This book is a collection of essays, intended for general readers, on a variety of topics, including the history and philosophy of mathematics (especially geometry), the place of mathematics in society, the infinite, mathematics and art, and others. The author showed that he is true mathematician by including problems at the end (“Two trains start at 7 am, one from A going to B…”). The essays were written in the 30s, 40s, and 50s of the last century and the book was first published in 1958.

Nathan Altshiller was born in Russia in 1881 and received his doctoral degree from the University of Ghent in 1911. He came to the United States, holding positions at Columbia (teaching evening classes), the University of Washington, and the University of Colorado. He was a member of the mathematics department at the University of Oklahoma from 1916 until his retirement in 1951. On becoming a citizen in 1919 he asked the judge if he could change his name to something more appropriate for a US citizen, and chose Court. He died in 1968. He was a geometer, and his *College Geometry* (1925) was widely cited. He also wrote *Modern Pure Solid Geometry* (1935).

Members of the MAA may not find a great deal that is new to them in the essays, but then not everyone is familiar with the anecdote about Lilivati’s wedding or why Brouwer rejected the law of the excluded middle. In any event, the essays have not dated too badly, are worth reading, and Dover is to be commended for keeping them available. Most of them raise timeless issues. For example, Court tended towards the view that mathematics is inevitable and if one mathematician failed to make a discovery, then another would. I’m not so sure. It is probably the case that calculus would have appeared even if Newton had died at birth (we are told that his birth was so premature that he was small enough to fit into a coffee cup) and Leibniz had never left philosophy. There was calculus pushing to get out of the works of Fermat, Wallis, and others, and no doubt someone would have carried on from where they left off. But we can’t know for sure. If Mandelbrot hadn’t thought of fractals, would anyone else have? My intuition tells me that it is quite possible that the world could have remained forever fractalless.

The book is well worth looking at, or (at a mere $8.95 a copy) for giving as a present.

Underwood Dudley has retired from DePauw University and is now living in Florida.