

The two meanings of mathematical terms - fluffster
http://lesswrong.com/lw/10q/the_two_meanings_of_mathematical_terms/

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slackenerny
Talking of mathematics as a bondage-and-discipline precise science always
seemed to me as misleading. This is not how mathematics is _done_ , even if
the _result_ looks so.

As to PG's definition of mathematics as _study of terms that have a precise
meaning_ , this is wrong too, as exemplified by problems of set theory and its
logic, from which mathematicians escaped into more loosy setting of category
theory and categorical logic.

I think article "When is one thing equal to another" by Barry Mazur somewhat
fits into the theme of this blog note
<http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf>

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fburnaby
He's just distinguishing between pure and applied maths.

Pure math -> "level one". Start with axioms and apply logic.

Applied math -> "level two". Take some pure math, and find an analogous system
in the real world.

The question in applied math is whether (or better yet when) the analogy is a
good one.

