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Turbulent Times in Mathematics: The Life of J. C. Fields and the History of the Fields Medal

Elaine McKinnon Riehm and Frances Hoffman
American Mathematical Society/The Fields Institute
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
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J. C. Fields (1863–1932), known today as the namesake of math’s Fields Medals, was the foremost Canadian mathematician of his day, but worldwide never received much attention for his mathematics (p. ix). The present book combines a biography of Fields with a study of the international political situation in mathematics during and immediately following World War I. The book includes a list of Fields’s scientific publications, but it concentrates on his administrative work and is not a scientific biography.

Fields’s greatest achievement during his career was organizing the 1924 International Mathematical Congress in Toronto. His task was complicated by the animosity still felt toward Germans by the rest of Europe after World War I. First New York City and then Toronto were picked as relatively neutral sites for the Congress, but the German mathematicians were still excluded. The Fields medals originated at the end of his life from his desire to do something to bring the mathematicians of the world back into cooperation, and the first medals were not awarded until 1936, four years after his death.

The writing is choppy. Some facts are repeated several times, and there are many jumps back and forward in time, making it hard to remember where you are. At one point I got so confused that I thought “the war” being discussed was World War II. The book often jumps forward in time to get someone’s much later perspective, then jumps back. For example, on p. 88, in a discussion of mathematics before 1914, we read “Somewhat later, in the spring of 1932, ...” with a discussion of Richard Courant’s assessment at that time of the influence of pre-1914 teaching. The jumping in time is compounded because some chapters of the book are told functionally, covering many years of Fields’s career, and some chapters are told chronologically, covering a few years.

The book includes an interesting appendix of thumbnail biographies of all the Fields medallists to date. There are a few minor infelicities and errors, such as Bernhard Riemann being referred to throughout by his first name as Georg Riemann, and on p. 111 Bertrand Russell being fired during World War I from Oxford (actually Trinity College, Cambridge), but overall the book is interesting and appears to be accurate and impartial.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at, a math help site that fosters inquiry learning.