2018年3月25日日曜日

In Search of God’s Perfect Proofs

In Search of God’s Perfect Proofs

aul Erdős, the famously eccentric, peripatetic and prolific 20th-century mathematician, was fond of the idea that God has a celestial volume containing the perfect proof of every mathematical theorem. “This one is from The Book,” he would declare when he wanted to bestow his highest praise on a beautiful proof.
Never mind that Erdős doubted God’s very existence. “You don’t have to believe in God, but you should believe in The Book,” Erdős explained to other mathematicians.
In 1994, during conversations with Erdős at the Oberwolfach Research Institute for Mathematics in Germany, the mathematician Martin Aigner came up with an idea: Why not actually try to make God’s Book — or at least an earthly shadow of it? Aigner enlisted fellow mathematician Günter Ziegler, and the two started collecting examples of exceptionally beautiful proofs, with enthusiastic contributions from Erdős himself. The resulting volume, Proofs From THE BOOK, was published in 1998, sadly too late for Erdős to see it — he had died about two years after the project commenced, at age 83.
“Many of the proofs trace directly back to him, or were initiated by his supreme insight in asking the right question or in making the right conjecture,” Aigner and Ziegler, who are now both professors at the Free University of Berlin, write in the preface.
The book, which has been called “a glimpse of mathematical heaven,” presents proofs of dozens of theorems from number theory, geometry, analysis, combinatorics and graph theory. Over the two decades since it first appeared, it has gone through five editions, each with new proofs added, and has been translated into 13 languages.
In January, Ziegler traveled to San Diego for the Joint Mathematics Meetings, where he received (on his and Aigner’s behalf) the 2018 Steele Prize for Mathematical Exposition. “The density of elegant ideas per page [in the book] is extraordinarily high,” the prize citation reads.
Quanta Magazine sat down with Ziegler at the meeting to discuss beautiful (and ugly) mathematics. The interview has been edited and condensed for clarity.

You’ve said that you and Martin Aigner have a similar sense of which proofs are worthy of inclusion in THE BOOK. What goes into your aesthetic?

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