Peter Borwein is one such mathematician. Executive director of Simon Fraser’s Interdisciplinary Research in the Mathematical and Computational Sciences (IRMACS) Centre, a cutting-edge computer lab that brings scientists together, he has written books on pi, and in the 1990s, he co-discovered algorithms that allowed the calculation of four trillionth, fortieth trillionth and quadrillionth digits of pi — twice with his brother Jonathan, a professor at Dalhousie University.
To mark Pi Day — a worldwide celebration of the enigmatic number held every year since 1988 on March 14, or 3.14, we asked Borwein about the fascination with 3.14159265358979323846 . . .
IC: Why are you professionally interested in pi?
PB: When I was working at Dalhousie University about 20 years ago with my brother John, I became interested in ways of calculating complicated numbers quickly, because I wanted to improve computations of many things including pi. Pi is one of the most famous examples of a complicated number, simply because it doesn’t end. We chose to learn more about pi for the same reason Edmund Hillary chose to climb Mount Everest: because it’s there. If you want to be a successful mountaineer, you always try to climb the highest peak. For a mathematician, pi is a high mountain peak.
IC: What kind of a number is pi?
Dr. Peter Borwein
Peter Borwein
PB: It’s a good example of a number that isn’t easy — the name for it is a “transcendental number” Most people think that numbers are easy to understand, like 1, 2, 3, 4, 5, or that maybe there are some slightly harder numbers out there, like the square root of 2. But, actually, mathematicians know that most numbers are like pi. To really understand how the world functions, you have to understand that most numbers are complicated. The most natural example of that is pi. It’s irritating how little we understand about the number, and this is part of the reason it stays in the public imagination.
IC: Why is this number so important to basic math?
PB: It’s more about testing theoretical knowledge than anything else. From a physical point of view, if you wanted to calculate really obscure things, like the radius of a universe, you would never need more than 15 or so digits of pi. However, it is fairly common practice to calculate digits of pi when you get a new supercomputer system up and running, because it stretches the computer. It doesn’t have to be pi, but because it’s such a well-researched number, it’s a useful calculation to do to see whether everything is going as you expected.
IC: Why are some mathematicians so obsessed with calculating pi?
PB: There’s a nice quote of Newton’s, which is roughly: “I’m ashamed to tell you how many digits I computed this to, having no other business at the time.” Are mathematicians really interested in learning all those digits? Personally, the answer is no. I can recite about seven of them to you. Do I care that I know how to work it out efficiently? Yes. That’s why, to a mathematician, pi is an essential entity in number theory. The mathematical quest is more interesting than the query.
IC: How many digits are calculated for pi?
Brothers Jonathan (standing) and Peter Borwein
Peter Borwein
PB: The largest calculation we know about is of a trillionth digit, or a thousand billion. And that was done by Yasumasa Kanada at the University of Tokyo. The techniques for calculation have become very sophisticated and complicated to explain, but the history of the calculations — now over 2,000 years old — still rests on understanding the ratio of the circumference of a circle to its diameter.
IC: Is there any use to knowing pi to so many places, just on its own?
PB: Not unless you get a surprise, which is rather unlikely. So I think in the sense you mean it — in the sense of “does it help you build a better supercollider” — the answer is no.
IC: How do you celebrate Pi Day?
PB: It varies from year to year. Many years, I give a public lecture on pi. Some years, we bring “pie” — the food. It’s the sort of thing that seems to have taken on a life of its own. At IRMACS, we use Pi Day as a time to bring in the public and show them the research we do. Our goal is to get good students interested in joining the institute, and Pi Day always does this.
