The Difference between Pure and Applied Mathematics
Angela Simones
Brooks Preparatory
Abstract
There is none; that’s my conclusion. But of course, applied
mathematics is mathematics done with some other end in view,
whereas pure mathematics is an end in itself. Whether we call
some mathematics “applied” depends on what the ultimate end
is. For instance, one might say that the theory of solvable groups
is “applied” because it can be used to develop Galois theory. This
probably isn’t what most people have in mind when they talk
about applications of mathematics. So only some ultimate ends
make mathematics “applied.” As an aside, I want to mention that
what Morris Kline, in his immensely influential essay1, refers to as
“applied mathematics” could be labelled more accurately as pure
mathematics whose subject is nature. He argues that such is the
only ultimately worthwhile direction for research, but the question
of “utility” is not important for him, so the point I’m making is
only tangentially related to his work.
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