This is a wonderful book, potentially of great value to students and those who advise them. It has some frustrating gaps too, but in a way they also emphasize how useful it is and could be. In brief, this book presents a collection of profiles of people who have (or had) a career that involves some aspect of mathematics. Nearly all the people here have at least one degree in mathematics; the few exceptions have degrees in field like physics, operations research, or a statistics-related area. Short essays at the end of the book discuss the processes of interviewing and finding a job, and what it’s like to work in industry (or, more broadly, outside the academic community).

There are 25 new entries in this new edition that bring the total number of profiles to 146. The “101 Careers” of the title is best regarded as meaning “lots of careers”; even the first edition had more than 101 profiles. Counting careers is also a little funny: they don’t match up one-to-one with people. As many of the profiles demonstrate, many people have more than one career. Indeed it is increasingly uncommon for people to have a single career throughout their lives.

There are several questions about the profiles that one might wish had been answered. Have any of the earlier entries been updated? How were people chosen to be included? The breadth of careers described here is considerable, but it is unlikely that the selection was random. For one thing, the proportion of profiles from high school or elementary school teachers is too small considering that other data (here, for example) suggest that these are the most likely occupations for those with mathematics degrees. Most likely the selection process aimed at breadth and variety. But it would be nice to know.

The first edition of this book was published in 1996, the second in 2002, and this update follows 14 years later. How have careers and career decisions changed since 1996? What’s been the effect of a couple of minor recessions and one big one? New kinds of careers in mathematics-related fields have developed in the last decade — in mathematical finance, data science, biotechnology. Jobs that involve “big data” are proliferating now. Can we extrapolate from the stories told here to guess how careers might develop in the next decade?

There is so much good data here that it is a temptation to wish that it had been assembled and analyzed more completely and methodically. But one of the great virtues of the book is that it is anecdotal. These are all individuals telling their stories about their lives and careers.

There are interesting and useful messages here for students. Some are explicit in the essays that conclude the book. Others are implicit in the profiles. Many of these point to the importance of flexibility and breadth of interests, or to the considerable value of well-developed communications skills and the willingness to learn to speak and understand the special technical languages of colleagues.

I can’t think of a better book for advisors to share with students. For anyone with any interest in mathematical careers, pick it up and browse. The sheer variety is fascinating.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.