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Re: As Math Grows More Complex, Will Computers Reign?
Posted:
Mar 18, 2013 3:47 PM


Dr. Jai Maharaj posted: > > As Math Grows More Complex, Will Computers Reign? > > 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 coauthor 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, 62yearold 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 coauthor 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 humancentric bigotry by mathematicians: a > preference for pencilandpaper 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 3,000yearold game. > Deducing new truths about the mathematical universe has > almost always required intuition, creativity and strokes > of genius, not pluggingandchugging. 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. > > Continues at: > http://www.wired.com/wiredscience/2013/03/computersandmath/all/
Forwarded post:
This headline is like saying, "as people learn how to make tools, will hammers and screwdrivers reign over humans?"
 Platos Cave
End of forwarded post.
Jai Maharaj, Jyotishi Om Shanti
http://groups.google.com/group/alt.fan.jaimaharaj



