My advisor in grad school used to say that applied mathematics is an attitude, not a subject classification. You can’t take an area of math and say whether it is or isn’t applied. Any area of math can be applied, or not, though some areas are applied more frequently and more directly than others.

Here’s a possible definition of applied math:

An area of math is applied, for you, if you’ve been paid to use it and not just to teach it or write about it.

By this definition, some rarefied areas of pure math are applied, but only for some people and not for others.

Here’s a less personal definition, and one that’s fuzzy rather than binary:

An area of math is applied in proportion to the amount of money people have made applying it.

Why the emphasis on money? Because that’s the common way people express their desires quantitatively. It’s a way of determining how much value the problem owner, not the mathematician, finds in the solution. Applied is in the eye of the client.

An interesting feature of both definitions is that they can change over time, especially in the personal definition. I’ve applied parts of math that I never thought I would. And there are also things I thought I’d find more use for than I have.

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