An Interview with Mathematician and Author John Mighton

PHOTO TK

 

For nearly three decades, John Mighton's career has defied categorization. His plays, including Half Life, The Little Years, A Brief History of Night and Possible Worlds (which was made into a film starring Tilda Swinton) have won every major playwriting award in his native Canada, including - on two separate occasions- the country's highest literary honor, the Governor General's Award. After almost failing Math as an undergrad, he now holds a Ph.D. in the subject from the University of Toronto, and in 2005 was named a Fellow of the Fields Institute for Research in Mathematical Sciences. He has taught university courses in Philosophy (Reasoning and Argument Analysis) and Mathematics (Graph Theory), and, after serving as a math consultant on Gus Van Sant's 1997 film Good Will Hunting, was cast in the role of Matt Damon's tutor. He is also the bestselling author of The Myth of Ability and The End of Ignorance, two books on intelligence, creativity and learning, but it is a charitable organization called JUMP—Junior Undiscovered Math Prodigies—that John founded in 2001 which he cherishes most.

What started in 1998 as an after-school tutoring centre run out of his own apartment (and staffed entirely by unpaid friends in Toronto's theatre community) has grown into an organization that provides tens of thousands of elementary school students with a radical alternative to the conventional mathematical curriculum taught in most schools. 

Mighton's unorthodox approach to teaching the subject, which centers on an intuitive pedagogy not reliant on expensive textbooks, has been met with strong resistance, both from traditionally-minded governments and school boards, as well as the multi-billion-dollar consulting and textbook-publishing industries that lobby them. 

In all his pursuits Mighton challenges the societal beliefs and educational structures that cleave the arts from the sciences, insisting that the potential for high-level proficiency in both is intrinsic in our species' natural urge toward creativity.  

We met early on a summer evening, in his office at the University of Toronto. He is notoriously shy, and so soft-spoken that- even with two recording devices- I had to replay parts of our 2-hour conversation several times in a silent room to transcribe his words. 

When I arrived John began struggling to clear a spot for me at a desk that was obscured by mounds of paperwork. Just as I sat down, he got up and went to the window. "I'm sorry," he said, drawing open the blinds, "But none of the lights in here are working. I've been meaning to do something about it for ages, but I can never seem to get around to it." 

—Marc Bendavid

I. PERSONALITY? 

THE BELIEVER: When did you first get the feeling that you were interested in the relationship between memory and forgetting?

JOHN MIGHTON: I guess I’ve always been fascinated by any kind of questions about personal identity, or what makes a person who they are. And that really came to a fore when I started doing philosophy and read about these experiments that were done in the fifties by Roger Sperry, who won the Nobel Prize for his work on the brain. They would cut the corpus callosum- the brain stem that joins the two halves of the brain- in epileptic patients, because they thought it would stop seizures. And he experimented on these patients, and did these incredibly elegant experiments where he found that the two halves of the brain were really functioning independently of each other.

He was able to feed information to one half of the brain, and the other half couldn’t be aware because of the way the body takes in information. But the two halves would find ways to communicate with each other, through facial expressions and things like that, even if one half couldn’t have direct access to the information. It would make up answers on some of the information it could get from the other half. And it was really clear that the two parts were functioning independently.

BLVR: Were the patients conscious? 

JM: Yes. And It was like there were two consciousnesses going on in the same head so philosophers really picked up on that. One thing that really fascinates me is the limits of the imagination. And that limit seems to be established more and more by science, or the boundaries of what we can imagine. So that’s an example: anyone could’ve imagined two identical consciousnesses in the same brain before that experiment, or two versions of a person, but until the experiments were done no one did. And it also fit with a deeper concern of mine, which has always been a fascination with the unthinkable, or the unknowable. And with memory and loss of memory. That’s part of a bigger fascination for me, around the whole idea of...

BLVR: Personality? 

JM: Well, how we know we’ve ceased to be ourselves. How do we know when we’ve changed into a radically different person? It was really clear in the nursing home where I visited my mum that these people weren’t who they were. They were losing more and more of their memories. They were even becoming different people in many ways. People who were perfectly happy were becoming bitter, and so on. So there you see the question viscerally: when do you stop being yourself? Is there any continuity between who we were before trauma and after trauma? And I’m fascinated with characters who think beyond their depth, who are constantly struggling with questions that are bigger that them and that they can’t answer. That’s the overarching fascination in all my plays.

II. KIDS CAN BE GREAT AT ALMOST ANYTHING                               

BLVR: You’ve written that almost any kid can be great at almost anything, and yet so many people hear the word, mathematics and they bristle, or it depresses them or makes them anxious. 

JM: First of all, that beauty, of seeing patterns, of seeing connections, of solving puzzles, of seeing resemblances, all those things; I think that’s a common experience for poets and mathematicians, for writers, for artists, for scientists. The sources of satisfaction aren’t that different in many ways. The big difference is you can’t as an artist verify, in any kind of public way, that your work is good, or sound or provable or true. Judgments of what has value are always changing. At least once you’ve proven something in mathematics, generally it’s considered true over the generations. But I also realized that it was the easiest subject to teach kids, to catch them up in. Mathematics is so easy to teach. People won’t believe that. My first student was in a grade six remedial class, and told he would never do math, and he finished his Doctorate at the University of Toronto. 

BLVR: But I’m wondering when you made the decision that it was going to be math, and not-

JM: Well, if you go back further, it’s a complete fluke. I was broke as a playwright, and saw a notice for a math tutor at a job placement office, so that’s how it started.

BLVR: And before then, math hadn’t seemed like any more attractive a possibility than, say...

JM: No, I’d almost failed calculus at University.

BLVR: Ok, but you were still taking calculus at University! I mean, that’s-

JM: Well I took it, but almost failed it. It was only about ten years later, I was helping someone in New York who was going into pre-med, and I re-read some of the calculus stuff and it was way easier than I remembered it. And I think that gave me the confidence to actually tutor. I was working my way through the material, and stuff that was totally mysterious to me in high school became easier and easier. 

BLVR: The first time we met, you said nothing is more peaceful than to lock yourself in a quiet room with a mathematical formula to work on.

JM: As things that I thought were just incomprehensible became clearer, I realized it was a pretty simple subject in many ways, but that it was endlessly entertaining to try and solve these puzzles. The other thing that drove me to it was that I’d read a lot of science fiction and popularizations of science when I was younger. But there’d always be places where I just could not make out what they were saying -- if they were talking about quantum mechanics, or things like that. And I realized as I did more and more math in my tutoring that this was allowing me to understand what I read. That’s when I decided to go back to University and do a degree in math in my thirties. Because I’d gained that confidence, and I wanted to understand more deeply what I was reading. 

III. ERASING THE PLAYWRIGHT

BLVR: When I mention to people that I was interviewing you, this fascination comes up a lot around the dichotomy in your life between fiction writing and mathematics. Those two things seem paradoxical to people, and obviously to you they don’t. 

JM: No, I think they go hand in hand. I mean, I’ve made discoveries in mathematics that came out of my literary and philosophical training. Particularly because when I do mathematics I have a sense of resemblance, or analogy, that’s always buzzing in my head when I look at things. I ask really strange questions sometimes, because I studied Wittgenstein, who asked really strange questions. Most of my work in the arts in inspired by ideas from philosophy or mathematics. There’s a deeper similarity: they’re just ways of exploring patterns and connections in the world. 

BLVR: But your plays seem less like explorations of patterns than explorations of individual relationships...

JM: But the playwrights that interest me the most, like Chekhov and Beckett and people like that, they’re exploring patterns at a much deeper level. There’s constant repetition and recurrence of elements in those plays, especially in Beckett’s plays, and a lot of interesting formal structure and ironies, too. Irony depends on you recognizing the similarity between two things, or the difference between them. So all those things involve the play of patterns in some way, or connections, resemblances, things like that. 

BLVR: Yet there are so many moments in your plays that are so unexpected, and poignant, at the same time seem to come out of left field.

JM: But that’s the breaking of a pattern, or the breaking of a symmetry in some ways. To have a sense of those things you have to have a sense of pattern.

BLVR: The way you talk about writing seems almost formulaic, but the plays read- and perform- so organically...

JM: It’s not formulaic. And maybe that’s the problem. When you’re doing creative work in mathematics or science, it becomes more and more organic, more and more a matter of seeing connections that are surprising, things that you’d never think go together. It’s hard to describe, because most people never get the chance to do creative work in the sciences. See, I’m not a very natural writer, because I came to writing so late in life, so I could never sit down in front of a page and have the ideas just pour out of me. It’s the worst thing I could possibly do. 

BLVR: How do you start?

JM: I used to keep lots of journals, I’d write down conversations I’d heard. Maybe that’s another element you want to add to the work of a scientist or mathematician: constant observation. You’re not inventing; you’re rarely inventing. Once I have lots of found material I start putting things next to each other, like snippets of conversation or ideas, and just look for what happens in the space between them. What are the patterns that start to emerge? Where are the resemblances? What are the echoes of other things? What’s ironic? Someone said something earlier, but then did something that’s in complete opposition. You’re always looking for those things. 

BLVR: It sounds like, in describing it, you’re erasing the playwright...

JM: Yeah.

BLVR: As though your work is about getting out of the way of an experiment that’s happening.

JM: That’s how I feel. I mean, there’s always the very limited filter of my perception and my interests, but I try as much as possible to let the world play itself out.

BLVR: And yet the play- I’m thinking mostly about Half Life now- it feels as if there’s some sort of justness, or rightness, that emerges at the end. This sense that it’s a complete thing. 

JM: But there was so much randomness that goes towards the production of that. In my mum’s room at the nursing home they had a woman who spoke like James Joyce. I mean, she had these stream-of-consciousness monologues where she’d go back fifty years, then come back to the present, these random associations, and they were the most beautiful things. In fact those speeches in the play are just word for word what she said. And one day she finally came to herself and said Oh I realize I’m keeping you up, you can put your mum to bed. So I closed the curtain between their beds, and all of a sudden her voice started again. And that moment tied together so many things. The question of the play- if you have all these people in a home who are gradually losing their qualities, when do they cease being themselves? When is someone intelligent, or a human, or whatever? All those things, it was the experience of drawing the curtain that brought them all together. So you depend on observation in gathering all these images and ideas, and then gradually they come into a structure. Which is very similar to what you do in the sciences.

IV. IMMORTALITY

BLVR: The first time we met you told me you really valued the work you do with kids in math, but that you weren’t sure whether any of your plays were any good at all. Why is that? I mean, all the awards, the prizes, everything... 

JM: Well, I don’t know. I’m not being- I’m getting so old I have to continually struggle for phrases now- what’s that sentence? Fake modesty?

BLVR: False modesty...

JM: Even though I talk about the potential in children, I realize that our intelligence, our imagination, is dwarfed by the Universe. It’s absolutely dwarfed. Probably most of we know now will prove to be false in some way, or limited. Everything passes, absolutely everything. And even things that last, like Shakespeare’s work, at this point it’s a work of collective intelligence. It has so many layers of interpretation that who knows if it’s even connected to Shakespeare now? And the things that do last may be transmuted to the point where they’ve got nothing to do with the author’s original intentions. But the vast majority of work will just disappear, and will mean nothing to anybody. So that’s what I live with constantly. And I think all artists live with that kind of insecurity. 

BLVR: The struggle for immortality.

JM: We live in a time where we think of an artist who had great success in their day but then their work was forgotten - we tend to think of them as a failure. And that’s very deep in us. This way of thinking really seems to have come out of the rise of Newtonian times, the idea that time goes on endlessly, and that every second is the same as the second before, indistinguishable, and just moves on endlessly. Before that, people thought time was circular, or would be brought to an end by God, and artists would create work just to glorify God. There wasn’t as much obssession about work lasting time. That obssession became more and more intense with the rise of the Industrial Age, with time having value. People used to measure time with candles, their hours weren’t even fixed. But gradually time became a more and more precise thing and it went on forever and we became more and more obssessed with work lasting time. So we began to think work had no value if it didn’t last. It’s not even clear what we’re looking for. You can have an amount of immortality that dwarfs any other amount, depending on the structure of the Universe. And what the hell are we looking for? Maybe we need to go back to a kind of idea of immortality that people used to have, that it depended on what your family thought of you, or your city state, or your reputation among your children - a kind of biological immortality. We don’t value that enough. 

V. MATH: HAVING IT

BLVR: There are so many nostalgic references in your plays about childhood. Does your hope for kids imply a reciprocal lack thereof for adults?

JM: No. Kids can find the simplest things wonderful. For some reason I remember this plastic bowling ball with eyes on it at a shop my mum took me to once. I just wanted to go back there all the time, because I had this wonderful experience with a plastic bowling ball with eyes. I don’t know why, maybe the fact that an inanimate object could have eyes and be alive. I don’t even know what game I played with it. I just remember being endlessly happy because of this experience and wanting to go back to that shop. It’s so simple for kids to be happy. Much simpler than for adults in many ways. That doesn’t mean adulthood is a total loss. But kids have that sense of wonder, and the experience of and exercize of curiosity and the sense that there’s always more to explore in the world, and I think that a lot of adults don’t, because of their experience at school. And because the world just overwhelms them and they may just not have time to think about those things because they’re trying to stay alive. But for most adults in the West, they could continue to experience that sense of wonder but it’s not possible because one door after another just closed on them at school.

BLVR: What about beyond school? The way society is structured, with work and competition and money... I mean, can the blame for de-wonderizing children all fall on the shoulders of educators?

JM: No, the most educators can do is teach their subjects in a way that will fascinate the kids and engage them. But the thing I am deeply interested in JUMP and in doing research in is the effects of hierarchies in classrooms. Beacause there’s research that shows that as early as kindergarten, children are comparing themselves to each other, and deciding who’s talented in any given subject.

BLVR: Do you think that’s at the suggestion of teachers?

JM: It’s a much bigger problem. Teachers are having to teach in a way that just exacerbates hierarchies. And the hierarchy seems so innocent: for example, nobody has any problem admitting they’re bad at math publicly, they just think it’s natural for some people to be gifted at math, and that the rest will maybe take consolation in having some talent somewhere else. Those ideas are so deeply engrained in our society, and I think they’re responsible for most of our problems.

BLVR: When did you first feel like there was something wrong with the way we perceive intrinsic capabilities? 

JM: It’s because of my own experience. I always had big doubts about whether I was intelligent, or would be able to do anything. And sometimes I did really badly at school. I always had that insecurity. My sister was studying psychology and had books about intelligence around the house, and they made it seem like you had to be born with these traits to do anything. Also, the sixties were really an age when people talked a lot about intelligence and giftedness and all of that stuff.

BLVR: So how do you account for talent then? Or do you think talent doesn’t exist?

JM: It’s a really complex question. Yeah, talent exists, and there are people who, through their efforts, and whatever abilities they started with... I mean, there is a genetic component to ability, but it’s pretty much available to everybody. The vast majority of kids appear to have the potential to do math at a high level. And the ones that are “talented”, why does that happen? Well, the world is random and complex. Kids can start feeling good about themselves or get a head start and that can just multiply. 

BLVR: I guess it’s hard to abandon- especially in the arts- this notion that there’s some sort of ephemeral, intrinsic thing that moves through the artist or performer. We call it “inspiration” or “the muse” but maybe it’s just another outdated idea. That feeling of possession by some exterior force.

JM: It’s like a chess player that can play thirty players blindfolded and still beat them. They get into this kind of groove. But where did that come from? It came from years of practice and training. Now maybe there are things in the arts that are not quite so demanding, where you don’t have to train so much, or- like acting- that we may be in training for every minute of our life, so you don’t have to do so much obvious training. I’ve often seen that the most talented actors when they’re young are the ones who drop out, and it’s the ones who persevere and just slog through are the ones who get better and better. There’s a psychologist named Carol Dweck who did a study that found that some kids had a fixed mindset, where they felt that their success depended on their innate ability or their natural talent, compared to ones who had a growth mindset, ones who believed that their success depended on their efforts and their work. And she’s got stunning results that show that the academic success diverges radically. The ones with the growth mindset do far better. 

BLVR: So it’s somehow about confidence.

JM: No, the ones who had the fixed mind set, first of all they don’t work, because they think if they have to work, then they don’t “have it” naturally. Secondly, when they encounter difficulty they tend to give up; they think, Well I guess whatever talent I thought I had wasn’t there. The ones with the growth mindset will persevere through anything. And they’ll learn, they’ll train themselves. They’ll learn. That’s where talent comes from. We keep pointing to these few examples of talent that appears to come out of nowhere. First of all it’s not always clear it came out of nowhere; there may have been an enormous amount of training that happened, we just didn’t see it. Second of all, even if it did come out of nowhere, that doesn’t prove that you can’t train the rest of humanity. Maybe there’s some mysterious way their brain works, or some bizarre thing that happened in childhood that started an avalanche of learning, who knows what. Or maybe there are people- like Ramanujan, this Indian mathematician- who happen to be born with brains that work differently. He had these bizarre talents, these bizarre ways of seeing numbers. But those are exceptions. We have this stupid argument that always goes, “Oh, this talented person seemed to get this ability out of nowhere, so therefore there’s no point trying to train anyone else to have these abilities. It’s just a ridiculous argument, it completely misses the point. We suppress a lot of natural abilities in the development of our brain because they’re not generally productive. There are autistic kids who have much more acute perception, that can see prime numbers and understand things about prime numbers, but people who perceive the world so acutely may suffer in other ways. And so we evolve to suppress a lot of those things. So sometimes we see people who haven’t suppressed those things, who have these outlandish abilities in certain areas, but that doesn’t mean they’re going to turn out to be Einsteins, because quite often those abilities don’t lead anywhere. That’s another problem with that whole argument: they point to these idiot savants and say, That’s just a God-given gift, and because it doesn’t occur with everybody, not everybody can be a genius. Those gifts aren’t always productive. The arguments people construct around those things are really full of holes. Again, it’s a failure of imagination.