By Natalie Wolchover, Simons Science News Wired.com March 4, 2013
This simple computation, written with math software called Maple, verifies a formula for the number of integer triangles with a given perimeter. (Illustration: Simons Science News)
Shalosh B. Ekhad, the co-author of several papers in respected mathematics journals, has been known to prove with a single, succinct utterance theorems and identities that previously required pages of mathematical reasoning. Last year, when asked to evaluate a formula for the number of integer triangles with a given perimeter, Ekhad performed 37 calculations in less than a second and delivered the verdict: True.
Original story reprinted with permission from Simons Science News, an editorially independent division of SimonsFoundation.org whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
Shalosh B. Ekhad is a computer. Or, rather, it is any of a rotating cast of computers used by the mathematician Doron Zeilberger, from the Dell in his New Jersey office to a supercomputer whose services he occasionally enlists in Austria. The name Hebrew for three B one refers to the AT&T 3B1, Ekhads earliest incarnation.
The soul is the software, said Zeilberger, who writes his own code using a popular math programming tool called Maple.
A mustachioed, 62-year-old professor at Rutgers University, Zeilberger anchors one end of a spectrum of opinions about the role of computers in mathematics. He has been listing Ekhad as a co-author on papers since the late 1980s to make a statement that computers should get credit where credit is due. For decades, he has railed against human-centric bigotry by mathematicians: a preference for pencil-and-paper proofs that Zeilberger claims has stymied progress in the field. For good reason, he said. People feel they will be out of business.
Anyone who relies on calculators or spreadsheets might be surprised to learn that mathematicians have not universally embraced computers. To many in the field, programming a machine to prove a triangle identity or to solve problems that have yet to be cracked by hand moves the goalposts of a beloved 3,000-year-old game. Deducing new truths about the mathematical universe has almost always required intuition, creativity and strokes of genius, not plugging-and-chugging. In fact, the need to avoid nasty calculations (for lack of a computer) has often driven discovery, leading mathematicians to find elegant symbolic techniques like calculus. To some, the process of unearthing the unexpected, winding paths of proofs, and discovering new mathematical objects along the way, is not a means to an end that a computer can replace, but the end itself.