Nov 23, 2017
My colleague Oscar Mur-Miranda has been kind enough to walk me through some basics of higher mathematics in the last couple of years: the conics especially, as I try to put together some thoughts linking the idea of parabola with the often-misunderstood work of parables in wisdom literature.
Sometimes, no kidding, what Oscar is telling me is so beautiful that I have to fight an emotional response—not just about the elegance of the ideas themselves, but at the profound loss I feel at having missed this real math—the not-about-numbers math, this mysterious-but-precise way of describing the world. Oscar was a classic prodigy; he’s shown me his childhood notebooks full of equations in his third grade hand. He was working out the sublime at an early age, and I was missing it, over and over and over. The only glimmer in my memory is being in geometry class in rural Arkansas and idly enjoying the relative ease with which I could turn shapes in my head. Geometry came naturally, where algebra was intractably opaque. I chalked up my affinity for geometry to the same spatial capacities that made me into an art-kid, and I was probably right. But I never saw any reason to take the classes offered beyond what was absolutely required.
So my sense of loss was doubled when I came across David Foster Wallace’s “Math Melodrama,” a review of mathematically themed novels originally published in Science and now in the collection called Both Flesh and Not.
Not just professional mathematicians, but just about anyone lucky enough ever to have studied higher math understands what a pity it is that most students never pursue the subject past its introductory levels and therefore only know the dry and brutal problem-solving of Calc I or Intro Stats (which is roughly analogous to halting one’s study of poetry at the level of grammar and syntax). Modern math is like a pyramid, and the broad fundament is often not fun. It is at the higher and apical levels of geometry, topology, analysis, number theory, and mathematical logic that the fun and profundity start, when the calculators and contextless formulae fall away and all that’s left are pencil and paper and what gets called “genius,” viz. the particular blend of reason and ecstatic creativity that characterizes what is best about the human mind. Those who’ve been privileged (or forced) to study it understand that the practice of higher mathematics is, in fact, an “art,” and that it depends no less than other arts on inspiration, courage, toil, etc… but with the added stricture that the “truths” the art of math tries to express are deductive, necessary, a priori truths, capable of both derivation and demonstration by logical proof.
It may be that mathematics is not generally recognized as one of the arts precisely because so much pyramidal training and practice is required in order to appreciate its aesthetics; math is perhaps the ultimate in acquired tastes. And it’s maybe because of math’s absolute, wholly abstract Truth that so many people still view the discipline as dry and passionless and its practitioners as social dweebs.
I was deluded by all these myths about math and mathematicians. Thank goodness for Oscar, and for Olin College, where faculty are one big super-department, so we find ways to see each other outside our disciplinary domains. And: Wallace essentially says that A Mathematician’s Apology by G.H. Hardy is the classic to read, so it’s not too late! More on parabola/parable to come.