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February 18, 1999
MATH JOKES. Math Chat has received a number of mathematical jokes, most of them terrible. This week's winner is a riddle from Peter Hegarty:
RIDDLE. Which mathematical term is named after a well-known American politician?
The answer is near the end of this column.
OLD CHALLENGE (Joe Shipman). Select the best occurrence in the world of each number from 1 to 10. For example, 12 is the number of eggs in a dozen or the number of months in a year.
ANSWER. Here is the winning response compiled from John Robertson, Henry Ricardo, Bob Swanson, Jean-Pierre Carmichael, and Ryan Grove:
(Can readers improve on this list?) Then there is this from Al Zimmermann:
Finally, in his beautiful response, David Shay relates that, "At the end of the Seder night, which begins the Jewish holiday of Passover, it is common to sing a song named 'Who Knows One.' This song gives an exact Jewish answer to your challenge, in the range of 1 to 13. Here it is:
NEW CHALLENGE. Critique the following short proof of Fermat's Last Theorem sent in by reader Rob Connelly. (In perhaps the biggest mathematics news of the century, Andrew Wiles recently came up with a very long and complicated proof to this 350-year old problem.)
Fermat's Last Theorem. The equation
(1) x^{n} + y^{n} = z^{n} has no positive integer solutions for n > 2.
Proposed proof. Suppose there were such a solution. Since x y, we may suppose x = y + a, z = y + b, with b > a positive integers. Consider the integer N defined by
(2) z^{n -1} = x^{n -1} + y^{n -1} + N.
Then
x^{n} + y^{n} = z^{n} = z(x^{n -1} + y^{n -1 }+ N).
Solving for N yields:
N = [(y+a) ^{n -1} (a-b) + y^{n -1} (-b)]/(y+b) = [F(y)]/(y+b) ,
so y+b divides F(y) and
0 = F(-b) = (a-b) ^{n } + (-b) ^{n}
0 = (b-a) ^{n } + b^{n} > 0,
the desired contradiction.
ANSWER TO RIDDLE. The mathematical term named after a well-known American politician is "Algorithm." (Readers are invited to continue to submit more jokes for future columns.)
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.
Copyright 1999, Frank Morgan.