[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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