Michel Couillard's career is a great illustration of the diverse opportunities
that are open to mathematicians. He has worked in Afghanistan to support soldiers.
And he even went to the middle of the Pacific Ocean to hunt submarines!
Couillard is a defense scientist with a PhD in applied mathematics. His
PhD research focus was finding underwater mines using automated robots. Now
he works for the NATO Centre for Maritime Research and Experimentation in
Italy.
"I am part of a team creating a system using automated robots to find and
neutralize underwater mines," says Couillard. "This means that sailors do
not have to risk their lives to find those mines. I use math to tell the robots
what to do, where to go, and how to do it in the best way possible."
Couillard's interest in math began at an early age.
"I liked math since I was a kid," he says. "First, I liked solving mathematical
puzzles. Then, as I grew older, I realized that math was a language in itself,
a language that could explain how the world works. I thought this was fascinating."
Couillard says there are certain personal qualities that are important
for mathematicians to have.
"I think it helps to be flexible, to be able to work on different problems,
to not be afraid of taking chances and working on new things," says Couillard.
"It is important to have perseverance -- sometimes problems are hard to solve
but you cannot give up. It is also important to be creative and think of new
ways to do things, as well as being able to work on teams."
Matt Davison agrees that mathematicians need to work well with others.
He's a professor of applied mathematics.
"You need to be flexible in your thinking and able to communicate, and
none of those things fit the standard stereotype of the crazy genius professor
sitting in a room filled with scraps of paper [who] hasn't had a haircut in
15 years and hasn't had a shower in three months...." says Davison.
"It's not like that. You need to be able to talk to people, you need to
be able to communicate with people and find out what they care about and what
they're interested in, and so there's a whole social component to it that
doesn't fit the stereotype." At first, Davison thought he'd become an engineer.
He got his first degree in engineering.
"When I was an engineering student I became really impressed by how many
completely different problems could get solved with exactly the same mathematics,"
says Davison.
"...I got fascinated by the power of mathematics to actually solve real-life
problems. And it seemed sort of like magic to me, that you could solve problems
in all these different areas using these techniques, and I really wanted to
be part of that -- that was worth putting in the time."
Davison now does a lot of work on the pricing and hedging financial contracts
in financial markets. He has a patent on recognizing patterns in large data
sets. Having knowledge in this area allows him to do some consulting in addition
to his university work. There were signs from a young age that Davison might
become a mathematician.
"I really liked doing math problems," says Davison. "Obviously, there were
difficult times and not every bit was enjoyable, but it was the kind of activity
I really liked. It wasn't really as much of a sacrifice as it might seem to
someone who isn't interested. So I think maybe interest is the key thing...
as well as talent."
Jill Pipher certainly had that mathematical interest at a young age. She's
the president of the Association for Women in Mathematics and a professor
of mathematics at Brown University.
"I was interested in mathematics, or at least in logical puzzles and mathematical
games, early on," says Pipher. "In junior high, I took (and finished early)
an experimental, individually paced, accelerated class in algebra, but I don't
recall being encouraged to go on to the next step in this program.
"In any case, I wasn't on a 'math track' before I started college," says
Pipher. "When I started college, I was interested in music, and also interested
in exploring many different subjects. I took a course in logic and set theory
out of curiosity alone, and found a passion for mathematical ideas that transformed
my undergraduate experience."
What was it about math that appealed so much to her?
"The sheer beauty of the ideas," says Pipher. "Concepts like cardinality,
and continuity, and the surprising realization that there were mathematical
mysteries -- apparently simple questions about integers, for example, which
had no answer...." There's no mystery to how to become a successful mathematician,
says Pipher. "Becoming a mathematician requires many of the same qualities
that lead to success in other professions -- curiosity, determination, a strong
work ethic, and communication and expository skills," she says.
Uncertainty is one challenging aspect of the career. The job of a mathematician
is never really done.
"Thinking about a mathematical (or any scientific) problem can take up
all the space you give to it... including evenings and weekends," says Pipher.
"So one has to have a certain amount of discipline and efficiency to deal
with the work/life balance issues."
Uncertainty and risk are present in all careers to some extent. For mathematicians,
taking leaps is how they get ahead with their theories, as well as their careers.
"Take chances," advises Couillard. "Do not be afraid of taking risks because
that's how you can have an exciting mathematical career. It is also good to
get involved in the mathematical community, for example in math student associations.
This is a great way to meet people with the same interests and discover different
areas where you might decide to work."