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The Navier–Stokes Millennium Prize Problem

https://simonwillison.net/2026/Sep/8/on-navier-stokes/
78•tosh•56m ago

Comments

tosh•34m ago
> My two favourite hypothetical questions regarding this used to be:

> If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.)

> If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"?

> My new preferred hypothetical for this is:

> If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first?

weinzierl•3m ago
Maybe just a rumor of a high value target having their API keys accidentally consumed in the context...
shellfishgene•32m ago
What's missing from the story I think is the part about "...then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear...". If only the two of them were working on the problem in secret, how did their breakthrough become a rumor?
dboreham•25m ago
They weren't working in secret?
tyre•20m ago
People talk. If you have a breakthrough solving one of the most famous problems outstanding, you're going to tell people.

You'll say, "Don't tell anyone", which they will ignore because they get a rush and perceived status by sharing it. So then they tell someone, along with "Don't tell anyone", etc.

It's a small enough world (both in academic math, one at Anthropic) that you get to OAI in very few hops.

dguest•2m ago
The reality is also that most of your colleagues have no interest in stealing your work: they have their own work to do anyway, and having a colleague effervescing about whatever they are working on is kind of the norm in pure research. Just because they are making progress it doesn't mean they are about to do anything interesting.
caughtinthought•25m ago
Basically no new info here, not really sure why this post needed to be written tbh.
iso1337•23m ago
Agreed. This person just loves to shill their blog and their pelican benchmark.
jdlshore•17m ago
There’s no shilling here. The person who posted the link isn’t the person who wrote the blog.
fimi•18m ago
Yes, you have ability to get information very quickly, but not everyone does.
kzrdude•12m ago
On the contrary, a level-headed summary that gathers information from all the different sources is necessary.
tyre•23m ago
Yeah, this was pretty shitty by OpenAI. Not surprising, sadly.

Them being assholes, trying to exclude an author just because he worked at Anthropic, shows the kind of culture within (that part of) their organization. The focus wasn't on supporting academics or expanding research. It was on getting great marketing.

If they had to burn millions of dollars solving a problem _that they thought was already being solved_ to do so, they'd do it.

dboreham•18m ago
The concept that "knowing something has been done" allows others to find the solution to an previously unsolvable problem is an old proven one. For example when Germany launched a rocket (V2 prototype) the British knew its rough trajectory and from spying it's rough size. Although they had previously believed that ballistic missiles weren't possible because no engine could provide the necessary thrust to weight ratio, given the obvious German launching of one, they went through all the known chemical compounds to arrive at the combination (Ethanol and LOX) used. [Story from RV Jones "Most Secret War"].
avs733•16m ago
I’ll go back to the point about authorship. I’m Not a mathematician but I am in academia. if you are fucking around with authorship you are immediately suspect.

That aspect alone would/should be unthinkable to any serious academic. Authorship reflects who did the work and changing it for business competition reasons should be a red flag for multiple different reasons. They include, the sheer tactlessness of treating a major theoretical advancement as a competitive posturing first, the norms of academia second, and all the misunderstandings of the culture of the disciplines culture that people will now suspect are hiding beneath the visible surface (insert topography joke).

Math as a field is fairly unique even in how they list authorship. It was long the norm that authorship to be alphabetical because the idea of first, second, senior etc authorship is harder to define than many other fields.

“The stated rationale for alphabetical order is that it treats co-authorship as intellectually joint work: every listed author’s name carries equal weight, and no one has to negotiate, or be seen to negotiate, over billing. That is a genuine advantage over position-coded conventions, where disputes over who is “first author” are one of the most common sources of authorship conflict in fields that use them” [0]

That norm is changing, slowly, but one option people are pursuing is notable: randomized author order. Their is a perception that alphabetical is too biased…that’s the world OpenAI is stepping into when they make that offer of authorship to one scholar with a demand that he exclude his partner.

I can’t speak to the facts of anything else in this, but if a grad student came to me and said someone made them that offer, I would tell them to run and if they were brave report it.

[0] a to the point lay description of the history of math authorship can be found here: https://casrai.org/guides/mathematics-alphabetical-authorshi...

sdcfgy•16m ago
My take home from this entire drama is that one should not use LLM services for confidential or proprietary information as they all seem to be run by assholes. And you’re sending them everything you are doing. Would you send your lab notebook to an asshole? Hell no.

I say that as a mathematician (on paper) who perhaps surprisingly doesn’t give a crap about the problem itself.

junofan•11m ago
Their privacy policy for normie subscribers says in plain English they use your Personal Data for research. I think it’s pretty unreasonable to use the service and expect otherwise.
ZeWaka•6m ago
>implying most users read them
andersmurphy•6m ago
You'd think theft would still be illegal regardless of what a privacy policy says.
sdcfgy•5m ago
If that is the case, why on earth would you use it in any professional setting?
hansvm•3m ago
Placeholder:
civvv•14m ago
LLM’s seem very good at solving mathematical problems of which there is an enormous amount of exisiting work/attempts in their training data. This is an amazing capability, but does not convince me that these models are «thinking» or «reasoning» in the way a human does. A human mathematician could in theory categorize/discover an entirely new field of mathematics tomorrow, based purely on their «human intelligence», I wonder if we will see similar examples by LLM’s soon. It seems to me currently impossible that LLM’s can replace human mathematicians, because of their (assumption) likely dependence on human input in the sense of enormous amounts of pre-existing attempts/data.

If an entirely new problem, within a new field of mathematics were to appear tomorrow, I highly doubt an LLM would be useful at all on their own. Is this the «ultimate ASI test»?

kdavis•13m ago
All your datum are belong to us!
aadyachinubhai•13m ago
LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?
matrix2596•8m ago
search, verifiability and compute
emil-lp•3m ago
That's a good question.

It is able to contribute code, but maybe not good code.

It's the same in math: it's able to solve problems, but not necessarily in a good way with a human readable code.

Math papers are a lot like software:

- theorems are like API

- lemmata like internal/private function API

- definitions are like types

- the proofs are the implementation

The proofs of ChatGPT are not necessarily readable or maintainable.

rao-v•13m ago
It’s reasonable to wonder about what chat usage data gets into models (to be honest probably quite little - carefully curating training data and creating higher quality synth data seems to be the current approach) and the implied risk to privacy and creativity (every new patent filed this year probably touched a model before filing).

What I cannot reconcile is the timeline and the concern in this specific case.

I don’t think training pipelines are anything close to the level of continuous training needed to incorporate Aug 15th ideas into a model that generates a breakthrough early Sept. Either OpenAI nakedly had someone with mathematical understanding dig into a specific user’s chats (a massive red flag) or this really is poor handling of a more classic parallel discovery situation (with one party clearly having worked on it longer)

octocop•13m ago
Is there a good tldr on this topic?
nicce•12m ago
Can’t wait to see the human verifying the results and then figure out that the AI model actually cheated and the results are not correct.
imjonse•2m ago
the proofs were verified in Lean, so unlikely.
josalhor•11m ago
I think this drama was blown up a bit out of proportion. The entire discourse I am seeing online seems to revolve around this:

> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models

I mean... yeah? What do you expect? What else can they say? How could you prove a negative in this case? I do not want to comment on specific OAI employee chat messages, but on the actual OAI discovery here.

emil-lp•1m ago
If they have zero-retention, then it is not possible.

So what they are saying is that they don't have zero retention.

bob1029•9m ago
> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ...

I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years.

I think giving someone hope that an answer exists might as well be the same thing as giving them the answer these days. Competition is a hell of a drug, and frontier LLMs aggressively compound that energy.

adg33•3m ago
It's something that happened before LLMs - multiple discovery. Calculus is a classic example.
l5870uoo9y•6m ago
I run a small SaaS[1], like so many others, that uses AI to generate and optimize SQL. Getting this to perform optimally has been a lot of work and now I wonder if OpenAI is outright stealing this knowledge, which without a doubt is highly valuable to them.

[1]: https://www.sqlai.ai

feverzsj•4m ago
It could be much worse.

OpenAI can easily identify these outstanding human behind their accounts. Human in OpenAI constantly check their logs for breakthrough. When they find something interesting, they brute force the result using their massive computing power.

No LLM is even needed.

cs_throwaway•1m ago
Maybe someone on the NYU team forgot to opt out of “improve the model for everyone”.

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