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The problem is that professional mathematicians have a common language that they all have learned which serves them well...and they're the ones writing the Wiki
by madhadron 5y ago
The problem is that professional mathematicians have a common language that they all have learned which serves them well...and they're the ones writing the Wikipedia articles. Imagine if all the programming documentation you worked with was at the level of a 1980's first book on BASIC.
Set theory is the concrete starting point after that training, and the first step of concrete problems is to translate them into an abstract form of maps on sets. It's a decoupling. Instead of translating n techniques into m domains (n*m bits of work), you develop n techniques in terms of set theory, and translate m domains into set theory (n+m bits of work).
Physics majors largely use the same pieces of math on the same domains, so this decoupling doesn't make sense for them. Similarly, most domains carve off some piece of math and statistics and specialize it. But if you're writing a reference, whose specialty do you choose?
- anon_tor_12345 5y ago>Imagine if all the programming documentation you worked with was at the level of a 1980's first book on BASIC. mathematical maturity is the same as "code sense". when i started writing code a couple of years ago i would get cross-eyed reading large blocks of code i.e. i would get lost in the syntax and the abstractions and the idioms. at the same time i had pretty decent "mathematical maturity" i.e. i could read papers and textbooks pretty handily. comparing it seems obvious that formal mathematics, with its idioms, abstractions, and syntax is basically the same thing (without pushing the curry-howard isomorphism too far).
- aaron-santos 5y agoMost computer science students get a set theory introduction and construction of natural numbers, rationals, and reals. Those with an interest in statistics get a foundation laid in measure theory. For other domains, what are good places to look for set-theoretic approaches? A set-theoretic approach to calculus has me intrigued.
- subset 5y ago> A set-theoretic approach to calculus has me intrigued. Well calculus (and more generally, analysis) really does hinge on set theory. For example, points of accumulation for limits and hence differentiation, Riemann integration via the supremum and infimum etc are all set-theoretic ideas. Just generally encountered in a Real Analysis class and introductory calculus largely abstracts over the fundamental set concepts that underpin the mechanics.