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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#31

Post by emil-lp »

aadyachinubhai wrote: post #17

LLMs can't contribute good code to some of the good OSS math libraries, How is it even solving these problems?

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.

Re: The Navier–Stokes Millennium Prize Problem

#32

Post by adg33 »

bob1029 wrote: post #24

> ... 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…

It's something that happened before LLMs - multiple discovery. Calculus is a classic example.

Re: The Navier–Stokes Millennium Prize Problem

#33

Post by weinzierl »

tosh wrote: post #2

> 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 h…

Maybe just a rumor of a high value target having their API keys accidentally consumed in the context...

Re: The Navier–Stokes Millennium Prize Problem

#34

Post by hansvm »

junofan wrote: post #22
sdcfgy wrote: post #14

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.

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.

My doctor's privacy policy is a bit more abusive than OpenAI's. It exists mostly because of a $%^&&* legal framework rather than malice, and I've grown accustomed to "if I don't want to die then I sign away these rights." Despite my having theoretically signed my soul away, my doctor isn't selling personal information to my exes or to life insurance companies (though they could in the US; that extremely personal information is no longer mine). OpenAI is engaging in the "technically legal maybe we'll see but obviously unintended" side of this transaction, and maybe that works out for them, but I wouldn't personally choose to be a shill for "it's unreasonble to expect somebody with 'legal' permission to do something other than the maximum 'legally' permitted" if I were in your shoes.

Re: The Navier–Stokes Millennium Prize Problem

#35

Post by dguest »

tyre wrote: post #8
shellfishgene wrote: post #3

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?

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.

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.

Also it's not like you're looking for a lost pair of car keys: just getting to the level where you can understand a problem well enough to "steal" it takes a huge amount of work. People are going to know if you're at the level where you could be a competitor.

So in general it's pretty safe to talk generally about whatever you're doing.

Re: The Navier–Stokes Millennium Prize Problem

#37

Post by emil-lp »

josalhor wrote: post #23

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 messa…

If they have zero-retention, then it is not possible.

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

Re: The Navier–Stokes Millennium Prize Problem

#40

Post by emil-lp »

avs733 wrote: post #13

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…

Yes, there is no doubt about scientific misconduct. I think the entire math community agree on that.
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