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Topic: As Math Grows More Complex, Will Computers Reign?
Replies: 4   Last Post: Mar 18, 2013 3:47 PM

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Posts: 139
Registered: 12/1/08
Re: As Math Grows More Complex, Will Computers Reign?
Posted: Mar 16, 2013 9:12 PM
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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

-- Mahipal, Maple... mua... me.

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