The mathematical mind
Madness, genius, and what mathematicians are really like. Published in California Monthly magazine.
First there was Proof, a play by David Auburn about the daughter of a brilliant but troubled mathematician who fears she has inherited her father’s mental illness along with his mathematical gifts. Then came A Beautiful Mind, the movie based on Sylvia Nasar’s biography of John Forbes Nash Jr., the Nobel Prize-winning mathematician struck down at the height of his career by schizophrenia. Both productions have been incredibly popular among audiences and critics alike. (Proof won the Tony Award for Best Play and the Pulitzer Prize for Drama in 2001, and A Beautiful Mind won four Oscars, including Best Picture.) What’s behind our current fascination with the connection between madness and mathematical genius? And is there really any truth to the idea, or is it simply something we non-mathematicians would like to believe?
History certainly provides plenty of examples of great mathematicians who were mentally ill. Apart from Nash, there was Georg Cantor and Kurt Gödel, both said to be driven into mental asylums by their contemplation of the infinite. Isaac Newton (who is credited with the invention of calculus as well as his better-known theory of gravitation) suffered from delusions and paranoia, and often flew into great fits of rage. But most mathematicians would say that such examples are hardly the rule. “From all my years of observing mathematicians, I don’t see any evidence of mental illness,” says Bob Osserman, Special Projects Director at Berkeley’s Mathematical Sciences Research Institute (MSRI), located high on Grizzly Peak. Last November, Osserman discussed the question with playwright David Auburn at a public talk about Proof organized by MSRI. But, in the end, the two were unable to agree.
Most Berkeley mathematicians take Osserman’s view. “I think mathematicians vary just as much as other people; they cover the same spectrum of behavior as anyone else,” says math professor Richard Borcherds. “There are certainly a few mathematicians who are slightly stranger than others, but most brilliant mathematicians are not weird at all. They’re just people who work really, really hard.”
But some in the math world, like Sara Robinson ‘90, M.A. ‘93, do see the darker side alluded to by Auburn. “It’s certainly not true that every brilliant mathematician is also mentally ill, it’s still a small fraction, but I would guess that it’s a larger fraction than in most other professions,” she says. A former Ph.D. student in the Berkeley math department, Robinson is now a science journalist, but maintains close ties to the department (last spring she was journalist-in-residence at MSRI). Her new career lends her a perspective that most mathematicians lack. “I think some people are eccentric enough to be classified as mentally ill,” she asserts. “I think there is a continuum between eccentricity and mental illness–I don’t think they are unrelated characteristics.”
Robinson recalls the time she rode up in the elevator of Evans Hall with a shaggy, bearded man wearing dirty clothes and smelling foul. When she casually reported to the building manager that a homeless person was roaming around the math department, his response was: “Oh, yes. That’s Professor —-. He’s back from sabbatical. Other people have thought that, too.” And, while she doesn’t for a moment suggest that this is typical, Robinson claims that this was not the first mathematician she had come across with an aversion to bathing.
Many mathematicians readily concede that they are a little odder than most. “There’s a lot of eccentricity among mathematicians,” admits Osserman. “But that’s very different from mental illness,” he reiterates.
Professor of mathematics Hendrik Lenstra has even developed a theory for this apparent eccentricity among mathematicians. When he was a professor in Holland, Lenstra says he didn’t buy into the stereotype of the oddball mathematician–his colleagues there were all perfectly ordinary. “I thought it was just a myth that mathematicians are odder than anyone else. But I must say, since I came to Berkeley, I’ve changed my mind,” says Lenstra. He believes this may be a function of Berkeley being one of the top math departments in the country. “Everybody in this department got here because at one critical moment in their lives they did something that nobody else did–they proved a theorem or found a method that nobody had thought of. Otherwise, you just don’t make it to Berkeley. Being at a critical moment different from other people is their success formula, so–naturally–they cultivate it.”
But when you’re strange, and in a math department, no one seems to mind. “If somebody is really passionate about mathematics and really brilliant and insightful and talented, this overrides any peculiarities,” says Robinson. “I love that about mathematics and mathematicians.” Paul Erdös, the subject of Paul Hoffman’s biography, The Man Who Loved Only Numbers, is a case in point. Erdös had no wife, no children, no job, no hobbies–he didn’t even have a home, choosing instead to live out of a tattered suitcase and an orange plastic bag, roaming from country to country as a guest at the homes of other mathematicians. He couldn’t stand to be touched, was celibate his whole life, and would compulsively wash his hands 50 times a day (but did not know how to operate a washing machine). He was obsessively devoted to math and wrote or co-authored more mathematics papers than anyone in history, 1,475 before his death in 1996.
Despite his behavior, Erdös was not just accepted by mathematicians, he was greatly revered by them. For example, any research mathematician in the world can tell you his or her “Erdös number”–1 if you co-authored a paper with the great man, 2 if you wrote a paper with one of his co-authors, and so on. (And such is the admiration for the man that Bob Osserman gasps in horror at the mere suggestion that Erdös, too, was mentally ill: “Erdös was not mentally ill! Eccentric, yes. But certainly not mentally ill.”) Sometimes, mathematicians simply cease to notice the eccentricities. “If you live in the world of mathematics, there are so many odd people, it becomes normal,” says Robinson.
“Mathematians are different,” explains Osserman, “but we’re notdifferently different.” In other words, mathematicians are not a world apart, they simply have their idiosyncrasies. Assistant professor Allen Knutson, for example, says, “Like many mathematicians, I ‘reflexively factorize.’ It’s a habit I picked up in grade school.” That is, whenever he sees a number–a telephone number, for instance, or a number on a license plate–he instinctively starts factoring it into its primes. (As an example: 210 would be factorized as 2 x 3 x 5 x 7.) Professor Lenstra shares the same predilection–in fact, he often has fun with numbers.
When the Archimedes Society was set up as a way to raise money for MSRI, Lenstra suggested that they would attract more funds if they did not use “boring” numbers like $50 or $1,000 for their donor levels. Instead, donor levels are now based on numbers of special interest to mathematicians. One becomes a Fibonacci donor by giving anywhere between $34 and $89 (both “Fibonacci” numbers), or a Ramanujan donor by giving $730 to $1,729. (The story goes that the renowned mathematician Srinivasa Ramanujan was visited in the hospital by his friend G.H. Hardy, who told him that the number of the taxicab he had arrived in was 1729, “a dull number.” Ramanujan immediately responded, “No! It’s a very interesting number! It is the smallest number expressible as the sum of two cubes in two different ways.” He instantly felt better.)
But if there is this playful side to mathematicians, there can also be a pedantic side, Lenstra continues. When he recently put up a notice in the math department about an upcoming talk, three or four colleagues pointed out a spelling error in the speaker’s name. “That’s the comment you get! Not, ‘Nice idea to invite this guy,’ or ‘interesting subject,’ or any social small talk. No, it’s, ‘You made a mistake,’” says Lenstra. “Mathematicians are just precise,” he offers with a shrug.
The biggest difference between mathematicians and academics in other departments, Osserman maintains, is their informal culture. “I remember when I was in graduate school, the English department would have sherry hours, the art department would have teas–and the mathematicians would drink beer,” he says. Mathematicians tend to dress much more casually, and there is less hierarchy in mathematical society. “Fewer people have these good diplomatic skills, so those skills are somehow less important,” says Robinson.
While mathematical intelligence and social intelligence appear to be independent of one another, some evidence from psychology hints at a link between mathematical strengths and social weaknesses. Among people with Asperger’s Syndrome (a mild form of autism that can occur in people of normal or above average intelligence) there is a subset who have very high math abilities. Such people have trouble understanding nonverbal communication, such as facial expressions, and they may fail to make eye contact and often miss “obvious” social cues. Richard Borcherds, the Berkeley professor who in 1998 won the Fields Medal–the equivalent of the Nobel Prize in math–says he read an article about autism a few years ago and was “surprised to notice how closely some of it seemed to fit me.” He later received a diagnosis of Asperger’s. But Borcherds found that he was simply accepted in the math departments where he made his career, and doesn’t feel that his condition has made much of a difference to him.
Asperger’s Syndrome is of course rare among mathematicians; a much more common characteristic is their single-minded devotion to their work. “Anyone who’s successful at math seems to me quite obsessive. You have to be obsessive, otherwise you wouldn’t do it, ” says math professor Jenny Harrison. “When I’m into something, I’m effectively working all the time–I’m thinking about it when I’m standing in line at the grocery store, and I wake up with ideas.” (Harrison says that the movie A Beautiful Mind did a good job of capturing the nature of this obsession.) This single-mindedness is so widespread that those that don’t have it feel that they are somehow “less of a mathematician.”
And the idea that math matters above all else is pervasive. Without a hint of irony, math professor Rob Kirby notes: “I’m as proud of my children as I am of my theorems.” In mathematical circles, apparently, theorems automatically come first. “Your theorems live after you die,” explains Kirby. “Do we remember Shakespeare’s kids or do we remember Shakespeare’s plays?”
Erdös, for example, used to work 19- and 20-hour days, and he liked to say: “A mathematician is a machine for turning coffee into theorems.” Fortunately, few mathematicians take their obsession that far. Harrison, for example, believes passionately in maintaining balance, for the sake of one’s sanity. So she gardens, plays the cello, spends time with her son–wholesome activities she insists are vital. “I always tell my students, ‘Keep a balance, because the obsession can take you over,’” says Harrison. “I haven’t seen schizophrenia [which John Nash suffered from], but I’ve seen depression from loneliness. It’s not uncommon. Mathematical thinking can draw you into an inner world to such an extent that you lose awareness of the outer world. Absentmindedness is a mild symptom, near autistic isolation is an extreme one. Those who spend too much time in isolation find that they don’t have the social skills [to break out of it], and they get into serious trouble.”
If we do find more eccentricity among mathematicians, or even mental illness, that shouldn’t be surprising, says Robinson. “A first-rate mathematician is more similar to a poet than, say, an engineer or an accountant. People envision doing mathematics as this dry, boring thing–adding up long columns of really big numbers–but it’s actually this intensely creative discipline,” she says. Many studies have shown that highly creative people are much more likely to be mentally ill. Kay Redfield Jamison’s book Touched with Fire, for example, describes how many poets and artists–including Byron, Mary Shelley, Tennyson, Van Gogh, and Hemingway–very likely suffered from manic depression.
“What I liked about the play Proof is that it really got across how math is a creative process,” says Robinson. One of the most common misconceptions about mathematics is that it involves difficult calculations. But mathematicians are adamant: math is not about calculations, and mathematicians are not calculating machines. Osserman says with great pride: “Like most mathematicians, I am terrible at arithmetic!”
If it surprises you to hear mathematics compared to poetry, he continues, that may be because what you learned in school wasn’t “real” math. “Very few people have the slightest notion of what real math is,” he says. “Almost everything most people see as math in school doesn’t have much to do with math. Real mathematicians do proofs–and that needs ingenuity, it needs creativity. There’s no formula for proving a theorem.”
In other words, it is only the end product, the proof itself, that is formulaic, each line following logically one to the next. Finding the path to that proof, on the other hand, requires almost divine inspiration. John Nash has said that, when he was young, mathematical solutions came to him as “nonrational flashes of intuition”; only later would he work out the reasoning. As schizophrenia took over, Nash became delusional. “But my ideas about supernatural beings came to me the same way my mathematical ideas did. So I took them seriously,” he told biographer Sylvia Nasar.
Robinson says that, while mathematicians themselves may be a little odd, the practice of doing math “is a beautiful thing, it’s a wonderful thing. It’s adding a lot of richness to our world, and people should be more aware of what it is and why people do it.” If mathematicians are like poets, it’s because mathematics is like poetry–it’s an art form. All mathematicians agree that there is real “beauty” in math and their faces light up when they talk about it. The aesthetics of mathematics is as genuine as that of a beautiful painting, says Osserman. “And it’s probably as hard to describe as trying to describe what makes a picture beautiful.”
Many mathematicians compare mathematical beauty to that of music. In fact, many mathematicians are themselves musical. (Each year the Berkeley math department puts together a small orchestra of about 15 people from among its ranks.) Pythagoras considered music to be a branch of mathematics, and composers from Bach to Philip Glass have used mathematical principles in their music. For those lucky enough to be endowed with both mathematical and musical talents, the connection between the two is intuitive. “If you have a pleasant musical experience, you feel that things are working together. It’s the same thing with math,” says Harrison, an accomplished cellist who gave up a musical career for mathematics. “You have this overview of where you’re going and then all the details–like the notes–have to fit together. When everything ‘agrees,’ in math or music, that’s harmony. When it’s right, you know it’s right.”
The experience can be incredibly rewarding. “For a rare few, the mathematical experience can transport them into a state of deep, inner joy,” says Harrison. But, unlike with other arts, few outsiders are able to appreciate the beauty in math. “The problem is that you have to know so much to get to a place where you can see the beauty. It’s a shame that the rest of the world can’t see what we see. It’s very frustrating–they don’t know how beautiful it can be.”