Q: Why do universities maintain math departments?
A: It’s cheaper than institutionalizing the math faculty.
—Joke told by mathematicians

The notion that some human gifts are trapdoors to lunacy has a pedigree tracing back at least to Plato’s observation that madness attended love, ecstasy, poetry, and prophecy. Down the centuries, as Western civilization organized itself upon grounds of kingdom, coin, and statute, prophets and persons who danced until they dropped became something of a nuisance, subject to arrest and worse, and by the time Shakespeare turned to consideration of god-struck human behaviors, only “the lover, and the poet” remained “of imagination compact” with “the lunatic.”

The connection between artists and mania holds firmly in the human imagination, though beginning in the 19th century, as men and woman began to suspect that the Baconian notion of science as a supplier of goodness was not the whole story, the ingenious use of logic fell under the same suspicions.

The masters of intuition were the first to sense this, of course, producing doctors Frankenstein, Jekyll, and Moriarty in rapid order. But the real world wasn’t far behind, soon serving up Thorstein Veblen, the notoriously unclubbable but brilliant economic theorist who gave each of his students an unvarying grade of “C”; Albert Einstein, with his great child’s eyes, struck-by-lightning hairdo, and impenetrable “theories”; and the depressive philosopher Ludwig Wittgenstein, as unreliable in his life as he was incomprehensible in his work—”Don’t worry, I know you’ll never understand it,” he assured two of his academic advisors regarding his doctoral thesis. (They happened to be Bertrand Russell and G.E. Moore.)

Of all the disciplines that run on high-octane reason, however, none became more associated with unquiet minds than mathematics, so that by 1925, the philosopher Alfred North Whitehead, who knew whereof he spoke (he had coauthored Principia Mathematica with Russell in 1910–13), was able to write, “Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings”—or, as most of the rest of us would say, from life.

Whitehead would most certainly have had in mind the manic, rage-prone Isaac Newton and the nomadic scholar and (likely) manic-depressive René Descartes. But he could also have been thinking of contemporaries such as Georg Cantor, the inventor of set theory, who believed that he was on earth to represent God in the field of mathematics; or the melancholic isolate and eventual suicide Ludwig Boltzmann, who developed critical proofs for the existence of molecules and atoms.

Whitehead’s thesis has since been powerfully reinforced by Kurt Gödel (1906–78), whose work I frankly don’t know how to understand or explain here, but who, I understand well, starved himself to death for fear that the food being served to him in his home in Princeton, New Jersey, was poisoned by his enemies; or Alan Turing (1912–54), probably the most brilliant Allied code-breaker of World War II and a progenitor of computer science, whose food was in fact poisoned, though it was he who sprinkled the cyanide. And then there’s the peripatetic Paul Erdös (1913–96) who spent decades living out of a suitcase in borrowed spare bedrooms in mathematicians’ homes around the world while collaborating with his hosts on hundreds of papers.

In 2007, Cantor, Boltzmann, Gödel, and Turing were subjects of a rather breathless BBC documentary titled Dangerous Knowledge, which intimated that pure mathematics is to intellectual pursuit what bomb squad duty is to police work: a specialty that draws those who are already nuts, and makes head-cases of the rest. A similar view has been delivered by three American movies: A Beautiful Mind (2001), the loose biography of schizophrenic Nobelist John Nash; Good Will Hunting (1997), in which Matt Damon portrays a volatile working-class prodigy; and then Pi (1998), a movie about a young, brilliant mathematician who escapes from a hell of calculation into happiness by trepanning his brain with a hand drill.

Theories as to why great mathematicians tend to be bonkers are in similar good supply and include the conjecture that gifts for math and mania are inexorably linked in the brain’s wiring. Mathematicians, so far as I’ve been able to find, have not gone out of their way to refute this claim, nor to protest the portrayal of their profession as unbearably difficult and dangerous. Is this further proof of their loopy indifference to “contingent happenings”? Maybe not. Rationalists at the core, mathematicians may well have figured out that every movie or theory of mental illness that portrays their profession as Everest-scaling only turns sharp young people from intended careers as poets or lead guitarists and toward the struggle to master the maddeningly complex orders of abstraction on which the universe floats like a bubble on a pond.

Our story on Paul Sally’s efforts to accrue mathematicians begins here.

Read more by Ben Birnbaum