This is exciting news! Though, there is more than just the math that needs to be done here. Namely, mathematicians not only need to formalize a concise language to bridge the gap with modern conformal field theory, but they will also need a way to understand the computability of models based on this system. And yet, there is also the human factor: namely, there needs to be an effort to sell this paradigm to existing theorists, which will require substantial effort.
Can you say more about computability of "conformal models" in the Langlands context (beyond vibes, perhaps cites)? In my understanding, "conformal models" are by construction computable..
Oops, yeah, my bad. I've been doing a deep dive into lean4 and ended up conflating the use of the term computability from that context. Sorry, for the confusion!
I'm curious what applications there might be if any in number theory. If I recall, langlands had motivations from string theory concepts which ultimately wasn't as successful as hoped in physics.
I'm not sure that's true. My quick searching around is that the first paper proposing strings as a possible description of space and time is Nambu, Nielssen and Susskind in 1969 whereas Langlands first stated his conjectures in his letter to Andre Weil in 1967[1] (ie before string theory had even really kicked off mathematically which didn't happen until Ed Witten got involved in the 1980s). In his letter, Langlands seems to motivate the conjectures entirely from abstract algebra and topology (although this is way above my mathematical pay grade at the moment so I'd be more than happy to accept I misunderstand).
Not particularly, it's so open ended it describes an enormous landscape of possible universes and lacks any specific testable predictions for our universe.
Unless it's been firmed up a great deal in recent times.
> lacks any specific testable predictions for our universe.
Predicts that special relativity holds up at all scales (check, according to all evidence so far), predicts general relativity at low energy scales (check).
So it's false that it has no testable predictions. None of this happened "in recent times" though, it's been understood for a long time.
How do people even find the time to work on this stuff without being distracted by life, family, and everything else? I think this is why so many of these people are in Europe. America is too chaotic and full of obligations and distractions to do serious academic work.
> The solution for these irreducible representations came to Raskin at a moment when his personal life was filled with chaos. A few weeks after he and Færgeman posted their paper online, Raskin had to rush his pregnant wife to the hospital, then return home to take his son to his first day of kindergarten. Raskin’s wife remained in the hospital until the birth of their second child six weeks later, and during this time Raskin’s life revolved around keeping life normal for his son and driving in endless loops between home, his son’s school and the hospital. “My whole life was the car and taking care of people,” he said.
> He took to calling Gaitsgory on his drives to talk math. By the end of the first of those weeks, Raskin had realized that he could reduce the problem of irreducible representations to proving three facts that were all within reach. “For me it was this amazing period,” he said. His personal life was “filled with anxiety and dread about the future. For me, math is always this very grounding and meditative thing that takes me out of that kind of anxiety.”
"If I'm designing a Research Institute, would the ideal design be something where you have babies screaming, and people are sleep-deprived, and you know, and are bombarded with responsibilities, and then they would produce better research?"
I couldn't from that quote understand Knuths view.
I have however the impression that some distractions of life are more fundamental than others. If the distraction is that you might not have food tomorrow or you fear for your safety, indeed I doubt you can focus on research. However other things like babies crying and "responsibilities" are only a distraction if you let them. My mental model is that "doing research" is somewhere is Maslow's pyramid which is not the bottom, but it's not as high up as most people would expect either. I'd like to hear other people's thoughts.
By my count at least four of the researchers are employed by American universities and therefore most likely live somewhere in the United States.
And "this stuff" to which you refer is the intended output of their full time jobs*. So presumably, they find time to work on it in the same way a software developer finds time to write code. You just sit down and do it, because you are being paid to do it.
*Did I miss something about how these papers were developed in their spare time?
In the article one of the authors of the proof describes a key breakthrough as happening when he contracted covid and was thereby forced to spend 3 months in bed with nothing to do but think.
As an aside, Europeans have families, lives, distractions etc just like people in the US. Source: have lived in Europe for 30+ years. Have a family and lots of distractions. Have not proved any major mathematical theorems. (yet I suppose- there's still time)
Mathematical research (as far as I know) requires significant amounts of ‘time off’ just pondering and meditating on ideas as much as it requires time sitting at a desk concentrating on a paper or working through things on paper. A lot of people have said their best work was done whilst standing waiting for a bus, in the shower, walking in the woods …and so on.
Karl Schwarzschild found the first exact solutions to Einstein’s gravitational field equations (general theory of relativity) while serving in the trenches in WWI, firing artillery at the Russians.
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