RENEE MONTAGNE, host:

Grigori Perelman is one of the world's finest mathematical minds. In 2003, he solved the Poincare Conjecture, which deals with shapes that exist in four or more dimensions. A solution had evaded mathematicians for a century. The Poincare Conjecture is one the seven Millennium Prize Problems, and solving any of what you might call the Seven Wonders of the Math World brings a million-dollar award.

Subtracting Pereleman's win, that leaves six more to be solved, and to talk about those, Keith Devlin, NPR's WEEKEND EDITION Math Guy joins us.

Good morning.

Professor KEITH DEVLIN (Stanford University): Ah, good morning, Renee.

MONTAGNE: Give us a simple version of what the remaining Millennium Prize Problems are. I mean if you can put it a tweet.

Prof. DEVLIN: There aren't enough characters in a typical tweet to be able to do it. There were six of them, as you mentioned, Renee. One is about how well computers can solve certain kind of problems. One is about what pattern do the prime numbers have - how much can you know about the pattern of the primes. One is about the fundamental nature of matter, the things that we and everything around us are made of.

One is an old, 19th century problem about can you solve the equations that describe how water flows along a pipe. And then there's another one connected with prime numbers and the structure of the whole numbers.

So they're in all different areas of mathematics: physics, computational mathematics, and patterns of prime numbers.

MONTAGNE: Well, let me ask you. I mean, most of these sound beyond me - and probably, most people. But let's say the mathematicians going at it are looking for something, and one would maybe be the thrill or the prestige of solving them. But what would the larger benefits be?

Prof. DEVLIN: Oh, boy. In these different problems, one of the other problems is a thing called the P versus NP Problem. If that were solved in one direction, it would mean Internet commerce and Internet cybersecurity would collapse in an instant. That much is at stake.

We think the answer is going to go the other way. But if someone comes along and solves one of these Millennium Problems about computation, and it goes in the way we dont expect, then it will tell us that everything we assume about the security of communications over the Internet is false.

MONTAGNE: Have computers helped in any of this?

Prof. DEVLIN: Computers have affected mathematics around the edges. But these are problems that mathematicians have to sit down, paper and pencil, close their eyes, think and dream and talk to each other from time to time, and try to solve them - in exactly the way that Grigori Perelman recently solved the Poincare Conjecture. And all of the other Millennium Problems are really of that nature.

MONTAGNE: Thats a lovely thought, except now that it's sort of out in the world - unleashed, as it were - one, he doesnt want to collect his big prizes. He doesnt want to collect the money attached to it because he doesnt want the publicity. Right?

Prof. DEVLIN: He's really the mathematical equivalent of J.D. Salinger. You know, he writes "Catcher in the Rye" and then disappears from view. But the unfortunate thing is, he has now solved one of the biggest unsolved problems in mathematics. And there's going to be a ceremony in Paris this June. Most of my colleagues that know something about Perelman believe that he's not going to turn up for that.

Whether he will arrange to receive the $1 million prize, quietly out of the limelight, I think we'd all be very surprised if he publicly turned up to receive a check and have photographs of him receiving a check. You know, one of these big checks like a lottery winner.

(Soundbite of laughter)

Prof. DEVLIN: Everything I know about him suggests he's not going to go that route.

MONTAGNE: Keith Devlin is author of "The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time." And you might know him also as the Math Guy on NPR's WEEKEND EDITION.

Thanks very much.

Prof. DEVLIN: OK. My pleasure, Renee.

Copyright © 2010 NPR. All rights reserved. Visit our website terms of use and permissions pages at www.npr.org for further information.

NPR transcripts are created on a rush deadline by Verb8tm, Inc., an NPR contractor, and produced using a proprietary transcription process developed with NPR. This text may not be in its final form and may be updated or revised in the future. Accuracy and availability may vary. The authoritative record of NPR’s programming is the audio record.