When I was in college, my advisor and I published a paper in a journal called “Applicable Analysis.” At the time, I thought that was a good name for a journal. It suggested research that was toward the applied end of the spectrum but not tied to a specific application.

Now when I hear “applicable analysis” I wonder what *inapplicable* analysis or inapplicable math in general would be. I’d hesitate to call any area of math inapplicable. Certainly some areas of math are applied more frequently and more directly than others, but I’ve been repeatedly surprised by useful applications of areas of math not traditionally classified as “applied.”

“I’d hesitate to call any area of math inapplicable”

Almost any bit of doodling that survives from a whiteboard into ink on paper to persuade another mathematician is “applied”, but that’s a pretty loose criterion. Applicable to what? Internally to mathematics proper, or external to the field? (Brings to mind a phrase from real analysis: “nowhere dense, but dense in itself”.)

How about the Axiom of Choice? Of course that’s applicable to all kinds of set-theoretic “constructions”, making that term into an oxymoron. How about Continuum Hypothesis? What application does that provide the fulcrum for?

Reminded me of G. H. Hardy’s “A Mathematician’s Apology”. In a time of war he was rejoicing of the uselessness of his field of work: number theory. Little did he know!

Here is the complete quote:

“It is sometimes suggested that pure mathematicians glory in the uselessness of their work16, and make it a boast that it has no practical applications. The imputation is usually based on an incautious saying attributed to Gauss, to the effect that, if mathematics is the queen of the sciences, then the theory of numbers is, because of its supreme uselessness, the queen of mathematics—I have never been able to find an exact quotation. I am sure that Gauss’s saying (if indeed it be his) has been rather crudely misinterpreted. If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.”