Why Applied Mathematics?

I read an essay called “A Mathematician’s Apology” by G.H. Hardy. I was an undergrad in pure mathematics, minoring in English literature; it was suggested to me by a professor who probably thought I was a hopeless excuse for a math student but who himself enjoyed reading.

G. H. Hardy, was a famous British number theorist known for taking Ramanujan under his wing. His essay was a humble-brag treatise on the moral and intellectual superiority of pure mathematics. In my literary opinion, he did a miserable job of trying to communicate the beauty of pure mathematics a privileged few are able to truly appreciate, but it was an interesting insight into the pure mathematician’s motivations.

The essay was written at an incredibly uncertain time for the United Kingdom—1940. He stated that his chosen field of interest, Number Theory, was absolutely useless to the scientists and engineers who debased themselves building bombs for the purpose of war. Although he is not alone in this apprehensive application of knowledge (e.g. Oppenheimer’s reaction to the atomic bomb), he was able to claim moral superiority in that, at the time, Number Theory was so useless that it was one of the only true forms of pure mathematics.

One of the greatest ironies is that, long after his death, many important and fundamental theorems in Number Theory are the basis for things like encryption and memory storage, central to computer engineering. While some mathematicians may revel in what many see as useless, history has borne out that what may be useless for the moment may likely be incredibly useful, read applicable, in the future. Sometimes that future date far exceeds the lifespan of any individual mathematician.


Here’s the reason for my glaringly negative review of his essay, so don’t feel bad if you don’t read it. To a somewhat uncertain end, in it he ranks mathematicians by ability. I forget if he said Euler or Gauss was the top, but it was like arguing over who should take the greatest of all time spot: Kobe Bryant or Micheal Jordan. He even put himself in the list, albeit a lowly, sub Fermat rank. It was worse than reading Dante talking with Greek philosophers in the Inferno.

I’ll leave you with a tongue-in-cheek quote from his essay that seems relevant to the question:

“We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.”

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