WHY IS MATHEMATICS IMPORTANT?
In this note we excerpt some
of the highlights of Professor
Arnold's May 2003 commencement
address, titled "Doing
the Math and Making an Impact",
and given by him for the mathematics
and statistics graduation at
the University of Illinois in
Urbana-Champaign. Professor
Arnold is the Director of the
Institute for Mathematics and
its Applications which is associated
with our department. The full
text of this interesting and
inspiring talk is online at
http://www.ima.umn.edu/newsltrs/updates/summer03
Asking "What makes the
math sciences so central?",
he answers by quoting Galileo:
"The great book of nature
can be read only by those who
know the language in which it
was written. And that language
is mathematics.", adding
"Math is the way to understand
all sorts of things in the world
around us." To elaborate
on this point he gives some
well-chosen examples, beginning
with some insightful comments
on the Swiss victory in the
2003 America's Cup. "...you
know that Switzerland is a small,
mountainous, land-locked country.
So how did the Swiss pull this
upset off?" While acknowledging
that a number of diverse factors
had to come together, he makes
his point: " Well Switzerland
may not have a great sailing
tradition (at least until now!)
but it does have a very strong
tradition in mathematics--Euler's
picture appeared on a Swiss
10 franc note--and the Swiss
team wisely brought this strength
in math to bear on the America's
Cup challenge. They enlisted
a group of mathematicians specializing
in mathematical modeling and
numerical computation led by
Professor Alfio Quarteroni at
the national polytechnical university
in Lausanne. The mathematicians
used partial differential equations
to model the flow of the sea
around the hull, the dynamics
of the air and the sails, and
the turbulent interaction of
the ocean, wind, and boat. They
then applied advanced numerical
algorithms to solve these equations
on high performance computers.
This allowed them to optimize
such things as hull and keel
design, sail geometry and placement,
and so forth. Their work was
essential to the design of the
Alinghi, and so to the Swiss
victory. They did the math and
made a big impact." ("Alinghi"
was the name of the Swiss boat.)
On the increasing role of mathematics
in biological sciences he comments
as follows: "Increasingly
math is making an impact in
the life sciences as well, prompting
biologist Rita Colwell, director
of the National Science Foundation,
to observe that "mathematics
is biology's next microscope--only
better." In their recent
bio textbook Keener and Sneyd
wrote that "teaching physiology
without a mathematical description
of the underlying dynamical
processes is like teaching planetary
motion to physicists without
mentioning...Kepler's laws;"
He then mentions still other
areas of applications: "And
math increasingly reaches outside
the sciences, to economics,
sociology, and business for
example. ...Illinois's new Applied
Mathematics Program ...involves
no less than 22 departments
from bioengineering to linguistics.
...Problems which need mathematics
for their solution also arise
throughout industry."
To underline how seriously this
is taken worldwide, he cites
a strategic plan published by
the British government in 2003,
seeking to exploit mathematical
research to improve the competitiveness
of industry in the UK: ""Mathematics
is the most versatile of all
the sciences. It is uniquely
well placed to respond to the
demands of a rapidly changing
economic landscape...Mathematics
now has the opportunity more
than ever before to under-pin
quantitative understanding of
industrial strategy and processes
across all sectors of business.
Companies that take best advantage
of this opportunity will gain
a significant competitive advantage:
mathematics truly gives industry
the edge." He also notes
that British government policy
in dealing with the hoof-and-mouth
disease outbreak a few years
ago relied heavily on studies
based on mathematical epidemiology.
He states that a major current
challenge we face is how to
get the most out of all the
data that has been accumulated
thanks to the modern technology:
"For example, how can we
exploit the world-wide network
of seismic sensors to predict
earthquakes? How can we mine
the vast genomic databanks to
advance biology and medicine?
How can we sift through the
massive amounts of text, video,
web, and satellite data to detect
terrorist events before they
happen? Well, data means big
collections of numbers--remember
that text and images are digitized
and stored as numbers--and data
mining means discovering the
patterns and structures hidden
in those collections. That's
practically a definition of
mathematics: the study of structures
and patterns in large numerical
sets. So you can be sure that
in the 21st century--the century
of data--math will again have
a huge impact."
In conclusion he exhorts the
graduates to cultivate and apply
logical, mathematical and quantitative
thinking even if they do not
become research mathematicians.
The full text of this interesting
and inspiring talk is online
at http://www.ima.umn.edu/newsltrs/updates/summer03
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