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From: ram@zedat.fu-berlin.de (Stefan Ram)
Newsgroups: sci.math
Subject: Re: it's a conceptual zoo out there
Date: 19 Jul 2024 14:06:23 GMT
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sobriquet <dohduhdah@yahoo.com> wrote or quoted:
>In particle physics, people used to refer to the particle zoo since
.. . .
>Can we expect something similar to happen eventually in math, given
.. . .

  I don't think so, because math has this reduction of
  entities build in right from the start. The mathematical
  structures are composed exactly in such a manner as to
  avoid unnecessary repetitions and redundancies, and in
  a sense that's the reason there are so many of them.

  You could avoid the terms by giving your preconditions anew
  each and every time. So, instead of, "Let G be a group, ", 
  you'd say, "Let (M,+) be a pair so that ...". So you would
  not need to introduce the term "group". But this wouldn't
  make reading the text any easier! You could then even avoid the
  term "pair" by writing a certain kind of set instead. So in the
  end, maybe you would only need basic concepts of set theory.
  But in most cases, it would be impossible to write or read
  such a text, just as it would make it impossible to understand
  a detective story to tell it by describing all the quarks and
  gluons the detective is made of and how they move in time.

>Can we kind of distinguish between mathematical reality and mathematical
>fantasy

  In mathematical reality, all your concepts need to be clearly defined
  and all you assertions need to be free from contradictions.

  In mathematical fantasy, you could have vague concepts and admit
  contradictions.