On Mar 16, 8:14 pm, use...@mantra.com and/or www.mantra.com/jai (Dr. Jai Maharaj) wrote: > As Math Grows More Complex, Will Computers Reign?
Where's the evidence, the mathematical proof, that math has grown more complex in the past decade? Show me the proof.
> 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, Ekhad?s earliest incarnation. > > ?The soul is the software,? said Zeilberger, who writes > his own code using a popular math programming tool called > Maple.
I like the pyramid of tennis balls. Nice touch that, to the soul.
> 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. > > Continues at: > > http://www.wired.com/wiredscience/2013/03/computers-and-math/all/ > > Jai Maharaj, Jyotishi > Om Shanti > > http://groups.google.com/group/alt.fan.jai-maharaj