The Navier–Stokes Millennium Prize Problem (simonwillison.net)

If you read the history of major scientific discoveries, this has been the case for a long time. There are many things that were independently discovered by different people at nearly the same time. Once people know something is solved or solvable, it gets a relentless amount of focus.

Would anyone be surprised if major model companies had tagged the accounts of competitor employees for extra tracking? Given the concerns about distillation and bench marking it hardly seems irrational, but how it is used matters quite a lot.

I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick.

The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters.

There are always a few competitive guys who spend the entire conference taking turns to play it. And every single time, the same thing happens.

Say the current high score is around 200m. Everybody fails somewhere around that number: 190m, 186m... Maybe someone manages 210m. And the high score moves up at a snail's pace.

Then, a new guy shows up and gets something like 500m on his third try. From their next turn on, everybody easily does 450 or more, even though they were struggling to get past 200 just one turn ago.

What makes it stranger is that the game is dead simple. It's not like the new guy discovered a move that unlocked this capability. And it wasn't a lack of motivation either - they'd all been playing for an hour already. They just started performing better after seeing it was possible. There has to be a name for this phenomenon.

Normally, when you tell a coworker that you're wrapping up a result, unless they're some kind of sociopath, their natural inclination would not be to try to steal it from you.

The text for all the Goosebumps books are certainly in the training data and to some small amount influenced the solve. But their contribution was so vanishingly small it would seem absurd to say R L Stein should have recourse for contibuting to the solve.

[Edit: they said "two of": "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. .. we launched an effort ... on all open Millennium Prize problems".]

However, how to we know the next field of mathematics isn't a novel combinations of several other sub-fields? That level of mathematics would be indistinguishable from magic to most people and so in their eyes the GPT did something truly inventive.

And an LLM could in theory also stumble upon entirely new ideas: there's randomness in how they generate their reasoning and answers after all.

I suspect that we are seeing a lot of advances coming from the combination of existing but somewhat obscure knowledge coming from LLMs at the moment, because LLMs are really good at this. At least compared to humans.

Even before our AI friends became good, they were already known for having read approximately every paper and every textbook published in any language. You only need to increase intelligence a fairly small amount from there to get to something like the 'convex hull' of human knowledge.

Compare https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/

The gist is that basically whenever anyone comes up with a new method you get a big burst of activity of picking up all the now lower hanging fruit, that was previously out of reach.

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.

Maybe next step is to filter your input client side through an unknown number of obfuscators where you ask LLMs to rephrase your question (onion router idea) such that no single provider can be certain that this is human input and not some slop feedback loop.

That in itself is a dark, dark pattern. There should at the very least be explicit warnings for users who have checked “do not train”; or they should not be presented with such dialogs.

Wait until you learn how many other SaaS and web 2.0 and cloud based things are also run by assholes.

You know this metaphor? https://en.wikipedia.org/wiki/Turtles_all_the_way_down

But instead of turtles, it's assholes.

But more seriously, no, none of what I wrote above is an attempt to excuse or play down the specific role of assholes in large AI companies.

This is something I feared would happen and where open source would be left behind. Maybe they can do something with crowd-sourcing computational power from volunteirs. They were after all able to get Leela Chess Zero to be comparable to AlphaZero by training from volunteer processing power but it seems to me we live in a world now where the best models keep their stuff closed.

In imagine generation too. I'm not sure how well Stable Diffusion can compete in following instructions with all those advanced models that are kept secret.

That’s obvious, isn’t it? Just like you wouldn’t upload your confidential documents to an online spellchecker, or your proprietary code to an online compiler?

The most direct line from problem to proof is OpenAI building off of conversations the mathematicians had with their AI.

That 100x step up from using 100 agents for Euler to 100_000 agents for Navier-Stokes, in a single day seems a bit sus.

I also think this is not ethical behavior. This is at least academic dishonesty, kind of a plagiarism or intellectual theft.

That’s why they wanted to credit Tristan and to give $1M award to him. But again, they acted unethically in that process as well. They wanted him to remove Levent (Anthropic affiliation) as co-author and threatened Tristan to “end his career”. Their behavior is actually telling, their work was not completely independent from Tristan&Levent’s unpublished work.

We know that LLMs are trained to recall relevant info. We know AI vendors are using user transcripts to train models. Two plus two equals four, right? I mean, an LLM that failed to recall the transcripts of those researchers would be a bad model.

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.

There are two benefits though.

One is recognition. Cred. The PhD candidate gets to put a ", Ph.D." behind their name, opening doors to future academic employment or other endeavors where people value titles. The AI lab gets to say their tech solved sth that humanity wanted bad for a long time. Both cases with substantial financial upside (higher income for Mr. PhD and higher company valuation for the AI lab).

The other one is that this is how scientific progress works. $1M or not. That number was just a PR campaign by the math community to point to some goals. It's clear that it would cost more than $1M to get there.

Basically, it would be a proof that all the REALLY hard (combinatorial) problems out there, have a much simpler solution, if we were able to find it.

EDIT:

NS is used daily in engineering and gas/fluid modeling. We sort of “know it works”. The smoothness proof is “just” formalizing what practitioners assume is true (very coarsely said, no intention to diminish the result!)

It’s a bit like the Collatz function IMO, empirical evidence isn’t proof, but we’ve got a huge amount of evidence for the behavior we’re trying to prove.

I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go.