It Doesn't Figure

By MICHAEL D. LEMONICK

Over the past few decades, Gregory Chaitin, a mathematician at IBM's T.J. Watson Research Center in Yorktown Heights, N.Y., has been uncovering the distressing reality that much of higher math may be riddled with unprovable truths--that it's really a collection of random facts that are true for no particular reason. And rather than deducing those facts from simple principles, "I'm making the suggestion that mathematics is done more like physics in that you come about things experimentally," he says. "This will still be controversial when I'm dead. It's a major change in how you do mathematics."

Chaitin's idea centers on a number he calls omega, which he discovered in 1975 and which is much too complicated to explain here. (Chaitin's book Meta Math! The Quest for Omega, out this month, should help make omega clear.) Suffice it to say that the concept broadens two major discoveries of 20th century math: Goedel's incompleteness theorem, which says there will always be unprovable statements in any system of math, and Turing's halting problem, which says it's impossible to predict in advance whether a particular computer calculation can ever be finished.

Sounds like a nonevent in the real world, but it may not be. Cryptographers assume that their mathematically based encryption schemes are unbreakable. Oops. "If any of these people wake up at night and worry," says Chaitin, "I'm giving them theoretical justification." --By Michael D. Lemonick. Reported by Matt Smith/New York

With reporting by Reported by Matt Smith/New York