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Saunders Mac Lane: A Mathematical Autobiography
Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Göttingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.
376 pages, Hardcover
First published May 25, 2005
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Displaying 1 - 4 of 4 reviews
December 16, 2021
As an aspiring category theorist (currently a masters student) I needed to read about the grandfather of category theory.
MacLane fills his book with stories about his family, his studies, his travels, his mathematical endeavors and his work in certain science associations. It was interesting for me to read because I actually had no idea what kind of mathematician MacLane was. I didn't know that he was interested about mathematical logic at first, though that makes sense with his later advances in topos theory. I didn't know that Saunders and MacLane were both surnames!
His viewpoint of the university life in Göttingen, especially in the nazi days, was interesting to me. After reading multiple other biographies of mathematicians in these ages - especially from Hilbert - it was fascinating to compare the different experiences, in particular the view of the international student MacLane and the view of the professor Hilbert who was at home. Most of what MacLane wrote overlapped with the overall scenery depicted in Hilbert's eyes.
The mathematics MacLane wrote about was a great and important part of the book. Sometimes I found it overdue to define objects such as groups or categories because I'm not sure anyone not familiar with these terms will learn them from a biography (instead of a textbook). I for instance didn't scrutinize his discussion of factor sets and glanced over it (even though I admittedly studied factor sets last year).
But maybe writing down these objects is needed and would otherwise disrupt the flow of the book? I'm not sure.
Anyhow, I enjoyed the mathematical part very much and learned about some origins of objects I use everyday. For example, I've read many times that the original motivation of natural transformations was the need to formalize some naturality about groups and that it originated from group theory. I didn't know that it was "just" the naturality of the universal coefficient theorem! I didn't even know that the UCT stems from MacLane and Eilenberg!
It is also fascinating how all this began with the computation of the homology groups of the p-adic solenoid after some discussion of number theory. This shows again how concrete examples drive mathematics.
I also enjoyed reading about the Eilenberg-MacLane spaces and how they motivated the study of group cohomology. There were many other mathematics-historical insights that I found interesting, but these were the ones that I liked the most.
From the book, I also gather that MacLane was quite a social person. Whenever he goes on travels, he seems to meet so many different mathematicians meaning that he made numerous acquaintances during his mathematical events which I find impressive. Reading mathematical biographies I also find it impressive how the great mathematicians of the time all seemed interconnected, as I knew and learned from most names in his book.
MacLane as a personality was certainly interesting. However, as someone who claims to have sternly learned about writing, I find his writing style disappointing. Reading the book, it seemed to have no flow, much seemed just like sentences put next to each other without any coherent meanings. So his writing style was unfortunately quite off-putting for me and many parts of the book bored me a lot even though I of course understand that they are essential parts of his biography. The discussions about the National Science Policies for example didn't catch my attention at all even though it should be an interesting topic. Maybe that's just me but I suspect that I'm also a victim of MacLane's writing style.
So for me his writing put a huge dent on my impression of the book. But this doesn't change the caliber of the mathematician MacLane is, and his experience should be an interesting read to any mathematician, in particular to pure mathematicians.
MacLane fills his book with stories about his family, his studies, his travels, his mathematical endeavors and his work in certain science associations. It was interesting for me to read because I actually had no idea what kind of mathematician MacLane was. I didn't know that he was interested about mathematical logic at first, though that makes sense with his later advances in topos theory. I didn't know that Saunders and MacLane were both surnames!
His viewpoint of the university life in Göttingen, especially in the nazi days, was interesting to me. After reading multiple other biographies of mathematicians in these ages - especially from Hilbert - it was fascinating to compare the different experiences, in particular the view of the international student MacLane and the view of the professor Hilbert who was at home. Most of what MacLane wrote overlapped with the overall scenery depicted in Hilbert's eyes.
The mathematics MacLane wrote about was a great and important part of the book. Sometimes I found it overdue to define objects such as groups or categories because I'm not sure anyone not familiar with these terms will learn them from a biography (instead of a textbook). I for instance didn't scrutinize his discussion of factor sets and glanced over it (even though I admittedly studied factor sets last year).
But maybe writing down these objects is needed and would otherwise disrupt the flow of the book? I'm not sure.
Anyhow, I enjoyed the mathematical part very much and learned about some origins of objects I use everyday. For example, I've read many times that the original motivation of natural transformations was the need to formalize some naturality about groups and that it originated from group theory. I didn't know that it was "just" the naturality of the universal coefficient theorem! I didn't even know that the UCT stems from MacLane and Eilenberg!
It is also fascinating how all this began with the computation of the homology groups of the p-adic solenoid after some discussion of number theory. This shows again how concrete examples drive mathematics.
I also enjoyed reading about the Eilenberg-MacLane spaces and how they motivated the study of group cohomology. There were many other mathematics-historical insights that I found interesting, but these were the ones that I liked the most.
From the book, I also gather that MacLane was quite a social person. Whenever he goes on travels, he seems to meet so many different mathematicians meaning that he made numerous acquaintances during his mathematical events which I find impressive. Reading mathematical biographies I also find it impressive how the great mathematicians of the time all seemed interconnected, as I knew and learned from most names in his book.
MacLane as a personality was certainly interesting. However, as someone who claims to have sternly learned about writing, I find his writing style disappointing. Reading the book, it seemed to have no flow, much seemed just like sentences put next to each other without any coherent meanings. So his writing style was unfortunately quite off-putting for me and many parts of the book bored me a lot even though I of course understand that they are essential parts of his biography. The discussions about the National Science Policies for example didn't catch my attention at all even though it should be an interesting topic. Maybe that's just me but I suspect that I'm also a victim of MacLane's writing style.
So for me his writing put a huge dent on my impression of the book. But this doesn't change the caliber of the mathematician MacLane is, and his experience should be an interesting read to any mathematician, in particular to pure mathematicians.
September 5, 2014
Pretty interesting to me, as it touched on lots of tangential interests. Saunders was over at the University of Chicago during the Hutchins era (Hutchins got him over there!), did important work in research (categories and algebra and other things I don't understand), and has lots of anecdotes about other famous mathematical figures of the 20th century — Irving Kaplansky, Haskell Curry, Howard's thesis troubles (of Curry-Howard isomorphism fame), etc (lots more than that, just those three came to mind right now). The book includes some of the founding history and psychology of American scientific and engineering organizations. He also gives some clear explanations, including a one-liner explaining what groups are. Too bad everything else was way over my head. I wish he'd given more advice for beginning mathematicians. One left a very good summary of his approach in an Amazon review of the book Algebra.
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September 4, 2015Probably 3/5 as a rating, but this is an autobiography that, without warning, slips into surveys of quite difficult, abstract mathematics (unsurprising, this being the co-inventor of categories). I can only give a proper rating if I am able to understand most (if not all) the mathematics.
That said, Mac Lane's book seems a tad unfinished. There is plenty of content, but somehow there is a lack of polish. For such an illustrious mathematician, one would have expected more story, more anecdote, more insight into the mathematical life. Yet Mac Lane's biography is still outstanding, in that it offers views of a mathematician that had great authority in much of his career (president of the AMS, NAS, etc in different periods of his career).
That said, Mac Lane's book seems a tad unfinished. There is plenty of content, but somehow there is a lack of polish. For such an illustrious mathematician, one would have expected more story, more anecdote, more insight into the mathematical life. Yet Mac Lane's biography is still outstanding, in that it offers views of a mathematician that had great authority in much of his career (president of the AMS, NAS, etc in different periods of his career).
January 22, 2014
Very enjoyable, with some interesting perspectives on history from a great man. The most interesting part by far was his perspective on Germany's mathematics community changing as the Nazis came to power. I didn't understand all of it, but I also absorbed some interesting math along the way.
Displaying 1 - 4 of 4 reviews