Freeman Dyson's Mathematical Prestidigitation

April 14, 2009

In a long article on eminent physicist and global-warming skeptic Freeman Dyson (New York Times Magazine, March 29, 2009) titled "A Civil Heretic," writer Nicholas Dawidoff recounts a story that highlights Dyson's mathematical acumen. Dyson, born in 1923, had been enthralled by mathematics in his youth.

Starting in the 1970s, Dyson participated in Jason, a small, government-financed group of top scientists, who gathered each summer to work on scientific dilemmas often of military interest to the government. In such company, Dyson had a way of answering mathematical questions as if they were parlor tricks.

Some scientists would be sitting in the cafeteria, the story goes, and a member might idly wonder if there is an integer where, if you take its last digit and move it to the front, turning, say, 112 to 211, it's possible to double the value.

Dyson would immediately claim, "Oh, that's not difficult," allow two short beats to pass, then add, "but of course the smallest such number is 18 digits long."

When this happened one day at lunch, one scientist recalled, the table fell silent. "Nobody had the slightest idea how Freeman could have known such a fact or, even more terrifying, could have derived it in his head in about two seconds," he said. When the meal ended, the assembled men, often described with words like "brilliant," "Nobel," and "MacArthur," would return to their offices—to work out what the famous physicist knew.

The number theory problem is suitable for the classroom. And the smallest such number turns out, indeed, to be 18 digits long.

(Answer: 105263157894736842)

Source: New York Times Magazine, March 29, 2009.