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A pet peeve of mine is when mathematics itself is described as a language, instead of distinguishing mathematics from mathematical language. It's like saying Ne
by jordigh 10y ago
A pet peeve of mine is when mathematics itself is described as a language, instead of distinguishing mathematics from mathematical language. It's like saying Neuromancer is just a language, that Neuromancer is just English.
There is content in mathematics that is independent of the language used to express it. Mathematical notation is also incidental. It is not mathematics itself.
- goldenkey 10y agoIt might be incidental but the history of mathematics is rich with dissent and conflicting methodologies and syntaxes. Just even the initial mathematical symbols that started to be used were quite the ambitious effort by Peano. [1] That reading will take you down the wormhole of efforts for a "universal language" between mathematicians based on latin. And then you'll end up reading about 20 different other takes on the ideas. No, it's not just incidental -- there were international congresses of mathematicians about these issues and the adopted solutions were mostly elegant and looked upon favorably. There are always going to be some dissenters though, and they have some validity - but well, conventions are usually a compromise between effectiveness and majority opinion. There is still huge rift in mathematics on the issue of constructive proofs vs intuitionistic proofs. There are a lot of camps in formal mathematics. Kinda like functional programmers and the constant "tripes" they'll knack on. Whimsical stuff :-) [1] https://en.wikipedia.org/wiki/Giuseppe_Peano https://en.wikipedia.org/wiki/Giuseppe_Peano
- marcosdumay 10y agoOH, ok, it's not exactly a language. Mathematics is a language generator, and has few other uses (if any).