Last week one of my students looked at the teaching schedule on my door and said, “That’s cool that you have Wednesdays off!” It took my wife years to keep from referring to my “summer vacation.” A graduate professor of mine said that he would not have raced through graduate school in three years if he had known what being a professor was like; he wished he had stayed a student a little while longer. I was a student for 22 years — from kindergarten through Ph.D. I thought I knew what being a professor would be like. I didn’t.
Most mathematicians spend 6 to 15 hours each week (and only 9 months a year) in the classroom. What else do they do with their time? A lot. But the fact is that even Ph.D. students do not know what professors do until they become one. In his new book, The Survival of a Mathematician: From Tenure-Track to Emeritus, Steven Krantz writes about the many aspects of life as a mathematician. It is something of a sequel to his book A Mathematician's Survival Guide: Graduate School and Early Career Development.
Krantz’s book covers a lot of ground: teaching, advising, promotion, writing papers, writing textbooks, applying for grants, writing recommendations, interacting with students, colleagues, and the administration, being department chair, and leaving academia. In addition to a wealth of factual information it contains Krantz’s opinions, advice, observations, recommendations, suggestions, and anecdotes. Moreover it each section is self-contained, so you need not read it linearly.
He provides very useful advice for research mathematicians. It ranges from the very concrete and practical — what to include in a referee’s report — to the emotional — how to handle professional rejection (“Most mathematicians, indeed most academics, are quite fragile… If you can muster the tenacity to pick yourself up and fight on, then you will have a great advantage over most of your colleagues.”).
I found Krantz’s attitude toward service refreshing. He does not echo the common water-cooler sentiment that you should do a bad job on committees and service projects so that no one will ask you again. Rather, he speaks about the importance of service, whether it is to the department, the school, the community, or the profession. In particular, he includes a very useful chapter (75 pages) on being a department chair.
Krantz devotes a relatively small amount of the book (about 25 pages) to teaching and teaching-related issues. I know he has thought deeply about teaching, for he wrote an acclaimed book on this topic, How to Teach Mathematics. However, his love of teaching does not come through in this book; instead he reinforces the unfortunate stereotype that mathematicians are not good a teaching and do not enjoy it.
The three facets of our job are teaching, scholarship, and service. The amount of time a mathematician spends on each of these depends on the school and the stage of his or her career. Krantz’s aim was to write a book that applies to any mathematician, and for the most part he succeeds. However, often his observations and advice lean toward schools like his own — one with a graduate program and one in which research is the primary focus.
It is clear from this book and his others that Krantz loves his profession. He wants mathematicians to be happy in their jobs, to develop healthy environments in their departments, and to come together to create a vibrant community. Although this book may not be a perfect job description for your job, his observations and advice ring true and would be valuable to anyone in the early part of his or her mathematical career. In short, this would be a perfect graduation gift for a new Ph.D. mathematician, especially if bundled with How to Teach Mathematics.
Dave Richeson is an Associate Professor of Mathematics at Dickinson College. He is the author of Euler’s Gem: The Polyhedron Formula and the Birth of Topology.