The September 8 event is comparable with the sputnik moment in the late 50ies. This was before I was born, but I felt the repercussions in my own education. We learned about set theory early in primary school. The “new math” revolution had come in the wake of the Sputnik shock. Also the moon program was a consequence too. I witnessed remember seeing this event when we were in Lausanne and I remember every second, the moment when the first human touched the moon’s surface. Books were in my parents library like “1980 is tomorrow” in which it was predicted that we would have mars colonies on Mars. Now, in 2026, we still fight to get back to the moon. It was enormous shock this Sputnik event.
Maybe the September 8th event is an other Sputnik moment. It is now not by competition of different super powers, like what happened during the cold war. I worked in my senior thesis on the Stoermer problem and mentioned one of the crazyness of the cold war like detonating atomic bombs in the atmosphere. It was all triggered by fear of having a space war coming up. Star wars was motivated by that etc etc. It was crazy. Now, we still have competition between nations, but the main competition is not human but robots. The Olympic events in China was not followed much in the west. They can now run 100 meters faster than Ursan Bolt at the Beijing games. Nobody seems to be concerned about this very much in the west, even not that technology wise, like in production of robots, the west is behind almost pathetically. The sputnik moment there is already over. There is no fight to balance this as we are so much behind in robot technology. Here at Harvard, there was once the Harvard bee, which was a cool thing but one has not heared anything groundbreaking in roboto technology in the west, if one compares with what happens in other places. There used to be Boston dynamics, but in comparison what one saw in Beijing, it does not compare. Very soon, the AI bots will invent, produce and improve bots. We have to look at the matrix movies again, before we are turned into batteries!
But now, we have the robots coming for mathematics and science in general. It is a huge wake-up call. Its no more just a hypothetical question of what we are going to do in 20 years, it is a question, what we are going to do right now. How do we measure the strength of a mathematician of a mathematician for example? (This is still important like when hiring faculty.) By solving problems? By proving theorems? By communicating results? By teaching? All of this is already done very well by the machines. We are inundated by AI generated youtube clips and blogs already. The open AI announcements this summer about developments also came with nice illustrations. Nothing left any more for the human mathematicians beside “digesting the proofs” as Tao pointed out in his talk on “mathematics in the age of AI”. It is a bit disturbing to hear that some slides were generated with help of AI.
At the moment, we still have just to digest the fact that scientists in general might become obsolete because machines can do much of it so much better. There will be an event on Friday here at Harvard about Navier Stokes. This Friday September 11 at 2:30 in Hall A. “New Math and AI developments in Fluid dynamics” by Javier Gomez-Serrano from Brown, maybe one of the last humans who worked on this problem! I will definitely see this and write a bit about it. By the way, on this page, I had blogged about one of the Millenium talks and also given my own view on how things on the Millenium prize front will be solved. That would have to be reviewed now, but I think the general consensus already in 2025 was that the Navier-Stokes problem would be solved soon. I would not have thought so fast then, years yes, but not not months. The next problem to fall will probably be the BSD problem, a clean cut problem. The Riemann hypothesis is probably wrong (as Turing thought), P-NP will never be solved (as it might be undecidable) ,Hodge is too opaquely to be formulated (this will be political) and the mass gap problem is an embarrassment in mathematical clarity. We do not even know what would be considered a solution. Already for Navier Stokes, the question whether forcing is allowed is politics as Fefferman allowed forcing in his article. I always thought that a forcing term is not allowed for the ultimate solution. In dynamical systems theory in general, it is much, much easier in general to get to blow-up using forcing and resonance. Like kicking the solar system slightly so that one of the planets goes away. It is much harder (and still unsolved), whether our current solar system configuration is actually stable. Probably not, if one looks at Arnold diffusion mechanisms, but with a forcing term, it could be much easier. Anyway, if there is no reason for something to be stable, it is probably unstable! (to morph an other “occams razor type of word of wisdom” that if there is no reason for something to be true, it is probably wrong. I learned something similar from Eugene Trubowitz, who once quipped that “if something is zero, it is probably due to some symmetry”.
