# The Difference between Pure and Applied Mathematics

**Angela SimonesBrooks 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 essay^{1}, 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.