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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
A co-publication of the AMS and Fields Institute.

2011; 258 pp; softcover
ISBN-10: 0-8218-6914-0
ISBN-13: 978-0-8218-6914-7
List Price: US$48
Member Price: US$38.40
Order Code: MBK/80
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Despite the renown of the Fields Medals, J.C. Fields has been until now a rather obscure figure, and recovering details about his professional activities and personal life was not at all a simple task. This work is a triumph of persistence with far-flung archival and documentary sources, and provides a rich non-mathematical portrait of the man in all aspects of his life and career. Highly readable and replete with period detail, the book sheds useful light on the mathematical and scientific world of Fields' time, and is sure to remain the definitive biographical study.

--Tom Archibald, Simon Fraser University, Burnaby, BC, Canada

Drawing on a wide array of archival sources, Riehm and Hoffman provide a vivid account of Fields' life and his part in the founding of the highest award in mathematics. Filled with intriguing detail--from a childhood on the shores of Lake Ontario, through the mathematics seminars of late 19th century Berlin, to the post-WW1 years of the fragmented international mathematical community--it is a richly textured story engagingly and sympathetically told. Read this book and you will understand why Fields never wanted the medal to bear his name and yet why, quite rightly, it does.

--June Barrow-Green, Open University, Milton Keynes, United Kingdom

One of the little-known effects of World War I was the collapse of international scientific cooperation. In mathematics, the discord continued after the war's end and after the Treaty of Versailles had been signed in 1919. Many distinguished scientists were involved in the war and its aftermath, and from their letters and papers, now almost a hundred years old, we learn of their anguished wartime views and their struggles afterwards either to prolong the schism in mathematics or to end it.

J.C. Fields, the foremost Canadian mathematician of his time, was educated in Canada, the United States, and Germany, and championed an international spirit of cooperation to further the frontiers of mathematics. It was during the awkward post-war period that J.C. Fields established the Fields Medal, an international prize for outstanding research, which soon became the highest award in mathematics. J.C. Fields intended it to be an international medal, and a glance at the varying backgrounds of the fifty-two Fields medallists shows it to be so.

Who was Fields? What carried him from Hamilton, Canada West, where he was born in 1863, into the middle of this turbulent era of international scientific politics? A modest mathematician, he was an unassuming man. This biography outlines Fields' life and times and the difficult circumstances in which he created the Fields Medal. It is the first such published study.

A co-publication of the AMS and Fields Institute.


Anyone interested in the history of mathematics and specifically Fields, and the Fields medal.


"This highly readable nonmathematical biographical study is a triumph of tenacity. It sheds significant light on the personal life, professional development, and lasting legacy of the foremost Canadian mathematician of his time."

-- Deborah Kent, Isis

"John Charles Fields is a little-known Canadian. He deserves to be better known. Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal, a fine biography and account of his career and work by Elaine McKinnon and Frances Hoffman, may help to rectify that situation. ... The authors of this book have done a superb job with exhaustive attention to the details of the history, both of Fields's efforts and of the mathematical organizations."

-- Douglas Wright, Literary Review of Canada

"Here, Canada-based authors Riehm (researcher) and Hoffman (historian) take the reader on a journey covering the life and times of this globally minded mathematician, along with the history of the creation of the medal, using much archival material. . . . Recommended. Academic and general readers, all levels."

-- M.D. Sanford, CHOICE

"The Canadian mathematician John Charles Fields is remembered through the Fields Medals, funds for which he endowed in his will, and more recently for the Fields Institute in Toronto, but little has been known about him personally: this gap is now filled by this engagingly written book. . . . It is well researched, well illustrated, and valuably amplifies our record of a man who set out to make mathematics more international at a painfully difficult time in its history, and succeeded."

-- Jeremy Gray, Mathematical Reviews

"...[Riehm and Hoffman] provide a richly contextualized picture of the historical times in which Fields lived. Turbulent Times in Mathematics offers an engaging narrative of Fields' struggle to further Canadian science and to make a lasting contribution to mathematics, a subject he clearly loved."

-- Sylvia Nickerson, Historica Mathematica

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