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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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Dr. Jai Maharaj

Posts: 276
Registered: 1/30/06
As Math Grows More Complex, Will Computers Reign?
Posted: Mar 16, 2013 8:14 PM
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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 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.

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



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