[HN Gopher] Axiomatics: Mathematical thought and high modernism
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       Axiomatics: Mathematical thought and high modernism
        
       Author : hhs
       Score  : 35 points
       Date   : 2024-10-27 14:47 UTC (8 hours ago)
        
 (HTM) web link (old.maa.org)
 (TXT) w3m dump (old.maa.org)
        
       | alan-crowe wrote:
       | The review distills the book's view of the difference between
       | pure mathematics and applied mathematics. "applied" split from
       | "pure" to meet the technical needs of the US military during WW2.
       | 
       | My best example of the split is
       | https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives
       | Wikpedia notes that "The list of unsuccessful proposed proofs
       | started with Euler's, published in 1740,[3] although already in
       | 1721 Bernoulli had implicitly assumed the result with no formal
       | justification." The split between pure (Euler) and
       | applied(Bernoulli) is already there.
       | 
       | The result is hard to prove because it isn't actually true. A
       | simple proof will apply to a counter example, so cannot be
       | correct. A correct proof will have to use the additional
       | hypotheses needed to block the counter examples, so cannot be
       | simple.
       | 
       | Since the human life span is 70 years, I face an urgent dilemma.
       | Do I master the technique needed to understand the proof (fun) or
       | do I crack on and build things (satisfaction)? Pure
       | mathematicians are planning on constructing long and intricate
       | chains of reasoning; a small error can get amplified into a error
       | that matters. From a contradiction one can prove anything.
       | Applied mathematics gets applied to engineering; build a
       | prototype and discover problems with tolerances, material
       | impurities, and annoying edge cases in the mathematical analysis.
       | A error will likely show up in the prototype. Pure? Applied? It
       | is really about the ticking of the clock.
        
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