[HN Gopher] New Shape Opens 'Wormhole' Between Numbers and Geometry
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       New Shape Opens 'Wormhole' Between Numbers and Geometry
        
       Author : theafh
       Score  : 116 points
       Date   : 2021-07-19 15:51 UTC (7 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | hammock wrote:
       | I enjoyed the way this article was written - it sounds like the
       | synopsis of a new TV show on Showtime or Netflix or something (of
       | course based in a stylized post-war Europe or similar with muted
       | colors).
       | 
       | It's also inspiring the way it's written, as opposed to a more
       | academic style.
        
         | twobitshifter wrote:
         | It was well written but I wish being a geometry related topic
         | there were some figures to help with the explanation. I'd like
         | to /see/ examples of how this all works to help me understand.
        
           | teekert wrote:
           | Yeah I'm really looking forward to the Standup Math or/and
           | (preferably and) 3blue1brown version.
        
             | langlands wrote:
             | I would be surprised if this gets a 3blue1brown episode -
             | this branch of mathematics takes a lengthy time to wrap
             | one's head around. 3blue1brown topics tend to show up in
             | undergraduate math, whereas the Langlands program (and the
             | Fargues-Fontaine curve in particular) would really only be
             | studied by a subset of graduate students studying Number
             | Theory.
        
         | austinheap wrote:
         | Yes! I just came here to say this too.
         | 
         | For academics: is this tone counter productive? For us lay
         | folk: is this tone helpful?
        
           | asymptosis wrote:
           | Depends on what you mean by counter productive. You wouldn't
           | cite Quanta Magazine if you were writing the next journal
           | article on this topic intended for peer review. Instead, you
           | would go to the original paper "Geometrization of the local
           | Langlands correspondence" and pull that apart to look for
           | ways you can improve upon what has already been done.
           | 
           | But mathematics is a big area (there is a reason why it's a
           | plural: it's better to think of it as more of a family of
           | topics than a single science.) And if you're a mathematician
           | from an unrelated branch of mathematics, an article like this
           | is written in a way where you can understand most of the
           | underlying concepts reasonably intuitively.
        
           | abecedarius wrote:
           | As more of a layperson, I have mixed feelings. As science
           | journalism goes, it's excellent, but reading this sort of
           | frontier news feels like a waste of time to me now. I only
           | really found out that progress is being made in fields I
           | don't understand. I bothered to check this article out
           | because multiple people posted that it's very good, but the
           | time I spent reading it would've been better put into getting
           | a little bit more real understanding of old related
           | discoveries like the unsolvability of the quintic, which _is_
           | within reach at my level.
        
           | scubbo wrote:
           | As someone who is maybe somewhere in the middle (I have a
           | Masters in Maths, but haven't used it in earnest since
           | graduating ~10 years ago) - I found this spot-on. Engaging
           | enough to pull me in, technical enough to give some idea of
           | what exactly is going on, but not too far in either
           | direction.
        
             | gipp wrote:
             | Read a similar article from this publication on quantum
             | mechanics, and have a similar background in that area, and
             | I concur completely. Maybe that's just the _exact_ audience
             | this is targeted to but it 's by far the best "popular-
             | press" publications on subjects of this level I've read.
        
           | hellbannedguy wrote:
           | I need more pictures. I'm obvious a layperson.
        
       | rohanphadte wrote:
       | Sizable article - write down a few highlights about the Langlands
       | program.
       | 
       | > Mathematics has received a rare gift, in the form of a mammoth
       | 350-page paper posted in February that will change the way
       | researchers around the world investigate some of the field's
       | deepest questions.
       | 
       | > The work is a collaboration between Laurent Fargues of the
       | Institute of Mathematics of Jussieu in Paris and Peter Scholze of
       | the University of Bonn.
       | 
       | > It opens a new front in the long-running "Langlands program,"
       | which seeks to link disparate branches of mathematics -- like
       | calculus and geometry -- to answer some of the most fundamental
       | questions about numbers.
       | 
       | > The Langlands program is a sprawling research vision that
       | begins with a simple concern: finding solutions to polynomial
       | equations like x2 - 2 = 0 and x4 - 10x2 + 22 = 0.
       | 
       | > "The Langlands program is a network of conjectures that touch
       | upon almost every area of pure mathematics," said Caraiani.
        
       | jesuslop wrote:
       | It's about Scholze work on perfectoid spaces. A nice intro talk
       | in Spanish is at https://cienciastv.org.mx/2020/08/el-mundo-
       | perfectoide-adria...
        
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       (page generated 2021-07-19 23:00 UTC)