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SCOTT SIMON, host:

This is WEEKEND EDITION from NPR News. I'm Scott Simon.

Switzerland is preparing to celebrate the birthday tomorrow of one of its most distinguished personages, and the planet will rock. Sunday marks the 300th birthday of one of history's top mathematicians, Leonard Euler. Now, luckily, we have a man who's just behind him on that short list of great mathematicians. Our own ambassador from the world of math, Keith Devlin, out of Palo Alto, California, to introduce us.

Good to talk to you, Keith.

Mr. KEITH DEVLIN (Mathematician, Stanford University): Hi, Scott. Nice to be with you. I've never had an introduction quite like that before.

SIMON: Keith, I - well, you deserve every second of it. Keith, we are talking about the man who invented pi.

Mr. DEVLIN: Oh, he not only did recognize it, but he was the one that established the Greek letter pi for denoting the circumference of a circle of diameter one. He was also the guy that established a lot of other standard notations that are familiar to high school math students the world over like E for the base of natural logarithms, I for the square root of minus one, writing a function as F followed by an X in brackets.

It was Euler that really studied sine and cosine functions for the first time. Most of the stuff that we remember from our high school mathematics class was actually either invented or established by Leonard Euler.

SIMON: Let me ask you about the use of that phrase, invent an equation, as oppose to discover an equation.

Mr. DEVLIN: Mathematics is, in a sense, invented but it's invented by the human brain as it tries to encounter the universe in which it finds itself. So the invention is not a free invention. For example, had Shakespeare not lived we would never have had "Hamlet." Had Euler not lived, we would eventually have had Euler's equation E to the I pi equals minus one. It might have taken several hundred years to find it. And the genius of Euler was that he found it in the 18th century.

But the invention in mathematics amounts to discovery, but it's essentially a discovery about the human mind and how the human mind encounters and interacts with the universe in which it finds itself.

SIMON: How do we understand his importance? I mean, we have to be careful with homey metaphors, I'm sure, but how does he compare with someone like Leonardo da Vinci at the quality of invention?

Mr. DEVLIN: That's an interesting one to mention because a couple of Euler's results, a couple of his theorems, I, on many occasions, have said that these are the equivalents of the "Mona Lisa" or the David statue. They are the epitome of elegance, beauty, insight, depth - I mean, the very things that make great art great.

SIMON: And he had a practical side, too.

Mr. DEVLIN: Oh, yeah. In fact, when he was in Berlin, Frederick the Great got him to do all kinds of things. He supervised the Observatory, the Botanical Gardens. He looked over the financial matters of the court. He managed the publication of calendars, maps, a whole bunch of very practical things, at the same time as producing more original mathematician than anybody else in history before or since him. He's really quite a remarkable individual.

SIMON: Euler, I gather, is the author of your favorite equation in mathematics.

Mr. DEVLIN: When I was a teenager, it was one of those epiphanies. When I saw that equation of Euler's, that was one of the things that made me decided I wanted to be a mathematician. There are really three basic constants in mathematics, other than numbers like zero and one. One is E, the base of natural logarithms; one is pi, the circumference of a circle of diameter one; and the other one is I, the square root of minus one.

These three constants seem to be very, very different and yet Euler discovered that if you take E and raise it to the power I times pi, you get the answer minus one. I mean, most people would think that if you take E and raise it to a power like I pi, the answer is going to be unbelievably complicated. No, it's actually equal to minus one.

That is absolutely staggering and I think many teenagers like me, when they see that, will say wow, there are things in this universe that we've just got to figure out. And Euler, through that one identity, is pointing to the way. It's one of the most amazing things in the world.

SIMON: And this inspired a piece of music?

Mr. DEVLIN: Yeah, indeed. And I think - justifiably so, because when you've got something with this kind of depth, that's really an insight into the depths of the human soul. And so it makes sense to try and come at it from different aspects: from a poetic aspect, from an artistic aspect, in terms of painting perhaps, and almost certainly from a musical aspect. I mean, it really would make sense to try and get at this through the beauty of music, to complement the beauty of mathematics, which it exposes in the first place.

SIMON: Keith, thank you so much.

Mr. DEVLIN: Okay. My pleasure indeed, Scott.

SIMON: Speaking with us from Palo Alto, California, Keith Devlin.

(Soundbite of music)

ZAMBER MUSICAL ENSEMBLE(ph): (Singing) - equals minus one.

SIMON: The Zamber Musical Ensemble singing in admiration of Leonard Euler.

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