The Navier–Stokes Millennium Prize Problem

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"].

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...

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»?

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

Is there a good tldr on this topic?