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"Connections Through a Matrix": Review of Proofs and Confirmations: TheStory of the Alternating Sign Matrix Conjecture, by David M. Bressoud.Reviewed by Herbert S. Wilf. Science, 7 April 2000, page 61.

"Proofs and Confirmations is one of the most brilliant examples ofmathematical exposition that I have encountered," writes the reviewer. Thisbook tells the story of the Alternating Sign Matrix conjecture, a famous openproblem in an area of mathematics known as combinatorics. The first proof ofthe conjecture drew on the talents of scores of referees worldwide, each ofwhom had responsibility for one part of the proof. When a simpler proof wasfound in 1996, it drew on ideas from statistical mechanics. The reviewer notesthat the book "is not for the faint-hearted", nor is it one that "can be readin an easy chair, like a novel." But for those willing to take on thechallenge, the book offers "a panorama of combinatorics today".

--- Allyn Jackson

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