[HN Gopher] The dirty secret of mathematics: We make it up as we...
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       The dirty secret of mathematics: We make it up as we go along
       (2018)
        
       Author : yamrzou
       Score  : 18 points
       Date   : 2022-09-14 05:25 UTC (1 days ago)
        
 (HTM) web link (medium.com)
 (TXT) w3m dump (medium.com)
        
       | morpheos137 wrote:
       | Mathematics may be made up in the sense of what we use for
       | notation or symbology but the underlying relations are timeless
       | and superuniversal.
       | 
       | In any universe or species pi defined as the ratio of the path
       | length traced by a set of coplanar points equidistant to a common
       | point to the path traced by a set of points in a different plane
       | intersecting exactly two points in the first path and the
       | aforementioned common point will be the same as our pi.
        
         | whycombinetor wrote:
         | Is this still true in hyperbolic geometry, where the
         | circumference of a circle of radius r is greater than 2.pi.r?
        
         | ska wrote:
         | I think you are oversimplifying in a way that eludes the point
         | OP was trying to make.
         | 
         | Or rather two points. First that the process of actually
         | creating mathematics is messy and largely made up as it goes
         | along. I can create a new mathematical structure that turns out
         | to not be very useful, etc. Secondly that the way math is
         | taught typically hides this, and creates a very linear
         | "greatest hits" approach which is misleading.
         | 
         | You are correct that one of the things that has come out of
         | centuries of studying mathematics are clear definitions of
         | abstract objects that almost _have_ to have been found; but the
         | day-to-day isn 't that.
         | 
         | On the other hand, how something is taught and how it is
         | practised often aren't that close to each other. Part of the
         | reason the pedagogy looks the way it does is to distill
         | centuries of thought and argument into a few credit hours.
        
       | robot_no_419 wrote:
       | Math is presented in a way that's supposed to be organized,
       | compact, and categorical. If we taught math the same way math was
       | proven and discovered, it would be so slow and inefficient that
       | we would still be covering linear algebra in post grad.
       | 
       | As an analogy: The 1,000th person to climb Mt. Everest takes a
       | well defined path that has already been mapped out as the most
       | efficient path to the top. If every single person had to go
       | through the treachery of finding the dead ends, cliffs, crevices,
       | and death traps that the first few climbers endured, it would be
       | a journey only a few could accomplish.
       | 
       | Most people (computer scientists, engineers, chemists,
       | physicists) using math only need to reach the top and see the
       | view from the peak. The few climbers that are really dedicated to
       | climbing (ie, the math researchers who reach the frontier of
       | math) will naturally learn about the rest of the jagged, unmapped
       | landscape as they climb harder and unconquered mountains.
        
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