[Fwd: du Sautoy]

[jim stasheff <jds@math.upenn.edu>]

with or without proofs?
a worthwhile activity

-------- Original Message --------
Subject: du Sautoy
Date: Sat, 15 Apr 2006 14:49:02 -0400 (EDT)
From: Peter Freyd <pjf@saul.cis.upenn.edu>
To: MathPeople@saul.cis.upenn.edu

   Most people's idea of what I do as a research mathematician is long
division
   to lots of decimal places. But fundamentally, mathematics isn't about
numbers
   - it's about finding structure and logic and connections that help us
   negotiate the complex world we live in.

                      Copyright 2006 TSL Education Limited
                      The Times Higher Education Supplement

                                  April 14, 2006

SECTION: OPINION; No.1738; Pg.14

LENGTH: 831 words

HEADLINE: Scales Fall Short Of Grand Symphonies In Maths

BYLINE: Marcus du Sautoy

BODY:

Pique children's interest in maths with elegant epics, enigmatic mysteries
and cold hard cash, says Marcus du Sautoy.

World pi Day was marked at 1:59 on March 14 - 3.14159 being the beginning
of the decimal expansion of pi. Although I am appreciative of any
publicity mathematics can get, I found that most people were interested in
how many decimal places I knew of this important number. They were
disappointed that five was my limit. To me, that response revealed the
deep misconception people have of what mathematics is really about.

Most people's idea of what I do as a research mathematician is long
division to lots of decimal places. But fundamentally, mathematics isn't
about numbers - it's about finding structure and logic and connections
that help us negotiate the complex world we live in.

The belief that mathematics is no more than long division is fuelled by
the way most pupils are taught the subject at school. Imagine a student
learning a musical instrument by playing only scales and arpeggios and
never even hearing a symphony. No one would judge them for giving up. Yet
all too often in pupils' mathematical education, this is all they are
exposed to.

Pupils I talk to are surprised to learn that there are complex
mathematical equations controlling the evolution of their PlayStation
games or that the sine waves that they learn about in trigonometry are the
building blocks used by their MP3 players to recreate the sound of the
Arctic Monkeys in their headphones.

Practical applications are a powerful way to awaken people to the
importance of the subject. But beauty and elegance can also attract many
to the subject. It is the great stories of mathematics, many of them
unfinished, that I believe have the potential to capture pupils'
imaginations when they doubt the value of mathematics. Therefore, it is
the responsibility of those who create these stories, the research
mathematicians, to bring the subject alive. There is no escaping the hard
graft of doing your arithmetic scales and arpeggios.  But if these are set
in the context of the big mathematical symphonies they help write,
students may feel more inclined to apply themselves.

The story of the primes is one of the sagas that I have found can pull
young people on to the mathematical bandwagon. They are the building
blocks of all numbers. And as you play with them, they very soon draw you
into one of our biggest mathematical mystery stories.

The great challenge is to understand how nature chose these enigmatic
numbers. The search for a pattern behind the primes goes to the heart of
what it means for me to be a mathematician. Yet intriguingly, our subject
seems to be built out of numbers with no patterns to them at all.

The biggest prime we know has more than 9 million digits - a number that
would take more than a month and a half to read aloud. But bigger primes
will always be discovered - there is a prize of $100,000 (Pounds 57,000)
waiting for the first person to break the 10 million digit mark. The
records to date are not held by boffins with big computers but amateurs
with desktops.

Money is a great incentive for getting kids' eyes to light up. And one can
use it to introduce the deeper meaning behind the headline. Once they have
won $100,000, then they can move on to the million-dollar prize of finding
the underlying structure that makes these numbers tick, which involves
solving the Riemann hypothesis.

The National Centre for Excellence in Teaching Mathematics, to be launched
in May, has the potential to communicate some of the big stories of
mathematics to teachers who can, in turn, spread the word in our schools
and colleges.  But it is important for those at universities to play their
part in keeping alive the narrative tradition. In our conferences and
journals, we are all engaged in telling the tales of our mathematical
adventures. If we want more young explorers to join us on the hard treks
across the mathematical mountains, then research mathematicians have a
part to play in telling those outside the ivory towers our best stories.

Scientific research consists of two important components: discovery and
communication. Without one, the other will die. Oswald Veblen, in his
opening address to the International Congress of Mathematicians in 1952,
expressed well this need to perform our theorems: "Mathematics is terribly
individual. Any mathematical act, whether of creation or apprehension,
takes place in the deepest recesses of the individual mind. Mathematical
thoughts must nevertheless be communicated to other individuals and
assimilated into the body of general knowledge. Otherwise they can hardly
be said to exist."

   Marcus du Sautoy is professor of mathematics at Oxford University and author
   of The Music of the Primes, published by Harper Perennial, Pounds 8.99. This
   article is based on his inaugural Drapers lecture on teaching and learning at
   Queen Mary, University of London.