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The Abel Prize 2013-2017

Helge Holden and Ragni Piene, editors
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Gouvea
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The first Abel Prize was awarded in 2003 and has gone on strongly ever since. The significance of the prize has been established in the best possible way: the list of Abel Laureates is impressive.

The activities surrounding the prize have always been important and extensive. In particular, the Laureates have been recognized in a series of books. After five prizes had been awarded, The Abel Prize 2003–2007 was published. Five years later, we got The Abel Prize 2008–2012. So it is no surprise that now after the fifteenth award was made, we get another volume covering the period 2009–2017. Of course, there have been two Laureates announced recently: Robert Langlands in 2018 and Karen Uhlenbeck this year. They will have to wait for the fourth volume.

The winners honored in this volume are Pierre Deligne (2013), Yakov Sinai (2014), John Nash and Louis Nirenberg (2015), Andrew Wiles (2016), and Yves Meyer (2017). As I noted in the reviews linked above, these books are well produced and full of interesting information. They not only document the winners and their work but also make for interesting reading. There are lots of photographs and updates on the previous Laureates. (The Abel Prize is given for a lifetime of mathematical work, but these Laureates are hardly going to stop producing mathematics!) There are even extra materials online, including video of the interviews with the Laureates.

The structure is mostly the same as in the previous volumes: for each of the five winners, we get the text of the prize citation, a short mathematical autobiography by the winner, expository account(s) of the Laureate’s work, a list of publications, and a short vita. At the back of the book, we find a selection of photographs from the prize-related activities, citations for all the winners so far, data on the Abel Board and Committee, and so on, including the updates mentioned above.

The expository accounts of each mathematician’s work are very well done, but my favorite element of these volumes are the autobiographies, where we can hear the ipsissima verba of some of our time’s greatest mathematicians. Thus, we hear from Deligne that

When I was in high school, I had no idea one could get paid for doing mathematics. My father would have liked me to become an engineer. I was planning to become a high school teacher, and do mathematics as a hobby. That I could earn a living by doing what I liked best came as a pleasant surprise.

I found myself in much the same situation (Deligne in the 1960s, me in the 1970s) when I decided to study mathematics rather than engineering. Of course, I eventually found that I loved teaching and have done a lot of that in addition to mathematics. Deligne had the good fortune of spending all of his life at research institutes.  I also enjoyed hearing Deligne’s comment that he would have found the typical American “distribution requirements” suffocating.

Sinai also has something interesting to say:

During my school years I participated in several Olympiads, always without success. (This might be useful for high school students who sometimes exaggerate the role of Olympiads.)

I never got to participate in an Olympiad or even take the Putnam examination, but I imagine I wouldn’t do very well either…

It is the same in each winner’s case. There is a lot to learn from the autobiographies, and the expository essays are mostly very good as well, and definitely worth reading. Future historians will use these books as historical sources, but we can use them now to learn more about people we admire.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College.