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Saunders Mac Lane: A Mathematical Autobiography

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Saunders Mac Lane: A Mathematical Autobiography is the personal memoir of the late Saunders mac lane, one of the most influential mathematicians of the 20th century. His life story takes the reader on fascinating and informative journey through the most important milestones of the mathematical world of the last ten decades. Saunders provides the reader with a glimpse into his "life and times" through a blending of professional observations with highly personal commentary. He recounts his experiences in pre-war Gottingen (where he studied under David Hilbert and witnessed the collapse of a great German academic and cultural tradition under the political pressures of a brutal Nazi regime). He reflects on his work with Samuel Eilenberg and the impact of their creation of a new mathematical language and theory. Here is the personalized and deftly written story of a century of extraordinary accomplishments and tragedies that will inform and inspire future generations of aspiring mathematicians and is therefore an essential addition to all college and university library collections.

I recommend this book heartily because it is such a tremendous failure that it has to mean something. I expected a lot from this title and this author, but in vain. Let us look at chapter 54: `Dorothy's Delights'. We find there a plethora of tiny details about his life with his wife in the winter of 1984-85 and it becomes clear at the onset that the chapter will end up with her death. The last sentence reads: "I remember with gratitude the stalwart help she gave me over more than 50 years, and the beauty and grace that she brought to my life." We may admire Mac Lane's discretion when he writes about his relation with his wife, but we cannot follow him when he does the same with his relation with mathematics. Indeed the whole book is constructed like this chapter: a flood of facts about his personal life, about mathematical results and mainly about his academic life. A flood which dries down to this last sentence: "All told, mathematics was a great career choice for me." What an unbelievable ending, what an unbelievable book!
A unique dim spark of life appears when Mac Lane talks about his crucial collaboration with Samuel Eilenberg. In chapter 13, `Eilenberg Enters', he describes his first encounter with him and he comes back to it in the penultimate chapter of the book. "It can be best summarized by a striking proof that 2 is more than 1 plus 1" (p. 347). There was a book to write on this proof alone, on the mysterium coniuntionis which gave us category theory, that pot of gold of contemporary mathematics. It is a pity that Saunders Mac Lane chose instead to talk about the NAS, the NRC and the AMS.

Saunders Mac Lane, who died while this book was in preparation, was a teacher nonpareil. In the mathematics genealogy program (www.genealogy.ams.org) he is listed as having 40 students (who earned Ph.D. degrees) and a total of 1,044 descendents, that is Ph.D. students who studied under his students or their students.

A graduate of Yale in 1930 he went to Germany to study at Gottingen, the premier center for mathematics in the world at that time. While there he saw at first hand the removel of the top mathematicians who had any Jewish connections. And later he saw that these refuge mathematicians made many significant contributions to the advancement of mathematics in the United States.

Over his career he worked on many mathematical problems, but he also worked on many other problems such as the teaching of mathematics at the K-12 level. As he ends the book, mathematics was a great career choice for me.