# Book Reviews

# The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time by Keith Devlin

List Price: £9.99

Paperback: 256 Pages.

Published: 07 March 2005 by Granta Books

Edition: New edition

ISBN: 1862077355

EAN: 9781862077355

In May 2000, The Clay Foundation in the US announced that a prize of $1 million would be awarded for the solution to each of the seven most difficult unsolved problems in mathematics today, known as the Millennium Problems.

These problems encompass many of the most fascinating areas of pure and applied mathematics , from topology and number theory to particle physics, cryptography, computing and even aircraft design.

Keith Devlin describes here what the seven problems are, how they came about and what they mean for mathematics, science and society.

## Reviews

A fascinating insight into the largely unseen and unknown world of pure mathematics.

As children, when we went to Primary School, we learnt “Sums”. At secondary school, in my day (a long time ago), we learnt arithmetic, geometry and algebra. Those of us who went on to further education, associated with some form of engineering, learnt that mathematics was the name for all these subjects and that there were two basic types of mathematics, applied and pure.

As an electrical engineer I learnt applied mathematics and I always wondered what, on earth, pure mathematics was and of what use it was. This book explains all. It describes what relevance pure mathematics has to the “real world” and what part it has played in all our lives.

One of the seven problems is described as the Travelling Salesman problem. It poses the question “If a salesman has a number of calls to make, and obviously wants to minimise his overall travelling time, what is the sequence of calls which will achieve this and bring him back to his starting point?”

To analyse this he constructs a chart showing his calls and the distance between each of the calls and every other call. This is all the information he needs to work out his best route.

However, this is where the “Fun” starts. For three calls there are just 6 possibilities and so it is easy to pick the correct one. If, however, he has 10 calls to make, quite a practical number for a delivery driver for example, there are 3,628,800 possibilities! To draw the chart(?) for this would take just over 20 years assuming 1 minute to determine the distance between each of the various calls and working normal hours.

For a busy delivery driver in a large city with just 25 calls to make the number of possible permutations is 15,511,210,043,330,985,984,000,000. Not very practical!

This is a book which, if you are like me, and not experienced in pure mathematics, you are very unlikely to understand the detail. If, however, you are like me and you just want to get a small insight into the world of pure mathematics it is well worth looking at.

I would, however, suggest that before purchasing the book a quick perusal in a library would be beneficial!