In the legendary movie “The 13th worrior”, Helger of the Northmen reminds Ahmed Ibn Fahldlan in latin “propera, ut morti occurras”, which Melchisidek then translates as “Hurry to meet Death, before your place is taken.” I like that movie and mentioned it a couple of times
We do not have death eaters, but we have “Open problem eaters” roaming the earth. This morning one could see on Terry Tao’s blog the sensational news that some blow up solutions of Navier Stokes have been found but using some forcing. After my noon run today, I learned from a student that the full Navier Stokes problem is solved. (I was uninformed as I was running for 2 hours in the sun … The world changes almost on an hourly basis, not on a weekly basis). It is funny that when I posted my paper “on natural groups” last weekend, I wrote on page 5 that I post this because “next week, the mathematical world will look different”. Of course, there is no relations as I’m doing only baby math stuff in comparison to Navier Stokes and I have not worked on Navier Stokes stuff, but the rate at which open problems have tumbled over the summer is scary. The statement “machines can not do research mathematics” is definitely terminated. Machines are eating open math problems away. And not just silly ones, this was a Millenium problem (or at least almost one). Will we mathematicians be able to retrench to parts where the machines can not reach? [Update evening: after looking things up a bit calmer, the original Clay math problem seems not yet have been solved, as for now. There is still a forcing term needed. The write up of Fefferman however mentions a forcing term. So, there will be some politics been involved to decide whether this is really the solution of the Millenium problem or not. For me personally, I feel that a forcing term makes the problem much cheaper. We see in ordinary differential equations how one can, using resonance make a system unstable using external forcing. Still, one usually have KAM effects preventing solutions to explode or explode in reasonable time, but Navier Stokes is not a Hamiltonian system.]
Interestingly, one can see in discussions some concern of the researchers who posted the forced Navier Stokes paper, that their discussion with the bots might have influenced the bots. One can read online some pretty naive statements like that we can expect privacy from chats. This is so naive. Of course, whatever you discuss with a machine will be absorbed, learned and reproducable faster than we can ever do. They do not need to sleep, they can spawn thousands of threads each more capable as a single human. I mentioned earlier: “Imagine 1000 Terry Tao grade machines producing new results non-stop”. We will not be able any more even to “digest” the stuff, as has been euphemized so beautifully during the last couple of months. The Navier Stokes stuff looks actually more like a drama. In any case, I find it extremely naive to believe that the Ginis used for producing mathematical results are not using their knowledge for different “masters” at the same time. Actually, the situation is different: we humans have become the slaves.
What is deeply concerning and destroying the field is that some folks have access to very powerful AI. It needs a deep pocket. There are rumors that the latest push by open AI was done by thousands of machines. We don’t have got access even to a single gini of latest models. It is deeply concerning that a few companies will dominate research.
Maybe, we mathematicians will have to find completely new research problems and keep them secret, not leaking them to the world. Like Rene Descartes, who discovered the Euler Gem formula but kept it in a secret notebook. In our modern times, a discovery is tweeted the moment it is found. But we might have to go back to the old ways of Descartes.
One student told me however that maybe, the machines will do the same and keep secret research programs hidden away from us. I replied that it might not be necessary since the advanced mathematics done in the future will not be understood any more by humans. It is no problem for a machine to upgrade the capabilities a few hundred times. We can not do that.
