image: David Bailey (top left), Jonathan Borwein (top right), Andrew Mattingly (bottom left), and Glenn Wightwick (bottom right) are the winners of the 2017 AMS Conant Prize. view more
Credit: Top left: Bailey, Lawrence Berkeley National Lab; top right: Borwein, Australian Academy of Science; bottom left: Mattingly, CJ Butler, IBM Research-Australia; and lower right: Wightwick, Joanne Saad.
David Bailey, Jonathan Borwein, Andrew Mattingly, and Glenn Wightwick will receive the 2017 AMS Levi L. Conant Prize. The four co-authors are honored for their article "The Computation of Previously Inaccessible Digits of Π2 and Catalan's Constant," Notices of the AMS, August 2013.
"This fascinating article will delight any mathematician who has ever been intrigued by the mysteries of the digits of Π," the prize citation says.
The number Π, known to the ancients, is familiar from many contexts, including its role in the formulas for the circumference and area of a circle. Catalan's constant, named after the mathematician Eugène Charles Catalan (1814-1894), is of a more recent vintage. This mysterious number crops up in various problems in mathematics, but it is not known whether it is transcendental, as is Π---or even whether it is irrational.
The article opens with a historical journey, from Archimedes to the computer age, with many interesting anecdotes along the way. It then goes on to discuss the remarkable "BBP" formula, discovered by Bailey together with Peter Borwein and Simon Plouffe. The formula allows one to calculate binary or hexadecimal digits of Π beginning with the nth digit without first calculating any of the preceding n - 1 digits. The article leads readers through not only an elementary proof of the BBP formula but also the unconventional search that originally led to this formula as well as similar formulas for Catalan's constant and Π2.
The article also provides intriguing insights into the age-old question of whether the digits of Π are truly randomly distributed.
Certainly the task of computing digits of Π has a practical side: running paired computations of Π provides a strenuous integrity test of computer hardware and software. But, as this outstanding article makes clear, it is the fundamental properties and deep mystery of Π that have made it so powerfully fascinating for so long.
David H. Bailey is a retired senior scientist at the Lawrence Berkeley National Laboratory, and a research associate at the University of California, Davis. Andrew Mattingly is senior information technology architect at IBM Australia. Glenn Wightwick is deputy vice-chancellor and vice-president (Research) at the University of Technology Sydney.
The prize will be awarded posthumously to Jonathan Borwein, who died in August 2016, before learning that he and his co-authors would receive the prize. Borwein was professor of mathematics at the Centre for Computer Assisted Research Mathematics and its Applications at the University of Newcastle. "Borwein's creative work and beautiful expositions will be sorely missed," the prize citation says.
Presented annually, the AMS Conant Prize recognizes the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years. The prize will be awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta.
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Find out more about AMS prizes and awards at http://www.ams.org/profession/prizes-awards/prizes.
Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.