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Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe, argues Professor Robbert Dijkgraaf, University Professor at the UvA since 1 January 2005
Photo: James O’Brien for Quanta Magazine
A time-honored practice in mathematical circles is to divide the field in two. There’s the traditional “applied versus pure” argument, which mirrors the experimental-theoretical divide of other disciplines — the tension between advancing knowledge toward a specific end and doing it for its own sake. Or we can bisect mathematics in the same way that our brain is split, with an algebraic “left hemisphere” that thinks in logical sequences and a geometric “right hemisphere” that has a more visual approach. But the field also breaks down according to a more subtle distinction: one’s preference between two flavors of mathematical beauty.
It’s tough for nonexperts to see mathematics as beautiful in the first place. Beauty is in the eye of the beholder, sure, but it’s also hard to see when the work of art is hidden in darkness, obscured by an impenetrable cloud of symbols and jargon. Trying to appreciate mathematics without understanding its inner workings is like reading a description of Beethoven’s Fifth Symphony instead of hearing it.
Yet mathematicians have no qualms about earnestly describing their equations and proofs as beautiful...
But the real world is very different from the idealized landscape of mathematics. Most sciences are tethered to the universe that describes the real world — but that’s just one out of an infinity of mathematical possibilities. As Jean-Pierre Serre reportedly quipped to his mathematician colleague Raoul Bott, “While the other sciences search for the rules that God has chosen for this Universe, we mathematicians search for the rules that even God has to obey.”
Source: Quanta Magazine
