A Conversation with
Melanie Wood
Joseph A. Gallian
University of Minnesota Duluth
MATH HORIZONS
14 September 2004
Although just beginning her first year as a graduate student in
mathematics at Princeton, Melanie Wood has won numerous honors. As a
junior in high school, she tied for first place in the USA Mathematical
Olympiad. She was the first female to represent the United States in
the International Mathematics Olympiad (IMO), a worldwide math
competition for high school students. In both her junior and senior
year in high school, she received Silver medals at the IMO. In 2002,
Melanie received the Alice T. Schafer prize for excellence in
mathematics by an undergraduate woman given by the Association for
Women in Mathematics. In 2003, she was the first American woman, and
second woman overall, to win the Putnam competition—a prestigious math
competition for college students. In 2004, she was the first woman to
receive the Morgan Prize, sponsored by three math organizations, for
research by an undergraduate. The Prize committee called her work “deep
and original.”
MH: When did you first realize
that you had a special talent for mathematics?
MW: When I was in seventh
grade, a teacher invited me to be on the school’s MathCounts team, and
I went to the competition without any preparation or any idea what it
would be like. I was shocked to win first place in my city, then my
state, and then 40th in the nation. Bob Fischer, the coach of the
Indiana MathCounts team and a middle school teacher, sent me problems
throughout the following school year to help me prepare for the next
year’s competition—in which I placed 10th in the
nation.
MH: Tell me about your
participation in the American Mathematics Competition for high school
students.
MW: In 9th grade, I did well
enough on the USA Math Olympiad to be selected as one of 32 students
from the nation invited to train during the summer for the
International Math Olympiad (IMO), at a program referred to as “MOP”
(Mathematical Olympiad Program).
MH: Please explain what goes on
at MOP.
MW: At MOP, students go to
several hours of classes a day where they learn all sorts of
mathematics outside the normal high school curriculum such as number
theory, combinatorics, and geometry. They also take three-and-a-half
hour exams every other day, and free time is filled with contests and
homework. All of this intense training is to prepare six students for
the IMO and to prepare younger students for possible future
participation at the IMO.
MH: How many girls were at MOP
when you were there?
MW: My first two years at MOP I
was one of only two girls and the next two years I was the only girl at
the camp.
MH: Did it bother you being the
only girl?
MW: There are social and
emotional issues that you have to deal with when there are so few
females at a program like this. That means dealing with these issues
in additional to handling the high-pressure training and
competition. It’s not an ideal situation for learning mathematics.
MH: Besides developing your
math ability, meeting a lot of talented people, and representing the US
in the IMO, what other benefits did you get out of MOP?
MW: One very important thing
was for the first time I met a mathematical role model that I could
identify with, specifically, a woman. One of the instructors was
Zvezdeline Stankova who had won two Silver medals in the IMO
competitions as a member of the Bulgarian team and had a PhD in
mathematics from Harvard. Her enthusiasm for mathematics, her clear and
lively lectures, and her desire to assist young students develop their
talent were great influences on me.
MH: Perhaps it is no
coincidence that you have these same traits.
MW: Having a role model like
that was a big deal in my life. Previously, I never knew a
mathematician that I could look at and think “in ten years I want to be
like that person” and so it was hard to imagine becoming a
mathematician. But with Zvezda, I could think that I wanted to be like
her in ten years. I’ve ended up following some of the same paths. We
both were instructors at the MOP and we both participated in the Duluth
REU as students and later as visitors.
MH: You were profiled in the
June 2000 issue of Discover magazine in the article “The Girl Who Loved
Math.” It included some unusual photos of you. What was the idea behind
them?
MW: The magazine put the table
of contents over a full-page photo of me doing a headstand in front of
a blackboard— supposedly suggesting “trying a novel approach to a math
problem.” We went out to Duke forest in search of trees suggesting
certain mathematical patterns—one of those shots appeared in the
article also.
MH: It is my impression that
the Duke University mathematics department recruits math stars the same
way the Duke basketball coach recruits basketball stars. Why did you
choose Duke for your undergraduate education?
MW: In 1999, I received
generous offers from Harvard, Stanford, and Duke. I visited Harvard and
Duke multiple times trying to decide which place was best for me. I
ended up choosing Duke because the math department is dedicated to
undergraduate education and undergraduate research, and because I liked
the friendly, cooperative attitude of the university. My choice ended
up being very fortunate. While at Duke, I was able to take graduate
level math courses and also do original research.
MH:Your first research
experience came in the REU in Duluth.Give the readers a brief
explanation of what you did there.
MW: I was unable to get
inspired by the first problem I worked on, but I was lucky to get a
second problem that was just perfect for my interests! Afew years
before me at Duluth, Manjul Bhargava had generalized the notion of the
usual factorial function that arises in combinatorics and number
theory. For number theoretical questions that were answered in the
integers by the factorial function, this generalization provided
answers in other Dedekind rings, including some classical questions
about polynomials raised by George Polya more than 80 years earlier. I
was able to relate these generalized factorials to the geometric
structure of the ring induced from the p-adic metric. I used this
relationship to prove certain kinds of regular bases for integer valued
polynomials couldn’t exist in imaginary quadratic number fields.
MH: So, that lead to your first
publication.
MW: Yes, it was published in
the Journal of Number Theory.
MH: What other research
experiences have you had?
MW: Richard Hain, a professor
at Duke who I never had for a class, came up to me one day and said
that he had an idea that he thought would be a good topic for an
undergraduate to work on. In learning the background material for the
originally suggested problem, I came across some amazing mathematics
that was part of a program Grothendieck proposed for studying the
absolute Galois group. This led me off in a quite ambitious direction
of research that has been really intriguing for me, and even modestly
successful.
MH: It also helped you win the
Morgan Prize for research by an undergraduate.
MW: Yes, that and the number
theory paper. I was fortunate to have had two opportunities to do
research in areas that I enjoyed so much.
MH: I hear that your math
jersey has been retired by Duke. Tell me about that.
MW: My Duke math t-shirt hangs
framed in the math lounge at Duke. It means that no mathematical
competitor at Duke will ever be able to have my number on his or her
Duke math shirt in the future. I don’t imagine this will cause too much
trouble, because my number was the simple ‘2’ while many go for
irrational numbers.
MH: Any story about 2 as your
jersey number?
MW: I think of 2 as being the
simplest number that has any structure, yet already it can lead to rich
mathematics, including things like Z/2Z cohomology and the algebraic
closure of the field on two elements.
MH: Among all the awards that
you have received, which one are you most proud of?
MW: The Theater Studies
department at Duke chose me as their one nominee from my class for the
Faculty Scholar award at the university. I am most proud of this
because the work I did in theater stretched me more than anything else
I did in college.
MH: When did you become
interested in theater?
MW: I’ve always enjoyed
theater. At Duke, I was involved in many productions, including
assistant directing Macbeth and producing a musical. I am interested in
vocal work for acting and text-based Shakespeare.
MH: On occasion I have
expressed the opinion that Shakespeare and Leonardo da Vinci are
geniuses as great as Newton and Gauss. Have you given any thought to
this kind of question?
MW: I think people often
overlook the similarity between what it takes to be a mathematical
genius and what it takes to be an artistic genius. Neither can be
achieved by technical skill alone, yet certainly a great deal of
technical skill is required for both. Both require creativity and the
ability to think in ways that others haven’t been able to imagine.
MH: What other interests do you
have?
MW: I love to learn all sorts
of things, and while at Duke enjoyed taking classes on everything from
moral philosophy, to psycholinguistics, to dictionaries.
MH: You spent your 2003–2004
academic year at Cambridge University. How was that experience?
MW: I had a great time at
Cambridge. I did a course work program, and was able to take great
classes in number theory and in other areas. Their program is very
different from those in the US because there are no problem sets or
exams during the course; there are only exams in June that cover the
classes from the whole year. What I enjoyed most about the year is that
I just had lots of time to think about math.
MH: Many students with your
ability graduate early from high school or college. It seems that you
chose not to do this. Why?
MW: I’m in no rush to get
through my education, and often I don’t understand why others seem to
be. I was lucky to be able to find interesting and challenging things
to do for all of my high school and college years. For example, I
attended courses at Indiana University my senior year in high school. I
could have started my PhD last fall instead of spending a year in
Cambridge, but I feel that I understand more mathematics and at a
deeper level for taking this time—and that is what is most important to
me.
MH: What are your long range
plans?
MW: I hope to do a PhD thesis
in algebraic number theory and to obtain a job at a major research
university. I am interested in both research and teaching.
MH: I enjoyed our conversation.
I hope to interview you again in ten years.