1
Further discussion:

https://simonwillison.net/2026/Sep/8/on-navier-stokes/, https://news.ycombinator.com/item?id=49621697

https://twitter.com/sama/status/2097385167002415140, https://xcancel.com/sama/status/2097385167002415140

On the Navier–Stokes Millennium Prize Problem
openai.com

Re: On the Navier–Stokes Millennium Prize Problem

#2
> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens

Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!

Re: On the Navier–Stokes Millennium Prize Problem

#3
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

Re: On the Navier–Stokes Millennium Prize Problem

#4

> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!

300e9 output tokens at the current Astra per-token API pricing ($50 per 1e6 output tokens) would be roughly $15,000,000 ignoring input tokens.

Re: On the Navier–Stokes Millennium Prize Problem

#5

> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!

Napkin math if we assume gpt 6 astra on max is >$15 million (just for output tokens) for those wondering.

Re: On the Navier–Stokes Millennium Prize Problem

#7
Is this truly the beginning of the AGI era?

Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution.

If this is what anyone calls 'slop' then slop has no meaning.

I'm all for it on the use case of solving mathematical breakthroughs!

Re: On the Navier–Stokes Millennium Prize Problem

#9

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

That is addressed in the article.
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