A little while ago I was asked to give a lecture at the very elegant Weisman Art Museum in Minneapolis on an assigned title: “Elegance in Physics.” As I get older, the things I'm asked to do get stranger, so I wasn't surprised. Alarmingly, the older I get, the stronger is my inclination to do the peculiar ones. So I accepted the invitation, and soon found myself brooding, not, as I had imagined, about the glory of the eternal verities, but about the highly contentious nature of elegance in physics.

Here is the first such difference of opinion I came upon. In a lecture at Fermilab with a title similar to the one I was given, Subrahmanyan Chandrasekhar talked about “harmoniously organizing a domain of science with order, pattern, and coherence.” He cited five examples of such pinnacles of exposition, one of them being Paul Dirac's celebrated book, Principles of Quantum Mechanics. “The translucence of the eternal splendor through material phenomena,” Chandrasekhar remarked, “[is] made iridescent in these books.”

Keeping that iridescent translucence firmly in mind, consider the following remarks of the eminent mathematician Jean Dieudonné:

What is Dieudonné talking about? He is addressing the approach to quantum mechanics laid out in Dirac's book.

Elegance in physics is as much in the eye of the beholder as it is in any other field of human endeavor. Dirac's formulation appeals to physicists because, by being a little vague and ambiguous about its precise mathematical structure, it enables them to grasp and manipulate the physical content of the theory with a clarity and power that would be greatly diminished if one were distracted by certain complicating but fundamentally uninteresting mathematical technicalities. But for mathematicians, those minor technical matters lie at the heart of the subject. Quantum mechanics becomes ill-formulated and grotesque if it does not properly rest on impeccable mathematical foundations.