The following article appeared in Saturday Night magazine, Nov. 18, 2000
By Karen Shenfeld
John Mighton is a cutting-edge mathematician, a poet, and a playwright. He fixed the math, and won a part, in Good Will Hunting. Some say he's a genius. He says there's no such thing
"Knots are mystical objects. They occur everywhere in mathematics and in nature -- in double-helix DNA strands, for example."
John Mighton is telling me this as we sit in his monastic top-floor office at the Fields Institute for Research in Mathematical Sciences in Toronto. The institute, named after Canadian mathematician John Charles Fields (1863-1932), is in an unprepossessing four-storey red-brick and limestone edifice on College Street. On the second floor, there's a grand atrium ringed by balconies and flooded with natural light. The open area is dominated by a free-standing fireplace and a monumental spiral stairway down which Mighton had descended to greet me this morning, wearing the grad student's uniform of choice: jeans and a T-shirt, with an untucked plaid flannel shirt overtop.
Mighton's career defies the famous description of mathematics as "a young man's game." He didn't begin a serious pursuit of mathematics until he was well into his thirties, and he received his doctorate only last year, at the age of forty-two. He's now doing post-doctoral research on knot theory, which he defines as "the study of curves in three-dimensional space." It's a branch of mathematics that's been around for a century, but has only recently turned out to have unforeseen connections with theoretical physics, molecular biology, and advanced computer studies.
As we walk up the stairs, Mighton tells me how he became interested in knot theory. "I was reading stuff on the theory of neural networks -- they're a kind of computer that simulates the actions of the brain and is used for pattern recognition -- and I noticed connections with knot theory," he says. "So I tried to follow up on that."
Mighton appears to have no qualms about explaining this to a non-specialist like myself. "Mathematics is a language," he reassures me. "With proper tutoring, anyone can learn to speak it."
In his office, I can sense his enthusiasm as he leaps to the blackboard and sketches a set of drawings:
"You can create an everyday knot by taking a string, crossing it over itself to form a loop, then drawing one end of it through the loop. To create a mathematical knot, however, you must join the two loose ends together. A mathematical knot is always a closed curve or line. Knot theorists consider even Figure A to be a knot. They call it the 'unknot.' The main problem in knot theory is to discover how to determine when two knots are 'topologically equivalent.' "
Mighton pauses briefly, noticing the look of bewilderment on my face. He is of medium height, with brush-cut hair and the build of a high-school wrestler. His unlined skin and his boyish tendency to blush make him look younger than his years. I notice that he has slipped off his Doc Martens and is standing in his stockings.
Mighton smiles, then continues: "All you have to do is imagine a sphere made from a pliable sheet of rubber. Now, imagine stretching and twisting the rubber to deform the sphere into a pyramid, perhaps, or a cube," he says, pulling on an imaginary rubber sphere with his two hands. "You may create any shape you like, so long as you don't actually tear the sheet of rubber or bring any distinct points of it into actual contact. Mathematicians consider the deformation of the sphere into a pyramid a 'topological transformation.' "
He turns to the blackboard. "Figure A and Figure C are topologically equivalent because by merely twisting and pulling, one can be transformed into the other. But no general algorithm or formula has yet been found to determine when two knots are 'topologically equivalent.' If such a formula could be found, it would lead to a deeper understanding of space and time, because you study space by studying curves in space, which is what knots are. And because human and viral DNA is knotted, knot theory can help scientists understand how a particular virus will attack a human cell.
"It's uncanny how the most beautiful and elegant results in mathematics often end up describing the natural world. It's this sense of beauty and symmetry that leads to discoveries in mathematics, and when you make them, it's like seeing a new vista. You get a feeling that's deep and mysterious."
Mighton's own life has been a series of transformations, driven by a search for the interconnectedness of things. He's studied philosophy, written poetry, painted abstract art, and acted in films. His radical views on education unexpectedly won him a supporting role in Gus Van Sant's Academy-award-winning portrait of a natural-born mathematician, Good Will Hunting. But it's chiefly as a playwright that Mighton has managed to capture public attention. Possible Worlds, the best-known of his five plays, received the Governor General's Award for drama in 1992 and has been performed in major cities around North America. Most recently, it has been adapted for screen by the protean Quebec director Robert Lepage, who describes it as "a Cubist love story."
For all that, Mighton instantly balks if you try to label him a creative genius, a modern-day Leonardo da Vinci. The very notion of genius is, he says, antithetical to his philosophical outlook on life, which presupposes that all men and women are created equal. "We have all been duped and damaged by an absolutely illusory hierarchy of intelligence," he says. "It's one of those unexamined prejudices, like the belief, fifty years ago, that men with white skin were superior to both women and people with dark skin." His is a controversial view of innate ability that for some -- educators in particular -- appears to fly in the face of common ssense.
It was these egalitarian ideals that helped Mighton land that supporting role in Good Will Hunting. "Someone involved with the project had contacted the U of T mathematics department looking for a specialist to check the accuracy of the math presented in the film. I was sent the script and I looked it over very carefully. The writers [who were also the film's lead and supporting stars, Matt Damon and Ben Affleck] had gotten a lot of the math wrong.
"The next day, Gus Van Sant, Ben Affleck, and Matt Damon turned up at my door. I didn't know who they were at first. I went over the script with them and told them how to make the mathematics work. But I also told them that I was completely opposed to the film's premise: that people are born gifted. I told them I thought the movie reinforced some stereotypes that are harmful, especially to young people, and I suggested some line changes I thought could make it more realistic, and even more dramatic."
Van Sant and his two stars were intrigued enough by Mighton's views to offer him a role as the graduate student/amanuensis for Professor Lambeau, the math professor who discovers Will Hunting's talent, played by the Scandinavian actor Stellan Skarsgård. "I improvised almost all of my dialogue and had a small opportunity to counter the film's viewpoint. At one point, the character I play remarks that 'most people don't get a chance to see how brilliant they can be. They don't find teachers who believe in them. They get convinced they're stupid.' "
They were not just empty words. After making the film, Mighton founded jump (Junior Undiscovered Mathematical Prodigies), a private, free agency for teaching math to kids who have for some reason failed in the regular school system.
Much to John Mighton's chagrin, his mother insists he was "always a genius, who could have done anything he wanted to." He was born and raised, until the age of twelve, in Hamilton, Ontario, one in a family with six children. He says he had an ideal childhood, roaming freely on the city's wooded escarpment. His father, Albert Mighton, was a doctor, and his mother, Marion Swent, a nurse. They endowed John with a strong and enduring social conscience.
"Both of my parents were involved with the charitable organization Crossroads Africa. We always had African university students billeted at our house, mainly from Nigeria and the Belgian Congo. My dad often travelled to Africa to do surgery in hospitals for free. My mother sat on the board of the United Way and other charities and hospitals. She was one of the original organizers of the Miles For Millions walk in Hamilton and also helped open a shelter for women in Huntsville."
We have wandered out of the Fields Institute to look for a bite of vegetarian lunch at a nearby Malaysian restaurant. Mighton greets the owner, then heads for the buffet to load up his plate with spicy mango salad, pad Thai, broccoli, and tofu. I get the feeling he would prefer to discuss his many environmental concerns (Ontario Power's use of coal plants, gas-guzzling SUVs, etc.), but I steer the conversation to his own childhood.
When he was twelve, his family moved, first to Huntsville, then to the rocky shores of the Lake of Bays in Muskoka, where he spent much of his early adolescence by himself, reading. "I read a lot of sci-fi," he remembers, "such as Isaac Asimov's Foundation Trilogy. I was also into playing war-strategy games -- Diplomacy, Risk, and Blitzkrieg."
Mighton also recalls reading a sci-fi story about kids who use the properties of a Möbius strip to travel in time. (A Möbius strip is a one-sided topological figure that can be modelled by taking a strip of paper, twisting it once, then joining the ends together.) "From that story," he says, "I got the sense that mathematics was a magical subject that would allow you to transcend the everyday."
Despite the confidence instilled in him by his parents, he didn't feel gifted in math. "I had accepted a lot of the myths that everyone accepts about intelligence," he says. "I assumed that if I could not do something immediately, I wasn't born to do it."
Mighton describes his public- and high-school record as "erratic." Yet he did well enough to be accepted into Victoria College at the University of Toronto, where he completed a four-year undergraduate program in philosophy in three years. Mighton, however, is scornful of the kind of person he was in his early university days. "I was vacuous and apolitical, only interested in drinking and parties."
The tenor of his life turned in his final year, when he met a fellow student named Dave Beck. "Dave was my first intellectual friend," he explains. "He was the first person with whom I could share philosophical ideas. He was diagnosed with cancer and died within a year of our meeting. His death affected me deeply. It made me more serious about my studies and my life. It made me feel that I had been living superficially and that I knew nothing."
Screenwriter and director Alan Taylor (whose film, Palookaville, won the prize for Best First Feature at the 1995 Venice Film Festival) met John Mighton at Victoria College. "John has always had two sides," Taylor says. "One side is almost religious in the graveness he displays toward life. The other side is playful, even wild. I remember we were eating dinner in the dining hall. I had glanced over at John and noticed that he'd picked up his glass of water, taken a sip from it, and was observing it curiously. Then, he took a clean bite out of the glass, slowly chewed it up, and swallowed it. John told me later that he had reasoned that since glass was made of sand, he should be able to chew it up sufficiently to swallow it without coming into harm's way. He wanted to see for himself if it was possible."
Mighton began to realize what might be possible for himself in the following years. In 1978, at twenty, he left Toronto to pursue an M.A. in philosophy at McMaster University in Hamilton, Ontario. He focused his studies on the writings of Ludwig Wittgenstein, who, Mighton says, profoundly influenced his own work. "Wittgenstein initially believed that philosophy, like mathematics, could be reduced to logic," Mighton says. "He felt that everyday language was too vague for philosophy. He inspired other philosophers to create artificial languages so you could talk about things precisely. The Tractatus Logico-Philosophicus was a bible to a lot of philosophers of science, but what they didn't realize was that Wittgenstein was a mystic as well as a logician."
Mighton says he learned a lot about writing from Wittgenstein. "He is a beautiful prose stylist. In his last book, Philosophical Investigations, published just after his death, Wittgenstein repudiated his early philosophy. He wrote it without philosophical jargon, aphoristically. He wanted his readers to read between the lines, to fill in the spaces between his arguments. I learned from him to trust the intelligence of my audience."
After lunch we head back to the Fields Institute and resume our discussion in Mighton's office. It was while studying Wittgenstein, he says, that he began to write in earnest. "I went into a hermit phase," he recalls. "I read all the poetry I could find -- by Margaret Atwood, Al Purdy, Robert Lowell, Mark Strand, Rainer Maria Rilke, and others."
When he read Letters Home, a collection of the correspondence of the American poet Sylvia Plath, it dawned on him that Plath had taught herself to become a writer. "She wrote imitations of poets she loved; she intentionally practised different verse forms; she studied mythology in order to enrich her personal store of literary allusions." Inspired by Plath's example, Mighton reasoned that he didn't have to be a "natural-born" poet. He, too, could teach himself the craft.
In 1983, following university, Mighton went to New York to help his friend Alan Taylor move there. "I had intended to go for several days, but stayed almost four years," he laughs. "It was such an exciting time to be there, the peak of the art scene and the club scene. Jean-Michel Basquiat was painting. Laurie Anderson and the Talking Heads were playing. DJs like Afrika Bambaataa and Soulsonic Force were spinning. You'd go out to The Roxy and there'd be two thousand kids from the Bronx, Brooklyn, and Manhattan, all dressed to the hilt in their district's fashion. And they'd be doing these incredible dances, breakdancing and hip hop. It was the start of rap."
New York unleashed Mighton's creative energies. By day, he worked as a nanny; by night, he began writing plays. "I honestly don't know why I started writing plays," he says. "Like most of what has occurred in my life, it seems accidental. But I wanted to capture the anarchy that reigned in the East Village."
He wrote six one-act plays in New York, a few of which he calls mere "character sketches" and some of which have since been lost. Unable to find backers, he produced his work himself. "I spent all of my savings in order to mount my first play, The Prediction, in a now-defunct theatre space. A week before it was set to open, we entered the theatre and discovered there was no electricity. We ended up running an extension cord from the building next door and opened the play with a single bulb dangling over the stage for light. And we had to give out blankets to keep the few members of the audience who showed up warm."
Mighton was ineligible to apply for grants in the U.S., and after four years of financing his own work, he decided he would have an easier time making connections and getting his plays produced back home. In late 1986, he moved to Toronto and settled into the old Kensington Market neighbourhood, supporting himself by tutoring math while writing Scientific Americans, which premiered at Theatre Passe Muraille in Toronto, in November, 1988.
It was about this time that Mighton met his future wife, Regan, who now teaches kids with learning disabilities. They were married in 1989 and have a daughter, Chloe, who is eight. Though they subsequently divorced, they still live a block apart and share in Chloe's upbringing. "John is a wonderful person and a marvellous father," Regan told me. "But he was also very difficult to live with. He's a perfectionist, a triple-A personality. I remember when John went back to school to study math. If he made a single mistake on a test, he would agonize over it for weeks. It makes him very demanding. He always wanted to make sure I lived up to his standards, especially when it came to protecting the environment, an issue he cares about passionately. If I threw the tiniest piece of lettuce into the garbage can instead of the compost heap, I'd never hear the end of it. Even now, he hates the fact that I drive a car. But I still love him dearly."
Mighton is reluctant to speak about his personal relationships, or the reasons why he and his ex-wife no longer live together. But he has never hesitated to explore the fragile, changing nature of love in his plays. He also uses drama to examine the nature of human emotions, intelligence, and creativity, the connections between artistic and scientific inspiration, and questions of ethics. And while his plays are informed by his study of philosophy and mathematics, Mighton maintains that he is not trying to explain scientific ideas onstage, or to demonstrate how they describe the world. "I am more interested in working metaphorically," he says, "throwing an idea onto the stage to have it reflect something outside itself. I want to provoke people to think about the way ideas reside in bodies, to make a person feel what it is to have a thought, which is how T. S. Eliot described the goal of metaphysical poets."
Scientific Americans is about a young physicist who moves to an army research station with his fiancée, only to have the relationship break down as he is drawn more and more deeply into military research. "Each of my plays has examined what a relationship is about from a different angle," he says. "Scientific Americans raises the importance of a compatibility of outlook and presents a couple trying to survive as they are losing that compatibility."
Body and Soul (1993), about a female mortician who's an unapologetic necrophiliac and a young man who volunteers for cybersex experiments, provokes its audience to consider the extent to which desire is conditioned and what forms it will take when we have the means to simulate experience.
Mighton's most successful play, Possible Worlds, draws on elements of science fiction, the thriller, and romance to spin a beguiling and mysterious tale. The story alternates between two homicide detectives investigating a series of ghoulish murders in which the victims' brains have been stolen, and a fragile, desultory relationship between George, a financial-risk analyst, and Joyce, who is identified, in turn, as both a neurologist and a stockbroker. Their relationship is marked by dizzying shifts in perspective. They encounter one another first in a crowded cafeteria and then in a crowded bar. On both occasions, they appear to be meeting for the first time. It is not until the end, when the mystery of the missing brains is solved with a sci-fi twist, that the connection between the mystery and the love story is revealed.
"Possible Worlds is about the extent to which a relationship happens in your head," Mighton says, "to what extent each of us fabricates our partner in our minds." The play was inspired, in part, by Mighton's study of a branch of modern philosophy called personal-identity theory, which attempts to determine what is essential to a person's identity -- the extent to which it's determined, for instance, by factors such as continuity of memory or a person's actions in a given situation.
"What I found fascinating about these philosophical explorations," Mighton explains, "was that they were originally sparked by scientific experiments." He is referring to studies conducted in the early 1950s demonstrating that the two hemispheres of the brain can operate practically independently of each other. "For the first time," Mighton says, "philosophers began to imagine the possibility of two identical consciousnesses inhabiting different brains, or of two different people possessing the same memories, the same dispositions. It seemed remarkable to me that no one had ever imagined this possibility and that, more and more, the sciences were delineating the boundaries of the imagination."
Possible Worlds premiered in Toronto and so far has been performed in Ottawa, Chicago, Prague, New York, and London. While most of the reviews were glowing, the New York Times theatre critic, Wilborn Hampton, wrote that the play "seems less a stage piece than an extended treatment for a Hollywood screenplay that needs some work. . . . Because of the indecision on its real genre, Possible Worlds ends up being a spoof of itself, both as a horror thriller and a love story."
Perhaps it was this very ambiguity, its anti-Hollywood quality, that attracted Robert Lepage, who claims to love the "blurred, invented aspects" of storytelling. "Mighton is quite brilliant," Lepage said recently. "From the beginning, I thought this was someone I could really work with."
In bringing Possible Worlds to cinematic life, Lepage marshalled his trademark techniques. His film translates into vivid imagery what the stage version can only suggest through lighting and sound effects. Cinematographer Jonathan Freeman shot the movie in the sombre, claustrophobic tones of a vintage film noir, in which the harsh, half-lit faces of the homicide detectives loom out of the dark. The screen is bathed in recurrent images of water: a tossing sea glimpsed through misted glass, sheets of rain drenching the cafeteria windows, sterile liquid bubbling in a glass beaker in which the cortex of a rat is suspended. It's a perplexing, edgy, and highly stylized rendering of the play.
Mighton suddenly asks me what time it is. At three o'clock he must close up his office at the Fields Institute and head home. For the past two years, each weekday, from four to six p.m., his apartment has doubled as the site of JUMP -- the agency he founded to tutor children in math. He lives on the second floor of a turn-of-the-century row house within walking distance of the institute, near a downtown Korean neighbourhood. The walls look as though they could stand a coat of paint. The hardwood floors need refinishing. The decor is Sally Ann eclectic. "I realized a long time ago that I could spend my time trying to earn money to buy things or I could have the freedom to pursue my interests," he says.
It was his ex-wife who encouraged Mighton to begin tutoring children. "I guess I was always complaining about the state of the world," he recalls. "Mainly about the destruction of the environment and about how the schools are failing to serve the needs of so many children. Regan told me I should stop complaining and start doing something positive."
About ten minutes before four p.m., the tutors for JUMP begin to arrive. I am introduced to Gerd Hauck, the Acting Head of the Drama Program at the University of Toronto's University College, Andrew Moodie, who has just finished performing in a play he wrote, called The Lady Smith, at Theatre Passe Muraille, and Adrienne Weiss, a poet and sketch-comedy performer. Each has volunteered to tutor at least one child, for one hour, each week.
Mighton has enlisted his friends from the theatre world -- in addition to math students -- to help tutor, because, he says, he likes using tutors who did not necessarily do well at math when they were in school. "They can empathize with what these kids are going through," he says. "The chemistry between a teacher and student is absolutely critical to the process of learning, even more so because we're teaching many kids who are in special-needs classes. You wouldn't believe the progress we've made. I began working with a grade-six student who couldn't count by twos. She's now in the seventh grade and successfully solving grade-nine problems."
Before the kids arrive, Mighton does a quick review with the three tutors of the algebra questions they will be helping their pupils solve today. They've acquainted themselves with the problems before coming, working from a manual that Mighton has written. "I started jump last year with eight tutors and fifteen kids. This year, we have seventeen tutors and thirty-five kids. That's why I decided to write the manual."
Mighton has written an introduction to his manual that is also a manifesto of his beliefs about the nature of intellectual and artistic ability, and the failure of the educational system to nurture those abilities. "After seeing how children flourish with even a modest amount of attention," he writes, "I have come to believe that when a child fails a test it should be regarded as a failure of our education system. And when millions of children, year after year, fail tests they could easily pass, it should be regarded as the failure of an entire society to care for its young." It is a passionate and angry document, and one that radiates his conviction that teaching children the elements and the beauty of mathematics will give them "a way of entering worlds that are so elegant and surprising they inspire a sense of awe, allowing them to develop a deeper respect for the interconnectedness of all living things."
Moments later, Mighton's door swings open and shut as three pupils let themselves in: two boys and a girl. They are all twelve years old and in grade six at Essex Public School in Toronto's west end.
I follow actor Andrew Moodie into a spare room to watch his hour-long tutoring session with Zack, a wiry, energetic boy whose sharp wisecracks and manic banter suggest he could have a fine career as a stand-up comic. Throughout the session, Zack is sucking on sugary Pixie Sticks, riffling through books he sneaks out of his knapsack, and asking Moodie distracting questions like, "Have you had too much cocaine?"
Moodie keeps directing Zack's wandering attention back to the task at hand: solving equations like 3x + 2 = 17. He uses warmth, enthusiasm, and jokes to keep Zack on target. He cries out, "Beautiful, man!" or "Perfect!" each time Zack gets a partial result. He gives Zack's ego a final boost by telling him that at the end of the session, he'll be able to solve a grade-ten question. "Well, you have to remember I am a genius," Zack laughs.
Seated at his kitchen table at the end of the day, when the kids and tutors have gone, Mighton tells me that he wants to run his program in several schools next year. He plans to enlist a hundred tutors. He feels that by using volunteers, public schools could tutor every child in math who needs it, without incurring any excess costs.
But he also wants to keep his feet firmly in his several different worlds. He'd like to dig deeper into mathematics, moving from knot theory into graph theory, which, he explains, is important to solving many problems in computer science. He has engaged an agent/manager to help him get his plays produced both inside and outside Canada. He also hopes to begin working on a new play and write some poetry. In the long term, he wants to return to the study of philosophy.
all this be possible? "Well," Mighton replies, "we live in an
age that is infused with the idea of possibility. As individuals, we can't
escape that. It's just part of the way we think about ourselves."