Issue
27(1)
Letters
to a young Mathematician. (2006). Ian
Stewart. New York: Basic Books (Perseus Books Group). 210pp.,
$22.95, (paperback), ISBN # 0-465-08231-5.
Review
by: Marie Dillon
Dahleh
Assistant Dean of Academic
Programs
Harvard
University
As
the title suggests this book is written as a series of letters
from a distinguished British mathematician to a young woman, Meg,
who is interested in mathematics. The book opens with Meg in middle
school and ends as she obtains a permanent faculty position. The
book is a collection of response letters arranged in chronological
order.
For
a student considering Mathematics as a career, this is an insightful
and easy read. It addresses many of the concerns held by those
contemplating an academic mathematics career from how to make
a living doing mathematics to how to create new mathematics. The
book is written in an informal style which suggests that the author
of the letters has served as one of Meg's mentors over the many
years spanned by the letters span and that there has been contact
in addition to the letters. He starts the last letter by saying
"It was very good to see you in San
Diego last month. I'm ashamed
to say I'd rather lost touch with your parents." (p. 35). Sprinkled
throughout the letters are interesting references to other books
about mathematics that could comprise a suggested readings list.
For instance in the chapter on the creation of new mathematics,
he suggests that Meg read To Talk of Many Things , the
autobiography of Dame Kathleen Ollerenshaw.
This
book is very specialized and therefore its use it somewhat limited
to those who advise students pursuing mathematics either as an
undergraduate or for a graduate degree. The first four chapters
are devoted to the study of mathematics prior to the university.
This section is of general interest since it largely concentrates
on what is mathematics and why it is worth studying. In the first
chapter, Stewart offers a compelling argument as to why one should
want to study mathematics, "It (math) makes me aware of the world
I inhabit in an entirely new way. It opens my eyes to nature's
laws and patterns. It offers an entirely new experience of beauty."
(p. 7). Chapters five through ten concentrate on the mathematics
experience at the University. In this section the author concentrates
on learning mathematics and in particular the importance of the
proof in mathematics. One does not have to major in mathematics
to benefit from this section although one does need to be exposed
to courses which use formal proofs. Chapters 11-17 are devoted
to the Ph.D. years. Information in this section is relevant for
all students pursuing a Ph.D. not just the ones working in mathematics.
For instance Stewart talks about how to choose a problem and also
an advisor. Although the examples he uses are based in mathematics,
the general principles are the same for many fields. "I don't
advise being that ambitious when you are working on a Ph.D.! Big
problems, like big mountains, are dangerous" (p. 95). The book
finishes with the post doctoral years, the assistant professor
and finally the permanent position.
This
book is well worth reading for those considering a career in mathematics
or for those who advise students pursuing this route. Many of
the student concerns are addressed through the different, yet
easily read, letters. The main weakness of the book is that it
is very specialized to one field, mathematics, and to a lesser
extent it focuses on the British system of education which may
make it irrelevant for those outside the U.K.
