Well, Igor takes out a scratch sheet of paper and starts doing calculations, but somehow he can’t get it. Landau says, “Igor, you regard yourself as an educated adult, yet you’re incapable of performing such a simple task.”
When I read this, I took it as a personal criticism. I regarded myself, rather arrogantly, as a very educated person, but I had never heard of calculus in my life. I hadn’t the slightest idea what this sequence of symbols meant.
I decided, as a personal revenge on Landau, to study the subject up to the point where I could solve this exercise. Landau said, in the biography, “Don’t waste your time on mathematicians and lectures and so on — instead, find a book with the largest number of solved exercises and go through them all. That’s how you learn mathematics.” I went back to the library and found the mathematics book with the largest number of problems. The book was in Russian, and I didn’t know Russian, but a young linguist is not afraid to pick up another language.
So I devoted a whole winter to this, and after maybe a month and a half, I came to the point where I could actually do this integral. But I had inertia, so I kept going. I couldn’t stop. And toward the end of about three months, I realized two things. Number one, I was fairly good at this kind of silly manipulative exercise. Number two, maybe this is not the only way to study mathematics. So I looked around and found I could take a two years’ leave of absence from my job.
And then you went to Oxford to study mathematics.
As far as I could see, Oxford was the only place that would allow you to rush through an undergraduate program in two years. I didn’t know English, but a linguist is not afraid to pick up another language.
After a while, I said, “This is what I want to do.” I resigned from my job and went to Princeton to get a Ph.D.
It’s an unusual path into mathematics.
I don’t think I’ve had an unusual life, but it would be regarded as unusual if you take the standard sort of life people are supposed to have in a certain type of society and try to fit me in it. It’s just a matter of projection, if you see what I mean. If you project on the wrong axis, something looks very complicated. Maybe according to one projection, I have an unusual past. But I don’t think so, because I was living my life day by day in my own way. I never tried to do anything weird — it just happened this way.
And now you’re both a mathematician and a collector of toys. Do you see your toys as a way to try to jolt people out of our complacency about how well we understand the ordinary world around us?
On the contrary — I’m trying to jolt myself out of my complacency. When I share, I just want to share with people. I hope that they’ll like it, but I’m not trying to educate them, and I don’t think people are complacent. People are struggling in their own ways and making efforts and trying to improve. Who am I to jolt them out of complacency?
But I like to be surprised, and I like to be proved wrong. Not in public, because that’s humiliating. But in private, I really like to be proved wrong, because that means that afterward, if I come to terms with it when the dust settles, I am ever so slightly smarter than before, and I feel better that way.
How do you find your toys? You’ve said that it involves looking at the world with the eyes of a child.
Sometimes adults have a regrettable tendency to be interested only in things that are already labeled by other adults as interesting. Whereas if you come a little fresher, and a little more naive, you can look all over the place, whether it’s labeled or not, and find your own surprises.
So, when I’m washing my hands with my child, I might notice that if you open a faucet very thinly — not so that it drips, but a thin, steady stream of water — and you lift your finger gradually toward the faucet, you can actually wrinkle the water stream. It’s really fantastic. You can see beadlike wrinkles.
It turns out that this can be explained beautifully by surface tension. And this was known to some people, but 99.9% of the world population hasn’t seen this wrinkling of the water. So it’s a delightful thing. You don’t want to let go of that feeling of surprise.
And so that’s what you do. You just look around. And sometimes you feel tired, or you feel dizzy, or you feel preoccupied by other things, and you cannot do this. But you’re not always tired and you’re not always preoccupied. In those moments, you can find lots of wonderful things.
Do you find that if a physical phenomenon surprises you, that’s a pretty reliable guide that it will surprise other people?
It’s not a reliable guide at all. Sometimes I think something’s really surprising, and people will say, “Well, so what?”
One thing that is a bit disconcerting is that nowadays, more and more people spend so much time in virtual reality, where anything happens, that then no one is surprised by much in the physical world. That can be a sort of break point between their surprise and my surprise.
One very common question that comes up at the end of a lecture is, “Does all this have any practical applications?” It’s really intriguing because this question is asked in almost exactly the same words wherever I go. It’s like listening to a prerecorded message.
I ask them, what do you think constitutes a practical application? It’s very surprising. Roughly speaking, people converge within five to 10 minutes onto two categories of practical applications. One is, if you manage to make several million dollars instantly. The other is, if you manage to kill millions of people instantly. Many people are actually kind of shocked by their own answers.
Then I tell them that, well, I don’t know about other people, but I have a practical application for my toys. When I show my toys to some children, they seem to be happy. If that’s not a practical application, what is?
Correction: This article was revised on November 29, 2018, to correct an anecdote about the physicist Lev Davidovich Landau. Landau asked his son for the indefinite integral of dx over sin x, not the definite integral.