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Topic: How to Fall in Love With Math
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Jerry P. Becker

Posts: 13,034
Registered: 12/3/04
How to Fall in Love With Math
Posted: Sep 19, 2013 5:20 PM
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From The New York Times, Sunday, September 15, 2013. See
http://www.nytimes.com/2013/09/16/opinion/how-to-fall-in-love-with-math.html?_r=1&
. Our thanks to several recipients for bringing this piece to our
attention.
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How to Fall in Love With Math

By Manil Suri

BALTIMORE - EACH time I hear someone say, "Do the math," I grit my
teeth. Invariably a reference to something mundane like addition or
multiplication, the phrase reinforces how little awareness there is
about the breadth and scope of the subject, how so many people
identify mathematics with just one element: arithmetic. Imagine, if
you will, using, "Do the lit" as an exhortation to spell correctly.

As a mathematician, I can attest that my field is really about ideas
above anything else. Ideas that inform our existence, that permeate
our universe and beyond, that can surprise and enthrall. Perhaps the
most intriguing of these is the way infinity is harnessed to deal
with the finite, in everything from fractals to calculus. Just
reflect on the infinite range of decimal numbers - a wonder product
offered by mathematics to satisfy any measurement need, down to an
arbitrary number of digits.

Despite what most people suppose, many profound mathematical ideas
don't require advanced skills to appreciate. One can develop a fairly
good understanding of the power and elegance of calculus say, without
actually being able to use it to solve scientific or engineering
problems.

Think of it this way: you can appreciate art without acquiring the
ability to paint, or enjoy a symphony without being able to read
music. Math also deserves to be enjoyed for its own sake, without
being constantly subjected to the question, "When will I use this?"

Sadly, few avenues exist in our society to expose us to mathematical
beauty. In schools, as I've heard several teachers lament, the
opportunity to immerse students in interesting mathematical ideas is
usually jettisoned to make more time for testing and arithmetic
drills. The subject rarely appears in the news media or the cultural
arena. Often, when math shows up in a novel or a movie, I am reminded
of Chekhov's proverbial gun: make sure the mathematician goes crazy
if you put one in. Hanging thickly over everything is the gloom of
math anxiety.

And yet, I keep encountering people who want to learn more about
mathematics. Not only those who enjoyed it in school and have had no
opportunity to pursue it once they began their careers, but also many
who performed poorly in school and view it as a lingering challenge.
As the Stanford mathematician Keith Devlin argues in his book "The
Math Gene," human beings are wired for mathematics. At some level,
perhaps we all crave it.

So what math ideas can be appreciated without calculation or
formulas? One candidate that I've found intrigues people is the
origin of numbers. Think of it as a magic trick: harnessing emptiness
to create the number zero, then demonstrating how from any whole
number, one can create its successor. One from zero, two from one,
three from two - a chain reaction of numbers erupting into existence.
I still remember when I first experienced this Big Bang of numbers.
The walls of my Bombay classroom seemed to blow away, as nascent
cardinals streaked through space. Creatio ex nihilo, as compelling as
any offered by physics or religion.

For a more contemplative example, gaze at a sequence of regular
polygons: a hexagon, an octagon, a decagon and so on. I can almost
imagine a yoga instructor asking a class to meditate on what would
happen if the number of sides kept increasing indefinitely.
Eventually, the sides shrink so much that the kinks start flattening
out and the perimeter begins to appear curved. And then you see it:
what will emerge is a circle, while at the same time the polygon can
never actually become one. The realization is exhilarating - it
lights up pleasure centers in your brain. This underlying concept of
a limit is one upon which all of calculus is built.

The more deeply you engage with such ideas, the more rewarding the
experience is. For instance, enjoying the eye candy of fractal images
- those black, amoebalike splotches surrounded by bands of
psychedelic colors - hardly qualifies as making a math connection.
But suppose you knew that such an image (for example, the Julia Set)
depicts a mathematical rule that plucks every point from its spot in
the plane and moves it to another location. Imagine this rule applied
over and over again, so that every point hops from location to
location. Then the "amoeba" comprises those well-behaved points that
remain hopping around within this black region, while the colored
points are more adventurous and all lope off toward infinity. Not
only does the picture acquire more richness and meaning with this
knowledge, it suddenly churns with drama, with activity.

Would you be intrigued enough to find out more - for instance, what
the different shades of color signified? Would the Big Bang example
make you wonder where negative numbers came from, or fractions or
irrationals? Could the thrill of recognizing the circle as a limit of
polygons lure you into visualizing the sphere as a stack of its
circular cross sections, as Archimedes did over 2,000 years ago to
calculate its volume?

If the answer is yes, then math appreciation may provide more than
just casual enjoyment: it could also help change negative attitudes
toward the subject that are passed on from generation to generation.
Students have a better chance of succeeding in a subject perceived as
playful and stimulating, rather than one with a disastrous P.R. image.

Fortunately, today's online world, with its advances in video and
animation, offers several underused opportunities for the informal
dissemination of mathematical ideas. Perhaps the most essential
message to get across is that with math you can reach not just for
the sky or the stars or the edges of the universe, but for timeless
constellations of ideas that lie beyond.
-----------------------------------
Manil Suri is a mathematics professor at the University of Maryland,
Baltimore County, and the author, most recently, of the novel "The
City of Devi."
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--
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244
E-mail: jbecker@siu.edu



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