On the Navier–Stokes Millennium Prize Problem

minimaxir

> 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!

jakevoytko

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

wesammikhail

https://x.com/kyanyang_/status/2097211154669998337 Just saw this a few mins ago.

colesantiago

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!

pavel_lishin

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

recitedropper

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..

seizethecheese

> [T]he group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents.

dorjoycb

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

lanthissa

5 million messages, 300b output tokens, done in 5 days, and achieving something humans couldn't. the first "Country of geniuses in a datacenter" moment.

nehan

"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.

tiborsaas

> 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?

floatrock

From the methodology section: > At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. Looks like they're shifting away from the "unprecedented hacking ability" backroom-PR strategy into more benevolent messaging.

mapmeld

> Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result. Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?

Jonasori

the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side. https://x.com/rynorhn/status/2097223532438487463

alasano

I don't know about you guys, but I'm hyped about the future. Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.

dmitrygr

> How we found the proof Easy, we stole it from Levent and Tristan https://x.com/kyanyang_/status/2097211154669998337

d_silin

The actual solution link https://t.co/tz1shoCZZo

railgunmerlin

Does seem like they gloss over Alpöge and Buckmaster's work with the following > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Which seems a bit irresponsible/rash?

seizethecheese

Elsewhere in the thread, others have calculated $15mm at API rates for just the output token. (So I’ll assume this cost about that much, taking input and human researcher time.) I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)

num42

I think it would be better for the proof to go through the peer-review process.