The book begins with the Fields’ parents and describes their life at Hamilton. Then it shows his life at the Toronto University, how he graduates with the gold medal in 1884, and enhance his four year sojourn at the Johns Hopkins University. There he gets his PhD. under the supervision of T. Craig. In 1892 he went to Paris, in 1894 stayed in Göttingen where he met F. Klein, and Berlin where he attended several courses and seminars and become friend of Takagi, Caratheodory, and Wilczynski among others. Finally in 1901 he went to Chicago where he knew to Maschke, Bolza, and Moore.

Back into his homeland, we read about his teacher career at the Toronto University: 1902 special lecturer, 1905 associate prof. 1914 prof. and 1923 research prof. Meanwhile he wrote his only book “Theory of the Algebraic Functions of a Complex Variable” in 1906. During those still years, he liked to travel to Europe and almost every summer met with some acquaintance as Mittag-Leffler etc.

The book now turns into the break out of the World War I and makes a thorough description of the events from the history point of view and also from the mathematical one. It gives a detailed account of the 93 pamphlet and the bitterness and confusion it created among mathematicians. Once the conflict ended, we read that Fields got the support to realize the International Mathematical Congress (the book explains perfectly well the difference between IMC and ICM) at Toronto in 1924 and as he couldn’t invited the mathematicians of Central Europe he realized the world needed some kind of solution. At the same time, the Nobel Prize, which was well established at that time, lacked of a Mathematical prize. So, Fields got enough support to create his counterpart: the medal that he didn’t wanted to bear his name or any other name of any institution or country, to promote the union that the world needed.

The reader can use the book also to learn about the history of the ICMs as he will find in the appendix all the winners with a brief account of their mathematical work from the one at Oslo (1936) up to and include the one at Hyderabad (2010).

Reviewer:

José L. Guijarro

Affiliation:

Universidad Complutense Madrid