Letters to a Young Mathematician

Book by Ian Stewart
Review by Marie Dillon Dahleh
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.

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Letters to a young Mathematician. (2006). Book by Ian Stewart. Review by Marie Dillon Dahleh. New York: Basic Books. 210pp., $22.95, (paperback), ISBN: # 0-465-08231-5