…truth beauty. That, as Keats heard in the silent voice of the Grecian urn, is all we know on earth, and all we need to know.
From a mathematician’s viewpoint, that rings true – as does Edna St. Vincent Millay’s claim that “Euclid alone has looked on Beauty bare,” and Hardy’s ” Beauty is the first test: there is no permanent place in the world for ugly mathematics.” Mathematics deals with truths that may be abstract, but are also absolute, as true in their way as anything in the universe can be. And you and I know that we don’t just do it for the huge paychecks, for the hordes of screaming fans, or for the million-dollar sponsorship contracts from the people who make those little white pencil erasers. We do it because it’s beautiful.
Of course, mathematics is useful too. When I was a graduate student, one of my undergraduate mentors mailed me a copy of Clarence R. Wylie Jr.’s beautiful sonnet “Paradox.” (Thanks, Ernie. I understood.) Look it up – I can’t do justice to it with as short a fragment as copyright legislation would let me quote. It does as good a job of expressing the deep and strange relationship between mathematics and its applications in fourteen lines of iambic pentameter as most of us could do in a ten-page essay.
Mathematics is not all of poetry, architecture, music, or art, any more than it is all of engineering or chemistry. Yet it underlies all of these – or maybe they exist separately and mathematics explains them to us. Perhaps, seen properly, the two ideas are the same. Or, if not precisely the same, as intimately related as a pair of adjoint functors.
There’s a significant literature of overtly mathematical poetry: one notable anthology is Strange Attractors, edited by JoAnne Growney, who also keeps a blog on mathematical poems. Artists such as Escher, Ferguson, and Dali have shown us snapshots of the visual beauty of our subject. And has any composer or architect ever managed to avoid bringing mathematics into their creations in one way or another?
My wish for you in this academic year: may your mathematics be beautiful, and may you succeed in showing that beauty to others.