Mathematicians, more than most academics, have always had something of an image problem. They are often seen by the world as seeking refuge from the messiness of reality in a mental cathedral of order and logic. The frontiers of much modern mathematics research are so arcane that a layman might be excused for believing that a scholar occupied by such details has little time left to appreciate the simple pleasures and basic niceties of everyday living.

In fact, mathematicians rarely live up to this stereotype. Not so Paul Erdos. The Hungarian mathematician epitomised the cloistered academic totally immersed in his subject. He had no home, no wife, no possessions, and no interests outside mathematics. Living out of a suitcase, he travelled the world visiting mathematicians and doing nothing but mathematics. Erdos had little knowledge of the mundane aspects of life. He could not perform many everyday tasks such as preparing food or driving a car: even tying his shoes presented difficulties. Art and literature held no interest for him. He would open a conversation not with "Good morning" but with a statement like "Let n be a positive integer..."

It is perhaps not surprising, then, that Erdos was the most prolific mathematician ever, publishing 1,475 papers with 485 collaborators. The "Erdos number" is used by academics to describe how many links separate them from Paul Erdos (where two people are linked if they publish an academic paper together): he forms the obvious anchor for such an exercise in the worldwide mathematical community.

Paul Hoffman bases his biography on personal contact with Erdos and many of his colleagues over ten years. We read about Erdos' sheltered childhood, the development of his idiosyncratic personality, and his mathematics. Hoffman assumes no mathematical knowledge of his readers and offers accessible explanations of many areas of Erdos's research, such as the prime numbers, combinatorics and Ramsey theory. For this purpose Erdos is a more convenient subject than most mathematicians, since his style of mathematics required a minimum of technical machinery. Hoffman covers many mathematical ideas that may be new to the layman, such as the concept of proof and the infinite. He captures the subject's aesthetic appeal, which particularly motivated Erdos's work.

ÁñÁ«ÊÓƵ

Hoffman is less effective at exploring Erdos's inner psychology. The book's style is almost entirely anecdotal, and although he always treats Erdos affectionately, Hoffman never delves too deeply into Erdos's character before he is sidetracked. His numerous digressions add colour and background, but many of them have only a tenuous connection with Erdos, and some topics have been covered amply by other authors. An example is a chapter on Fermat's Last Theorem, a problem eventually solved by Andrew Wiles using vastly complicated mathematical techniques after a long period of isolation from his colleagues. Erdos's style was quite the opposite, characterised by simplicity of argument and collaboration with others.

Despite not restricting himself to Erdos's work, Hoffman's picture of the world of mathematics is still incomplete. Many mathematicians are motivated not by the beauty of the abstract, as Erdos was, but by the power of mathematics when applied to problems such as the design of industrial technology, or the mechanisms of physical and biological phenomena.

ÁñÁ«ÊÓƵ

Students looking for academic inspiration should be advised that the full breadth of mathematics is greater than they will find in the life story of the subject's most single-minded exponent. But they will find great personal inspiration in Hoffman's illustrations of Erdos's tremendous kindness and charity, which earned him the utmost respect of his colleagues, and which displayed a deep-rooted humanity, beneath his eccentricity, towards which we all might aspire.

James Lawry is a postdoctoral researcher, centre for Industrial and Applied Mathematics, University of Oxford. Rebecca Gower is a mathematician, Department for Education and Employment, and has an Erdos number of 3.