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Saunders Mac Lane: A Mathematical Autobiography

Saunders Mac Lane
A K Peters
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Shell-Gellasch
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Since Saunders Mac Lane’s death in April 2005, there have been several memorial pieces written giving personal accounts of experiences with Mac Lane and this review is no exception. Saunders Mac Lane was my mathematical Grandfather. Though my area of research is worlds apart from his, I was lucky enough to work with him briefly on my doctoral dissertation. Saunders is the father of category theory with an early and lasting interest in logic; my thesis advisor was a student of Saunders’ in logic with an interest in history; I am a historian of mathematics and the subject of my thesis topic, mathematician Mina Rees, went to graduate school at the University of Chicago with Saunders Mac Lane.

During my research into the life and work on Mina Rees (1903-1997) I found references to Saunders Mac Lane in her writings. Since he and my advisor Bill Howard were still in close contact, Bill suggested I contact “Uncle Saunders” for an interview. On the appointed day, I made the short drive from the University of Illinois at Chicago to the University of Chicago with my questions and research in hand. Within moments of starting my interview, Mac Lane turned the tables on me by asking questions about my research, testing my knowledge, and in general making me feel nervous and unprepared.

Upon my return to UIC, Bill said not to worry. Over the course of the writing of my thesis I sent portions to Saunders for comment.

At the 2001 Joint Mathematics Meetings in New Orleans , I was asked to give an invited talk on Rees. This was a big deal for me, having only received my degree the previous spring, and I was nervous. When I found “Uncle Saunders” right in the middle of the front row, memories of our interview a few years earlier came flooding back. At the finish of my talk (which I am happy to say went well), Saunders stood up and shared a few personal memories about Mina Rees. I was honored that he added such a person touch to my talk (and relieved that he didn’t start asking questions about my presentation!)

Knowing something of Mac Lane’s personality and reputation first hand, I was anxious to read his autobiography when I first heard about it’s publication in early 2005. I am glad to say that it did not disappoint. It contains all of the enjoyable aspects of a good biography with surprisingly few of the drawbacks of an autobiography.

Leslie Saunders MacLane was born into a Protestant clergy family in 1909. He has been known by his mother’s maiden name since birth when his father, “put his hand on my head, looked up to God, and said, ‘Leslie forget.’” The spelling of MacLane is an attempt by the family to Americanize the Scotch MacLean, while the space in Mac Lane was added by Saunders later to facilitate the typing of his numerous mathematical papers by his wife Dorothy.

Mac Lane is best known in the mathematical community for his work in logic, algebra and most notably the co-founding of category theory. He was President of the MAA (1951-52) and the AMS (1972-74). His membership and dedication to the National Academy of Sciences (elected 1949, vice President 1973-1981) and his influence on national science policy as a member of the Nation Science Board (1973-1981) were acknowledged in 1989 when he won the National Medal of Science. Though he taught at various institutions, including two stints at Harvard, the University of Chicago was his mathematical home until his death. Mac Lane has over 1000 mathematical descendents. But for those who did not have the honor to study or work with Saunders, his presence at mathematical meetings the world over in his signature MacLean plaid gave literally many thousands the chance to hear him speak.

Given his strong personality and success in research and publishing, I was curious to see what would appear in his autobiography; who would be mentioned and what he would say about himself and his research. As the sub-title suggests, the book is part autobiography and part mathematical memoir. Mac Lane pulls off the delicate act of presenting his life’s work with grace and humility. His narrative is honest without the bombast that might be expected in an autobiography of one so successful in his chosen field. He gives generous praise to those who played an integral part in his research and life. In particular, Samuel Eilenberg, co-founder of category theory and his first wife, Dorothy, are awarded primary roles throughout the book (Eilenberg also provides the preface for the book.) I was very pleased to see that his wife of 50 years, Dorothy Marsh Jones Mac Lane (1907-1983) was awarded an entire chapter of her own, one of the longest in the book. He also dedicates space to many of his graduate students. (I was also pleased to see that my advisor Bill Howard was mentioned in more than a cursory fashion.)

The book is subdivided into fifteen parts and sixty-four chapters. The chapters are short and in many cases stand alone. All aspects of his life are recorded: family heritage, schooling, research, travels, the NAS and so on. The development of his mathematical work, instead of forming just one part of the book, is a thread that is woven through the book without becoming overbearing or a burden to the reader. Category and homology theory are advanced mathematical ideas, accessible for the most part to those with an advanced background in algebra. Mac Lane is able to present the mathematics in such a way that it reads smoothly and enjoyably for those with a background in the material as well as for those without.

The sections that I found most interesting were those about the National Academy of Sciences, The National Science Board, and national science policy. In fact, my one complaint is that I would have liked more on those topics; including what he did, who he worked with, and what were the results.

As I mentioned earlier, this work is refreshingly free of bombast and preaching. Mac Lane does, however, allow himself to voice his opinion on a few items near the end of the book. In Chapter fifty-six he does not hold back in his opinion of the uselessness of a graduate advisor evaluation form proposed by the Committee on Science, Engineering, and Public Policy of the NAS in 1998. Likewise in chapter fifty-seven he criticizes the 1960s idea of rating graduate programs based on the annual scholarly output of each program’s faculty. Lastly, in chapter fifty-eight he voices concern over how realistic were reports published by the NAS Government University Industry Research Roundtable on, again, the productivity of academic research and education.

Finally, in section fifteen entitled Contemplating, Saunders concludes with his personal thoughts on mathematical departments and collaborators and his choice to have a life in mathematics. He discusses the people and circumstances that made places like Chicago , Harvard, Yale and Princeton conducive to a dynamic mathematical environment.

Overall I thoroughly enjoyed Saunders Mac Lane ’s mathematical autobiography. After my brief encounter with “Uncle Saunders” while in graduate school, I had wanted to learn more about him, his views and his mathematics. In reading his autobiography, I feel that I have been given the gift of a small window into his life and his thoughts.

Amy Shell-Gellasch is currently a freelance math historian and mother of baby Brian. She lives in Grafenwoehr, Germany, while her Army officer husband is on a three year tour of duty in Germany and is currently deployed to Afghanistan. She received her bachelor’s degree from the University of Michigan in 1989, her master’s degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000. Her dissertation was a biographical piece on mathematician Mina Rees. Most recently, she was an Assistant Professor at the United States Military Academy (USMA) at West Point, NY from 2000-2003 and conducted research with V. Fredrick Rickey on the 200 year history of the USMA Department of Mathematical Sciences.

The table of contents is not available.