Like the recently proved Fermat’s Last Theorem (xn + yn = zn, where x, y, z, n are all integers, has no solutions for n > 2), these conjectures are tantalizing and can sometimes become, if one is not careful, all-consuming obsessions. Such an obsession is the fate of Uncle Petros. His brothers think little of him and of his quixotic attempt to prove Goldbach’s Conjecture.
Petros in turn has disdain for their petty concern with the family business in Athens. Interestingly, Petros also has a low regard for applied mathematics, which he compares to glorified “grocery bill” calculations and which, he believes, shares none of the austere beauty of pure number theory.
This mutual contempt between mathematicians and more practical sorts has a long history. The British mathematician G.H. Hardy, a colleague of the fictional Uncle Petros in the book, exulted in the uselessness of mathematics, particularly number theory.
Happily, this adversarial attitude has softened in recent years, and even number theory, arguably the most impractical area of math, has found important applications. Cryptographic codes, which enable the transfer of trillions of dollars between banks, businesses, and governments, depend critically on number theory.
They depend, in particular, on the simple fact that multiplying two large prime numbers together is easy, but factoring a large number (say one having 100 digits) into prime factors is extraordinarily difficult and time-consuming.
Finally, I come to the million dollar contest. The U.S. publisher of Uncle Petros and Goldbach’s Conjecture has promised $1 million to the first person to prove the conjecture, provided the proof appears in a reputable mathematics journal before 2004.
The late, great number theorist Paul Erdos used to offer small monetary prizes to anyone solving this or that problem, but he didn’t have to pay up often. If I were the publisher, I wouldn’t worry about the offer’s financial risk, but I would be apprehensive about the torrent of false proofs that will soon be heading their way.
Professor of mathematics at Temple University, John Allen Paulos is the author of several books, including A Mathematician Reads the Newspaper and, most recently, I Think, Therefore I Laugh. His “Who’s Counting?” column on ABCNEWS.com appears on the first day of every month.