[HN Gopher] In the 'Wild West' of geometry, mathematicians redef...
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       In the 'Wild West' of geometry, mathematicians redefine the sphere
        
       Author : bryanrasmussen
       Score  : 25 points
       Date   : 2023-11-10 22:04 UTC (2 days ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | paulpauper wrote:
       | there are two types of mathematics: cutting-edge stuff like this
       | ,and then the stuff that fills textbooks, random arxiv pre-
       | prints, etc that is more mundane
        
         | uxp8u61q wrote:
         | I'm not sure what you mean by that. The "stuff that fills
         | textbook" is at least a century or two old. "Random arXiv
         | preprints" are (usually) literally cutting-edge research.
        
           | paulpauper wrote:
           | That is literally my point restated. mathematicians who write
           | textbooks are covering stuff which is old, not cutting edge.
           | most arxiv posts are not cutting edge, only a tiny percentage
           | are, like the stuff mentioned here.
        
       | mysterydip wrote:
       | I thought this was going to be something like "pi is really 3.2",
       | but it was much more interesting.
        
       | SquibblesRedux wrote:
       | While I understand manifolds, this article is the first time I
       | have seen the term "contact manifold." Does anyone know of an
       | original source where "contact manifold" is first formally
       | defined?
        
         | teunispeters wrote:
         | Way outside of my field - but from the link above: -
         | https://www.jstor.org/stable/1970165 On Contact Manifolds Their
         | reference - https://core.ac.uk/reader/82059800 - A Brief
         | History of Contact Geometry and Topology - HansjSrg Geiges
         | 
         | Seems solid enough. There's lots of other fun links there. I'm
         | fascinated by this field but I don't have a degree of any kind
         | so ... lots more learning to go!!!
        
         | narinxas wrote:
         | but when I understand manifolds both contermporary flat-
         | earthers and scientific academics(?) get mad at me?
         | 
         | but I wouldn't claim to understand manifolds, I just understand
         | that they have something to do with flatness perception at
         | small scales (or short distances)
        
         | daynthelife wrote:
         | Not an original source, but the Wikipedia page [0] gives a good
         | introduction. A contact manifold is then just a manifold
         | equipped with a contact structure.
         | 
         | A more in-depth discussion can be found in many differential
         | topology texts, e.g. page 581 of [1].
         | 
         | [0] https://en.m.wikipedia.org/wiki/Contact_geometry
         | 
         | [1] Lee, Introduction to Smooth Manifolds
         | https://math.berkeley.edu/~jchaidez/materials/reu/lee_smooth...
        
       | narinxas wrote:
       | but when I do it I'm called insane and commited to github
        
       | codetrotter wrote:
       | It had to be the topologists :)
        
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       (page generated 2023-11-12 23:00 UTC)