Tuesday, April 26, 2016

Theory and application, and age...

An op-ed yesterday by Manil Suri in the NY Times, celebrating the 90th birthday of the mathematician Ivo Babuska, was in part a meditation on "pure" versus applied math, that should ring a bell for economists and game theorists too: The Mathematician’s 90th-Birthday Party.

Suri contrasts Babuska's career with the famous views of G.H. Hardy (he of "A Mathematician's Apology")

"Hardy believed that the only important questions in the field arose internally from this game, that the sole purpose of a mathematician was to create beautiful and “almost wholly useless” theorems.

"But ever since its inception, mathematics has also been driven by another powerful force: applications. From the early commerce and measurement needs that motivated the Sumerians to the subject’s symbiotic co-development with physics, mathematical inquiry has been spurred by questions from external fields. Although Hardy disparaged any math that could be applied to real life as “ugly,” “dull” and “trivial,” surely usefulness should be an additional measure for a mathematician’s worth?
"Hardy dismissed exposition as “work for second-rate minds,” but such activity is critical for a field notoriously inept at communicating its results to outsiders.

"It’s of course unfair to criticize Hardy, given how much the world has changed since his day. The division he created between “beautiful but useless” and “useful but ugly” mathematics has long been breached; even his own “useless” research area of number theory has become essential in cryptography and cybersecurity. Conversely, many elegant and aesthetically pleasing mathematical theories have emerged from the most utilitarian applications — even from the analysis of machine parts, as I can personally attest.

"Let’s cherish Hardy’s theorems, not his opinions, and recognize mathematics as a field with diverse goals and needs, where people can expect to make useful contributions regardless of gender or age."

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