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Publisher:

World Scientific

Publication Date:

2013

Number of Pages:

238

Format:

Hardcover

Price:

29.00

ISBN:

978-9814556613

Category:

General

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

P. N. Ruane

03/2/2014

In 1884, an international conference of twenty-five countries, including France and Britain, took place in Washington. The aim was to establish a line of longitude serving as the prime meridian to standardize the partition of the earth into twenty-four time zones. Among the three options were the longitudes of the Paris Observatory and Greenwich (London). To the annoyance of France, the ‘award’ went to Britain, and Greenwich mean time has since been universally recognized.

As a member of the French ‘Bureau des Longitudes’, Henri Poincaré sought to restore national self-esteem and to encourage France to abide by the new standard time Noticing that the Greenwich meridian passed through the French city of Argentan, Poincaré mischievously suggested that France could save face by referring to the new standard time as ‘Argentan mean time’.

In this book, there’s an interesting chapter devoted to this affair, and it includes excerpts from reports on the conference written in the *New York Tribune* (Nov. 1884) and *The Sun* (Nov 1884). Although in these articles there is no specific mention of Poincaré’s involvement in the meridian conference, he is the subject of many other newspaper articles that appear in later parts of the book. One chapter concerns Poincaré as a source of evidence in the Dreyfus affair, and another describes his role in the dispute with French Catholics concerning geocentricity.

So here we have a book that explores the life and work of Henri Poincaré by placing emphasis on what was written about him in French and American newspapers from around 1894 to his death in 1912 at the age of 58. In typical biographical style, the early chapters describe Poincaré’s family background, his childhood and his embarkation on a career in mathematics, which started to take shape during his years at the École Polytechnique. Remarkably, whilst subsequently preparing for a career as a mining engineer the École des Mines, he simultaneously worked for his Ph.D thesis on partial differential equations. This was awarded to him at the age of 21 in 1879.

The most mathematical chapters are those on Poincaré’s discovery of Fuchsian functions and the one concerning the prize awarded to him by the King of Norway for his paper on the *n*-body problem in celestial mechanics. One gets little idea of his work on the foundations of algebraic topology, fluid mechanics, Kronecker’s index or his application of automorphic functions to non-Euclidean geometry.

Poincaré’s (unwanted) fame increased in his later years, which was mainly due to his regularly published papers in popular science and philosophy journals. All such material subsequently appeared in the form of four books that are often reprinted in various languages. They discuss the role of logic in mathematics, the emergence of set theory, modern geometry and contemporary developments in physics.

On February 22^{nd}, 1908, the New York Times reviewed the first volume, opening with the caption

Abstruse Romance in Mathematics

French Scientist Investigates Essential Nature of Geometry withAstonishing Results.

The full review (given in chapter 9 of this book) gives an excellent description of Poincaré’s interpretation of non-Euclidean geometry and his wider views on mathematics, and it would make very informative reading for contemporary students of this subject.

I very much enjoyed reading this book, although the later chapters are less readable than the others. It isn’t by any means a definitive biography, and nor does it claim to be. But it does portray many lesser-known aspects of Poincaré’s life and work; and it is richly illustrated with facsimiles from a variety of unusual sources.

Peter Ruane has taught mathematics to people of greatly varying abilities between the ages 5 and 55. Or rather, he tried to teach them how to learn mathematics.

The table of contents is not available.

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