Genius or Gibberish? The Strange World of the Math Crank

by George Johnson


The letter, dated Christmas Day 1998 and addressed to a professor at the Niels Bohr Institute in Copenhagen, began portentously: "Nowadays, we seek to comprehend our comprehensions and call that comprehensiveness knowledge in the mistaken belief that as a science it is immortal. Such omniscience diffuses like Helium-3 into the penetralia mentis of omnipotent impotency within any God-head such that any caveat actor is saved."

Within a few sentences, the writer was holding forth on Heisenberg's Uncertainty Principle and "the concept of nothing" as the empty set, before launching into speculations involving number theory: "It's enough to make me conjecture that infinity's prime and Riemann's Zeta function accounts for fractional charge subatomically just for the Higg's boson with an involucral matrix of ogdoad parity as midwife!"

The letter was typed single-spaced with the tiniest of margins and embellished with hand-drawn diagrams and colored annotations. Copies were sent to a list that included the linguist Noam Chomsky, the physicists John Archibald Wheeler, David Deutsch and Stephen Hawking, and the mathematician John Casti.

"It has all the hallmarks of a crank," said Dr. Casti, who is affiliated with the Technical University of Vienna and the Santa Fe Institute in New Mexico. "It's amazing all the stuff you can get onto a single piece of paper."

But was it not just possible that couched in the obscure mix of mathematics, physics and Egyptian mysticism ("ogdoad parity" refers to four pairs of gods with names like Darkness, Absence and Endlessness), there lay an important insight?

Didn't two Cambridge University mathematicians dismiss the great self-taught Indian number theorist Srinvasa Ramanujan as a crackpot when he sent them long eccentric letters from India early in this century? Only their colleague G. H. Hardy had the foresight to recognize Ramanujan as a genius. And didn't the great German mathematician Carl Friedrich Gauss foolishly throw away unread a groundbreaking paper from his young Norwegian colleague Niels Heinrik Abel, calling it "another of those monstrosities"?

Physicists get their share of mail from amateurs attempting to reconcile quantum mechanics and general relativity or to show that Einstein was wrong.

"You can't just say Ramanujan was a genius and these other guys were cranks," Dr. Hersh said. "With a superficial look, there is hardly any visible difference. There is not always a sharp line between eccentric mathematicians and intelligent but maybe obsessed amateurs."

Until recently much of the mail contained supposed proofs of Fermat's Last Theorem. But since Dr. Andrew Wiles of Princeton University recently proved this famous puzzle and number theory, Dr. Paulos said, the focus has shifted to disproving Dr. Wiles. Another favorite diversion is Goldbach's Conjecture, which holds that all even numbers are the sum of two primes. Though no one has found a counter example, this would-be theorem remains unproven, unless the solution has been crumpled up in a math department wastebasket somewhere.

Copyright 1999 The New York Times (February 9, 1999)



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