Comment by bmacho

2 years ago

I don't think that's a problem: if there are uninteresting languages, then you must study them, then work hard to prove that they are uninteresting first. That is, mathematics indeed does study uninteresting languages.

.. mathematics is the same for me as GP said: you have a set of symbols, a set of rules, now derive true statements. (Or at least this is a good view, but other views can be also good.)

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bmacho

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btilly  2 years ago

Most mathematicians don't feel that way.

There are uninteresting languages that can be considered, but nobody considers them unless a reason arises to do so.

Attempting to prove that they are uninteresting is not itself an interesting problem, because it is easy to prove that such proofs do not generally exist. Indeed things become interesting not because they are inherently interesting in and of themselves. But because something else that is already interesting turns out to connect to the not yet interesting thing, and studying the not yet interesting therefore becomes relevant to the interesting one.

  • vlovich123  2 years ago

    The uninteresting languages are still part of mathematics though. It’s just that we choose not to explore them because we don’t think there’s any value. If you limit it just to the languages that we find interesting, then “what is mathematics” is a fluid definition depending on what we choose to focus on today whereas my definition is a bit more durable.

    Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that. At least if I recall the apocryphal story told to me in class correctly. Erdos seems like he’d line up time wise and focus wise but I can’t find any quotes from him to that effect so maybe I’m misrembering?

    • btilly  2 years ago

      I don't hold with drawing the strokes too broadly. If we take a broad definition of mathematics, both computer science and chess would be branches of mathematics. Such a definition doesn't capture what I want to think of as mathematics.

      The anecdote that you refer to is usually cited with G. H. Hardy as the mathematician, and https://www.arvindguptatoys.com/arvindgupta/mathsapology-har... is where he said it. Except he didn't quite say exactly that. Instead he said things like this:

          There is one comforting conclusions which is easy for a real
    mathematician. Real mathematics has no effects on war. No one
    has yet discovered any warlike purpose to be served by the theory
    of numbers or relativity, and it seems very unlikely that anyone
    will do so for many years.

      Given that he wrote this in 1940, relativity was a bad prediction. The theory of numbers also become useful thanks to cryptography.

      He also makes reference to a belief that Gauss said something like, "if mathematics is the queen of the sciences, then the theory of numbers is, because of its supreme uselessness, the queen of mathematics..." But he argues this only to undermine it.

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    • bmacho  2 years ago

      > Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that.

      I know a version that the motivation was that they can't use it in wars (so the mathematician was a pacifist instead of an arse). I can't find a source for this anecdote either. I probably heard it about Paul Turán, but anyone doing discrete math at that era (number theory, graphs, combinatorics) would do.

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