Numbers at Work: A Cultural Perspective

Numbers at Work: A Cultural Perspective, Rudolf Taschner,   2007, 209 pages ,  $39.00, hardcover, ISBN-13: 978-1-56881-290-8, A K Peters Ltd., www.akpeters.com

Numbers at Work is a collection of  8 essays originally published in Germany as Der Zahlen gigantische Schatten by Rudolf Taschner, a Professor of Mathematics at the Technical University of Vienna who was named "Scientist of the Year" by the Austrian Association of Science Journalists in 2004. Each essay focuses on an important historical figure and how number was critical to the development of that person's work. For example: 

The essay "Hoymannsthal: Numbers and Time" starts with an examination of how the Greek philosophers such as Parmenides dealt with time, moves on to the many attempts to create an ideal yearly calendar and finishes with Einstein's Theory of Relativity and its implications for building clocks. Throughout the essay, the role of number is dealt with.

The essay "Bach: Numbers and Music" contains a thorough and interesting development of how numbers play an important role in understanding the structure and tonal qualities of many of Bach's most famous works. 

The essay "Laplace: Numbers and Politics" traces the development of probability theory and follows it from Laplace's early work related to gambling to how statistics are fundamental to insurance agencies and how probability plays such an important role in our current  lives.

The essay "Descartes: Numbers and Space" traces the role of number in the development of geometry as a tool for understanding space.  Starting with the Babylonians' use of the Pythagorean Theorem, the essay examines Eratosthenes determination of the size of the earth, Bessel's measurement of the parallax of a fixed star in 1838 and ends with Descartes' contribution to our understanding of  space.

These are just a few of the essays and there are many more. They all are very readable and full of fascinating detail. I reread each one a couple of times and each time learned something more.  If you are interested in the history of  ideas and how important the concept of number has been in the development of human thought this is a must read. If you are teacher and are looking for a good source of supplementary material for your courses, this is well worth reading.

Jon Choate, Mathematics Department, Groton School , Groton, MA

See also the MAA Review by Sarah Boslaugh.