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.)
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.
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?
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.)
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.
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?
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