[HN Gopher] Monumental proof settles geometric Langlands conjecture
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       Monumental proof settles geometric Langlands conjecture
        
       Author : jandrewrogers
       Score  : 109 points
       Date   : 2024-07-26 17:14 UTC (5 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | proof_by_vibes wrote:
       | 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.
        
         | vinnyvichy wrote:
         | 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..
        
           | proof_by_vibes wrote:
           | 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!
        
       | downvotetruth wrote:
       | Prior:
       | 
       | https://news.ycombinator.com/item?id=40280760
       | 
       | https://news.ycombinator.com/item?id=40453822
        
       | paulpauper wrote:
       | 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.
        
         | antognini wrote:
         | The article does in fact discuss precisely this:
         | 
         | > 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 Faergeman 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."
        
           | calf wrote:
           | Are they tenured professors?
        
           | senderista wrote:
           | Quote from Knuth:
           | 
           | "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?"
           | 
           | https://github.com/kragen/knuth-interview-2006
        
         | leephillips wrote:
         | 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.
        
         | anthomtb wrote:
         | 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?
        
         | xanderlewis wrote:
         | 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.
        
       | slanderaan01 wrote:
       | 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.
        
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