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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#321

The real story here: the priority dispute and its implications on AI. When your hosting provider has unlimited resources to throw at any problem, all they need to know are the good problems, and they can learn that from your logs, how can you trust them? They could easily have looked at the logs. We don't know. We'll never know! You can't trust places like OpenAI or Anthropic with your IP if you're a business. They c…

I think we can follow the incentives. We know…

Re: On the Navier–Stokes Millennium Prize Problem

#322

Earlier quoted context omitted.

The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin…

Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.

If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.

Re: On the Navier–Stokes Millennium Prize Problem

#323
post #299

Earlier quoted context omitted.

> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.

It seems like there were a couple of human mathematicians that were higher on the 'solving complex problems ladder' than this machine.

[deleted]

Re: On the Navier–Stokes Millennium Prize Problem

#324
>The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents… The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched.

The Millenium Prize is $1M, what is the ROI? (Edit: since I was not clear, and confused some - I mean for a hypothetical of a third party paying commercial rates to use AI to solve mathematical challenges and claim prize money, not for scientific value alone or as a promotion of an AI lab’s capabilities)

My napkin math - If you get 33 output tok/s each agent will burn 10.5M tokens over 88 days. At $50/MTok (Astra cost), that is $525 per agent. With 10,000 agents, you’d spend $5,250,000 to get back a million.

(We also know that they were running more groups that varied in size and this model is a generation ahead of astra)

Re: On the Navier–Stokes Millennium Prize Problem

#325

OMG this is going to affect the lives of so many people! We have definitively reached AGI

Navier Stokes existence and smoothness has approximately zero bearing on engineering applications

Existence of AI capable of solving millennium problem has enormous bearing on everything though.

Re: On the Navier–Stokes Millennium Prize Problem

#326
post #107

Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at fronten…

So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “gene…

We are very likely at the begging of the next industrial revolution.

Re: On the Navier–Stokes Millennium Prize Problem

#327
post #299

Earlier quoted context omitted.

> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.

It seems like there were a couple of human mathematicians that were higher on the 'solving complex problems ladder' than this machine.

Yes a couple of elite mathematicians working on the problem for a year, which AGI solved in a fraction of the time. What about everyone else 100IQ? What about as the models are even better 1 year from now, 2 years? The trajectory hasn't abated.

Re: On the Navier–Stokes Millennium Prize Problem

#328
post #130

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…

What about ripping off the prompts?

Re: On the Navier–Stokes Millennium Prize Problem

#329
Resources:

YT playlist on Millennium Prize Problems By Harvard math department in March 2026

https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnL...

On Navier-stokes problem definition:

https://www.youtube.com/watch?v=XoefjJdFq6k

https://www.youtube.com/watch?v=ERBVFcutl3M

https://www.youtube.com/watch?v=Ra7aQlenTb8

Re: On the Navier–Stokes Millennium Prize Problem

#330

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 informat…

National Public Radio?
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