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April 18, 2002

**OLD CHALLENGE.** If you had to disappear, so that no one could find you, where would you go to live?

**ANSWER** (Joe Shipman).

1) If I only had a little money, I would become a migrant farm worker or laborer. They have no fixed address, work on a cash basis, and don't get asked many questions. 2) If I had a fair amount of money (say $25,000) I would set myself up in a cabin in the wilderness. 3) If I had a lot of money (say $250,000) I would buy a good houseboat that could be sailed singlehandedly and move from port to port every couple of months.

**POINCARÃ? CONJECTURE PROVED?** In 1904 the great French mathematician Henri PoincarÃ© conjectured that the 3D sphere (easily pictured in 4D space) is the only compact, connected 3-dimensional manifold in which every loop can be shrunk to a point. The appropriate analog in all other dimensions has been proved. In 2000, the Clay Mathematics Institute offered a prize of one million dollars. Recently, the English mathematician Martin Dunwoody of Southampton University announced a proof, of uncertain status. "A proof of the PoincarÃ© conjecture? (revised version eight, 11 April 2002)" can be found on the web at www.maths.soton.ac.uk/pure/preprints.phtml

**VIETORIS DIES AT 110.** The famous topologist Leopold Vietoris, Austria's oldest citizen, died last Thursday at home at the age of 110.

**QUESTIONABLE MATHEMATICS.** John Shonder of Oak Ridge National Laboratory reports that The Reuters news service, reporting on a press release from the British Antarctic Survey, claimed on March 19 that

"The Antarctic Peninsular has warmed by 36 degrees Fahrenheit over the past half century, far faster than elsewhere on the ice-bound continent or the rest of the world."

Shonders continues: Warming up by 36° F seemed a little high to me, so I went to the web site of the British Antarctic Survey itself to see what they said:

"During the last 50 years the Antarctic Peninsula has warmed by 2.5° C, much faster than mean global warming."

Reuters apparently substituted 2.5 into the formula F = (9/5) C + 32 for converting temperatures (not for converting changes in temperature!).

Readers are invited to submit more examples of questionable mathematics.

**NEW CHALLENGE** (Jeff Repka). A sponsor of the Chicago Cubs radio broadcasts will attempt to give away a million dollars this season during each game. Before each game, a fan is selected from a random drawing of entries. Also, a position (excluding pitcher) is selected at random. If the Cubs player who starts the game at that position hits a grand slam in the seventh inning, the fan wins the million. If any other Cubs player hits a grand slam in the seventh inning, the fan wins ten thousand dollars. How safe is the sponsor's money?

Copyright 2002, Frank Morgan.

Send answers, comments, and new questions by email to Frank.Morgan@williams.edu to be eligible for* Flatland *and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.

THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).