Mathematical Disciplines Need the “Re-injection” of “Empirical Ideas”

(p. C4) Mathematicians have faced a similar choice between pure and applied work for millennia. In his 1940 book “A Mathematician’s Apology,” G.H. Hardy made a hard-core case for purity: “But is not the position of an ordinary applied mathematician in some ways a little pathetic?…‘Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one.”

On the other hand, John von Neumann rebuked purity in his 1947 essay “The Mathematician”: “As a mathematical discipline travels far from its empirical source…it is beset with very grave dangers. It becomes more and more purely aestheticizing,…whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas.”

I think von Neumann has the better of this argument. In his own career, he used his mathematical talents to pioneer fields like game theory and computer science, leaving a titanic legacy, practical as well as intellectual.

For the full commentary, see:

Frank Wilczek. “WILCZEK’S UNIVERSE; Beautiful, Impractical Physics.” The Wall Street Journal (Saturday, Oct. 31, 2020): C4.

(Note: ellipses in original.)

(Note: the online version of the commentary has the date October 29, 2020, and has the same title as the online version.)

The John von Neumann essay mentioned above is:

Neumann, John von. “The Mathematician.” In Works of the Mind, edited by Robert B. Heywood. Chicago: University of Chicago Press, 1947, pp. 180-96.

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