From the Director
Doing the Math and Making an Impact

Doug Arnold, 
IMA Director 
On May 18 I had the pleasure of delivering a commencement address
for the math and stat graduation at the University of Illinois
in UrbanaChampaign. I thought that the address might be of interest
to some of Update readers, and so I present it here.
Wow! You did it! You really did it! With lots of hard work and
concentrated effort, innumerable small advances and setbacks,
invaluable support from Mom and Dad, undoubtedly a few memorable breaks
to recharge batteries, andoh yessome pretty darn good classes and
professors...you have earned that degree. And not only have you
earned a degree of higher learning from a first rate research
university, you have gotten a degree in math or statistics, the math
sciences, among the most centraland toughestfields there are.
Congratulations!
What makes the math sciences so central? As Galileo put it, "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." Math is the way to
understand all sorts of things in the world around us. But only about
1 in 100 undergraduate degrees in this country is given in math and
statistics and only a small portion of the population has any facility
with that mathematical language Galileo spoke about. So you're a
valuable commodity!
So what are you going to do now with all that math? What can you do?
Well I was invited here to deliver some advice, so let me make some
suggestions. How about competitive sailing?...Not sure what math
has to do with winning a sailboat race? Well, a couple of months ago,
Team New Zealand, the defenders of the America's Cup, were trounced by
the Swiss team sailing a boat called the Alinghi. The Swiss team won
the bestofnine series five to zip, after having beaten their way
through the previous rounds in similar style. This was no small
upsetit marked the first time in the 150 year history of the race
that it was won by a European team. Now you studied math, not
geography, but you know that Switzerland is a small, mountainous,
landlocked country. So how did the Swiss pull this upset off? Well
Switzerland may not have a great sailing tradition (at least until
now!) but it does have a very strong tradition in mathematicsEuler's
picture appeared on a Swiss 10 franc noteand 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.
Now I'm not claiming that the mathematicians alone were responsible for
winning the America's Cupcertainly not. Other scientists and
engineers made important contributions, for example, material
scientists who developed the composites used in the hull. And of
course there was the Alinghi sailing team which brought together sailors
from a dozen countries under the brilliant Kiwi skipper Russel Coutts.
Not to mention the generous financing of Swiss bankers. But the
Alinghi example illustrates my main point here today: math and
mathematicians make crucial contributions to all sorts of challenging
problems. Math makes an impact. And youbeing mathematically
trainedoh the places you can go and the things you can do!
By the way, you may wonder what that Lausanne math modeling group does
when it is not helping to win the America's Cup? Their primary
research concerns the simulation of another sort of fluid flowthe
flow of blood through the human circulatory system. Just as they
achieved great results optimizing the Alinghi, they use mathematical
modeling and numerical computation, in collaboration with doctors, to
design surgical stents and other devices and to optimize a variety of
medical interventions. If I had a difficult cardiac condition, I
wouldn't want my mathematician friend Alfio Quarteroni operating on me.
But I would sure feel better knowing that his kind of mathematical
simulation had been fully utilized in the planning.
If you poke around a large research university like this one, you will
see math popping up all over the place. There are long established
linkages between math and the physical sciences, as in fluid dynamics
example just presented. 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 microscopeonly 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; you can observe that there is a full moon every 28 days,
but...you cannot determine when the next...eclipse will be."
And math increasingly reaches outside the sciences, to economics,
sociology, and business for example. Yesterday I attended a workshop
here for Illinois's new Applied Mathematics Program. It involves no
less than 22 departments from bioengineering to linguistics. Clearly
researchers all over this campus understand that math makes an impact.
And it is not only in academics and research where math plays a central
role. Problems which need mathematics for their solution also arise
throughout industry. A quarter of US math doctorates and many more
math bachelors go to work in industry. And a quarter of the thousand or so
scientists who come by my research institute each year, the Institute
for Mathematics and its Applications, come from industry. Why? I
can't put it any better than was done in a strategic plan published
last year by the British government, seeking to exploit research to
improve the competitiveness of industry in the UK. The report stated:
"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 underpin 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." And it is not
only industry, but government as well. I can stay in Britain for a
recent example of the impact of mathematics on government policy and
its outcomes. In dealing with the hoofandmouth disease outbreak a
few years ago, British decision makers relied heavily on studies based
on mathematical epidemiology. This led them to the controversial
decision to aggressively cull herds, which successfully contained the
outbreak.
In the 1967 film The Graduate a family friend approaches the new
graduate played by Dustin Hoffman and declares, "I just want to say
one word to youjust one word'plastics.'" Well I hope that my
advice will be a bit more useful, but if I were forced to limit my
advice to just one wordand "math" was not allowedthe word would
be "data." Thanks to the Internet, to increasingly powerful and
ubiquitous sensors, and to new storage technologies, many scientific
fields and many companies and organizations have been able to build up
huge stores of relevant data. We are awash in torrents of data, with
terabytes more flooding in every day. The grand challenge we face at
the beginning of this century is how to get the most out of all that
data. For example, how can we exploit the worldwide 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 numbersremember that text and images are digitized
and stored as numbersand 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
centurythe century of datamath will again have a huge impact.
As a small example of thinking mathematically about data, consider the
outcome of a blood test. That's a data point described by 10 or 20
numbers, cholesterol 188, triglycerides 376, HDL 32, and so forth. So,
mathematically speaking, a blood test describes a point in 20
dimensional space. Now my doctor tends to get worried if one of those
numbers falls out of an expected range or starts to change. He thinks
in terms of a collection of intervals. But blood is a complicated
system of interacting chemical components and biological structures,
and the collection of acceptable values almost surely form a complex
region which reflects the equations relating the various consituents.
A complicated geometrical region in 20 dimensional space, not just a
collections of intervals. Now you've studied multivariate calculus and
so you have some experience with surfaces described by equations in
space. You know for example, that there are directions normal to a
surface and directions tangential to it and that if a point in the
surface moves in a normal direction then it will leave the surface much
more quickly than if it moves tangentially. That's the kind of
understanding that can make a big impactin the future it may help to
design a wearable sensor system, for example, which will warn us when
our blood chemistry is getting out of whack or help us decide what to
eat.
In concluding I want to emphasize that you don't have to become a
professional mathematician or researcher to make an impact with the
math you have learned. Wherever you go, whatever you do, you will
surely be confronting problems. With math you learn to be a better
problem solver. You learn to think logically, to reduce complicated
situations to their essentials, to emphasize the relations between
things over nonessential details of the things themselves, to abstract,
to generalize. Cultivate this kind of thinking in yourself. Apply it
whenever you can. Continue to develop it. Seek out important problems
and think mathematically about them. Just because the people around
you do not approach a problem logically, quantitatively, or
mathematicallyand most probably won'tshould not stop you from
doing so. To the contrary, as the mathematician in a team you bring
something special. So my advice to you is simply:
do the math and make
an impact!