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May 2001

What color is my hat? This is the crux of the hat problem,'' as presented to readers of the Science section of the New York Times on April 10, 2001. The article, dispatched from Berkeley by Sara Robinson, describes the puzzle as follows:

 Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.     No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical \$3 million prize if at least one player guesses correctly and no players guess incorrectly.     The same game can be played with any number of players. The general problem is to find a strategy for the group that maximizes its chances of winning the prize.''
There is a strategy, and the surprising thing is how well it works. In fact, when the number n of players is 1, 3, 7, 15, etc. (one less than a power of 2) the strategy promises a win n/(n+1) of the time. That strategy is given in terms of Hamming codes, a special class of error-correcting binary codes that sit at the intersection of electrical engineering and abstract algebra. Robinson interviewed Elwyn Berlekamp, the Berkeley math professor who worked out this strategy. She quotes him giving the following life lessons to be deduced from the problem: The first is that it's O.K. to be wrong as long as you contrive not to be wrong alone. The other, more important lesson is a need for teamwork that goes against the grain of most mathematicians. If the evidence suggests someone on your team knows more than you, you should keep your mouth shut. Most of us assume that each player's strategy is oriented toward him getting it right, and it's not. It's the whole team."

Schools'  New Math' = Trouble for City Kids. was the headline inside the April 17, 2001 New York Post. BIG FAT MINUS'' was the grabber on the cover. The story, by the Post's Education Reporter Carl Campanile, is about the NYC Board of Education's implementation of the NCTM guidelines, which are characterized thus: The so-called constructivist' programs minimize use of algorithms, long division and other basic math equations is favor of students working in groups and discovering' their own answers from reading passages.'' Campanile quotes mathematicians Fred Greenleaf (NYU): We're condemning an entire generation of students with fuzzy math'' and James Milgram (Stanford): Why should they use these programs in New York after what happened in California?'' Supporters of the program don't get much room. There is only Spud Bradley, an NSF program director, telling us that ... low-income kids ... have performed better than with traditional materials,'' and this important point is not expanded on. A suplementary article by Campanile (Bad news for children, good news for tutors'') tells how professional tutoring services are teaching the basics (familiar equations and algorithms'') to students frustrated with the  fuzzy' math.'' An opinion column by Rod Dreher rounds out the spread: Constructivist math is in part based on a bizarre theory that traditional arithmetic is biased towards white males.''

Fun with Fermat.

Chris Thompson as Daniel Keane and Jonathan Rabb as Fermat in Fermat's Last Tango.'' This photograph, courtesy of Carol Rosegg, may not be downloaded.

1. Fermat's Last Tango had a six-week run in New York last winter. For reviews (and additional picures) see CurtainUp and Theatre.com. The Clay Mathematics Institute taped the production and have a website documenting the operation.

2. The Fermat's Last Theorem Poetry Challenge was issued by Jeremy Teitelbaum at the BU lecture series in August 1995 presenting the completed proof. The results are on his website. Many nice poems in almost as many genres including the following piece, which has been described as possibly the worst limerick in the world,'' due to Hendrik Lenstra, David Moulton and Everett Howe, and reproduced here with their permission.

 "My butter, garçon, is writ large in!" a diner was heard to be chargin'. "I had to write there," exclaimed waiter Pierre, "I couldn't find room in the margarine."

Alan Alda, math wannabe. Science reporter K. C. Cole has a long and erudite piece about Alan Alda and the popularization of science (Alda Takes On an Ancient Role in Popularizing Science''), in the April 26, 2001, Los Angeles Times. The comedian has been involved of late with bringing science to a large TV audience through his programs for Scientific American Frontiers. His ambition is promoting understanding.'' How do you figure out what to believe," he asked Cole, and went on to explain that discerning the truth doesn't require that we all become scientists, but it does require that we base our beliefs about the world on investigation rather than faith. And learning how not to be fooled. This is the context in which he told Cole that he wished he'd learned more math, and that he has plans in that direction. "Maybe I could learn to do an equation!" Alan Alda is currently embodying the protagonist in QED, a play about Richard Feynman at the Mark Taper Forum in L. A.

Pulitzer for Proof. Felicity Barringer's April 17, 2001 New York Times story about the 2001 Pulitzer Prizes had a sidebar about the individual awards. The prize for drama went to Proof," David Auburn's surprise Broadway hit." Proof' focuses on the madness and death of a famous mathematician, his ardent student and his two daughters, one of whom may have inherited her father's genius, his illness, or both. Structured as a mystery about the authorship of a mathematical proof, it is really about more ethereal mysteries - the chemistry of love, the nature of genius." The Times obtained the following modest quote from Mr. Auburn: I never knew that this small play with mathematicians as characters and set on a back porch could attract so much attention."

Benjamin Peirce in The New Yorker. The April 23 & 30, 2001 issue of that magazine contains, embedded in Louis Menand's Dept. of Avarice" piece She Had to Have It," a colorful portrait of Benjamin Peirce, the Harvard professor who was the first internationally recognized mathematician the United States produced." The context is Pierce's 1867 appearance as a witness for the defense in the suit brought by Hetty Green (1835-1916) against her aunt's estate. Hetty had produced a second will, bearing her aunt's signature in two places, and leaving the aunt's considerable fortune almost entirely to Hetty. According to the estate, this document was a forgery; their evidence was that the two new signatures were absolutely indentical to the aunt's signature on her original, witnessed, will. Pierce and his son, the equally famous Charles Sanders Peirce, calculated that the likelihood of such a pair of sequences of coincidences was one in 530. In the end, the case was decided on a legal technicality (Hetty lost). But here is part of Menand's portrait of Benjamin Peirce.  ...he cultivated a certain wizardliness of manner. His hair was iron-gray; he wore it long with, in later years, a thick beard. And his obscurity was legendary. It was said at Harvard that you never realized how truly incapable you were of understanding a scientific matter until Professor Peirce had elucidated it for you."

"A Beautiful Mind"- the movie. The cast is assembled in Princeton, and filming has begun on the screen version of Sylvia Nasar's biography of John Nash. (The movie will now bear the same title as the book.) Jennifer Yachnin reports the goings-on in From Brawn to Brains" (Chronicle of Higher Education, April 6, 2001). As the title suggests, the piece is focussed on Russel Crowe, and the transition from his Oscar-winning dusty, sweaty gladiator to a mathematician blessed with unique intellectual power but crippled by mental disease. Apparently some Princeton undergraduates think Crowe too crude for the job. As Yachnin reports, `The actor didn't help his case any when he was caught on camera giving the finger to a junior who was trying to take his picture." But in fact Crowe's attitude seems completely appropriate to the contentious and prankish young genius portrayed by Nasar in the first half of her book.

-Tony Phillips
Stony Brook