The two meanings of mathematical terms(lesswrong.com)
lesswrong.com
The two meanings of mathematical terms
http://lesswrong.com/lw/10q/the_two_meanings_of_mathematical_terms/
2 comments
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.
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.
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