an LLM-related bet, and a prediction
Apparently OpenAI published a preprint that contained a proof of the Navier-Stokes Millennium Problem which was supposedly generated by some unreleased LLM model. Let it be known I was actually in Silicon Valley at the time. Cycling around the Google Mountain View office, in fact, where in true dystopian fashion there was not a soul in sight and yet still cars on the street—driverless Waymos creeping around in cyclic intervals, contributing to the atmosphere of dread that kept blaring (sometimes literally through loudspeakers) that I was being constantly watched.
There is some controversy as to whether this was actually an original proof or not. In either case, what is uncontroversial is that it was built on ideas illegally stolen from human researchers, as this is exactly what LLMs do. The whole incident is a giant stain on mathematical history and just furthers the show of corporate meddling in some of the most fundamental aspects of humanity. It is overall a deeply shameful enterprise, and in general contributes to the point I hand-wavingly made in my last blog post: we, as mathematicians and researchers, should absolutely not be engaging in any kind of good faith with people who work in LLM-related ventures, and particularly not with people for or with OpenAI and Anthropic. In fact, we should actively disregard them, probably insult them and their families every time they attempt to engage with us in any manner, and remind ourselves that these are not good people. In fact they are very bad and evil people1, and we should treat them like Nazis and feudal lords, and be generally allergic to anything that they try to say or claim, and certainly not ally with them in any manner. This incident more than anything has proven that these guys do not give a shit about mathematics or humanity more generally.
Unfortunately, what is true is that they seem to have a theorem-proving weapon at their disposal2. What is up in the air is whether this thing can actually do math instead of just prove theorems. Recently Terry Tao (far too late, I fear) has taken to precipitating some of these questions. His concern is that the solutions AI comes up with do not provide insight into general techniques for solving these problems. He is right. These things are computers. They compute. The classic example is the ‘slop’ original proof of the insolvability of the quintic, the Abel-Ruffini theorem, which was later proved beautifully by Galois in a development which laid much of the groundwork for future mathematics—there is no indication the LLM can produce Galois’ proof, and even if it can, it has no incentive to make these ideas understandable to human beings. LLMs may very well lead to math being ‘solved,’ but in doing so it will kill the whole point of mathematics.
It is currently not clear whether the proof of Navier-Stokes singularities gives any additional insight into the mathematical ideas surrounding the problem. My guess is that it provides much less insight than proof that would have been made by a human. It’s a classic monkey’s paw that God develops so wholeheartedly for our race: you may find the answer to every mathematical question you choose, but in doing so those questions will become meaningless. Nevertheless, it certainly seems like LLMs are going to keep getting better and keep solving all these things we hold so dear, but they will fail to contribute to the human exercise of understanding and loving mathematics.
This leads to the following prediction I make now:
By December 31st, 2027, there will be an LLM-generated proof that $\mathbf{P}\neq\mathbf{NP}$ along with a Lean formalization. This proof will not contain any insights into the crucial mathematical ideas underlying the problem of $\mathbf{P}$ vs. $\mathbf{NP}$. The proof may not even be understandable or digestible by a human being: it could possibly be an assemblage of formal logic that is technically correct, but crucially it will absolutely not be a proof that a human being could ever come up with, nor will it suffice as a satisfactory proof that ‘ends’ the $\mathbf{P}$ vs. $\mathbf{NP}$ project.
This forms part of a bet with Jake Januzelli of Columbia University. I give him €100 if it doesn’t pan out. He gives me €50 if it does. If it doesn’t pan out, it will be the happiest €100 I have ever spent.
I am also happy to make other bets with people, especially one that involves a public safety incident caused by an autonomous AI system that leads to some number of human deaths. If you wish to make one send me an email along with an upfront deposit. If I lose I will return it in kind along with your winnings.
The kicker here should be that they obviously do not care one whit about mathematics. You can go look at literally any thread in which they write ‘cope and seethe.’ I would like to see these people cope and seethe when their own livelihoods are taken from them. I constantly need to remind people of this: these guys are our enemy. They are our nemesis. We cannot work “together” with them, whatever that means—just as you cannot work together with, as I said, Nazis and feudal lords, you cannot work together with these clowns. We should not give them even an ounce of our time.
To lower the risk of sounding like shifting goalposts, this in itself can be catastrophic: for example, it doesn’t matter whether the algorithm that the NSA develops using LLMs to perform the Arora-Ge attack with, I don’t know, $O(n^{\sqrt{B}})$ samples is a ‘good’ algorithm that advances our knowledge of the field, or whatever, it still ultimately breaks the lattice parameters we use to safeguard post-quantum migration, including TLS v1.3, allowing them to continue to spy on us even in the absence of a functioning quantum computer. Presumably the NSA can write some kind of prompt saying “come up with a piece of humanly-undetectable spyware which is self-propagating and only targets Huawei phones. make no mistakes” and the damn thing will do it for them after like 60 hours of ‘compute’ or something. My smaller, secondary predictions are that we will shortly hereafter start seeing disruptions in the global supply chain, including China possibly invading or at least attempting a naval blockade of Taiwan. If the technology is indeed here there will be geopolitical consequences that could include nuclear war. I should probably get out of the bay area while I have the time—Paris is ‘too pretty to bomb,’ anyway.