The Man Who Loved Only Numbers

Paul Hoffman

From time to time I like to read books about maths. This book is the story of Paul Erdos, one of the great mathematicians or our time. Actually I hadn't heard of him before but I'm not sure if that's because he was more famous in America or because maths celebrities simply don't get the exposure they deserve. When I heard about this odd genius who drifted from friend to friend, arriving unannounced to stay at their houses for weeks or months and declaring merely on their doorsteps "my brain is open", I just had to read the book.

Paul Hoffman has written Erdos's life story but since the life of a mathematician on the face of it yields little material for an incident-packed biography he has also padded the book out with some simple mathematical theory, some entertaining anecdotes and a few diversions into the life stories of other mathematicians. It makes for quite a good mix. However if you check the reviews in Amazon there are several angry reviewers who condemn Hoffman for, basically it seems to me, his lightweight approach. I can only presume these reviewers were after a less accessible, more serious and more academic book. Fine if you're a maths graduate and that's what lights your fire.

It was a monkish life. Erdos had no interest in either sex or money. In fact he had little interest in anything that wasn't maths. Hoffman depicts Erdos doing maths day and night, sometimes alone but usually in excited collaboration with others, as work and as recreation, indoors, outdoors, scribbling theorems on whatever was at hand; paper, blackboards, table tops, napkins. It's a great story of a true eccentric genius.

It's also a view into another world, a world populated by hundreds of intelligent and creative people, not just Erdos, working feverishly and excitedly on numbers. Just numbers and maths. It's easy to understand the attraction - it's the purity of proof, absolute right or wrong answers, something that no other human pursuit provides us.

In later chapters Hoffman asks an interesting question - are these people, Erdos and other mathematicians, providing the real world with anything useful and usable, or are they simply engaged in a gigantic intellectual hobby? His answers are inconclusive. There are several stories of Erdos and his closest collaborators solving important problems to do with telephony. There's also a fascinating story of mathematicians providing an answer of a sorts to the "bin stocking" problem. This is the apparently simple issue of how to load objects of different sizes and weights into lorries (or warehouse bins or whatever) in the most efficient manner. This is a problem I have actually faced myself in designing software for industry and I had always assumed that there existed an algorithm or a formula which would duly deliver the ideal fit. I was amazed to learn that no such answer exists. In fact the reverse has been proved - that it is mathematically impossible to determine an ideal and that formulas can only provide a best-fit solution.

On the other hand, there are many examples where the problems which Erdos and others chewed over for months or years were of demonstrably no practical use to the rest of us. Prime numbers, exponents, the Fibonacci numbers, e (the natural logarithm) and pi ... these have invaluable properties and are of immense interest to the natural world but mathematicians are truly obsessed by them, above and beyond their practical usefulness. It's always nice to end a maths related review with a staggering fact: pi has been calculated to more than 50 billion decimal places. Sounds like an esoteric exercise but, hey, knowing pi to millions of decimal places is potentially useful in engineering, huh? However, according to Hoffman, in order to compute "the circumference of a circle girdling the known universe with an error no greater than the radius of a hydrogen atom" pi's value needs to be computed to ... just 39 decimal places. Wow.