sonata in the key of calculus

I have been reading The Rest Is Noise, Alex Ross’s chronicle of the 20th century through the lens (or perhaps microphone) of music. I just completed the section about Duke Ellington and the origins of jazz. Much was made of Ellington’s proclivity towards collaboration (so much so that he never finished the opera he undertook, because it was such solitary and large-scale work), and I was reminded of how I’ve been doing math recently. Whenever I've had some time with someone I thought would be interested, I’ve pulled out a pet project and gotten their perspective on it. I have thereby garnered, synthesized, and built upon a variety of useful insights and motivations.

Then I began to reflect on certain analogies that are often drawn between mathematics and music, as well as between their histories. One compares Euler with Mozart and the Bernoulli family with the Bachs. There are notions of what is “classical” and what is “for amusement” in both mathematics and music. More modern comparisons are less frequently made, and so I thought it would be nice to have a notion of a “jazz mathematician”. Someone with a distinctive sound, but capable of improvising on a thousand different themes with hundreds of collaborators. Based on that description, I guess the nearest mathematical equivalent to Duke Ellington would be Paul Erdős, although many mathematicians fit the profile.

Given how many mathematicians are music aficionados, I wonder that more such analogies between contemporaries in these two fields haven’t been drawn. Who would be paired with Messiaen? Or with Grothendieck? Is Cauchy or Gauss more like Beethoven? There is an increasing voice in the Western world for Eastern music and mathematics. Do these two influxes share distinctive aesthetic qualities, or is one or the other merely another source of human labor for doing “more of the same”? Twentieth century music is characterized by experimentalism and division among radically different movements. One can discern echoes of the same in the mathematical world—neo-classicism and minimalism and stark modernism—so, again, are there pairings that indicate shared aesthetics? Or are all such comparisons in the end folly, because the roots of such tendencies lie in unique individuals and historical paths?