Last Summer, two biographies of Paul Erdös appeared. They are "The Man Who Loved Only Numbers" by Paul Hoffman (Hyperion, New York, 1998) and "My Brain Is Open" by Bruce Schechter (Simon and Shuster, New York 1998; a new edition came out in late 1998). Each book was reviewed not only by most major mathematical and scientific journal, but also in almost every major newspaper in the United States and Europe. So the life of perhaps the most colorful mathematician of this century has had ample public exposure. Rather than write yet another review, I will comment only briefly on these books and the sprit of these reviews written about them. I met him in April 1953, wrote a paper with both him and Leonard Gillman outside of his major field of interest the next year. We met many times over the years and I last saw him in Budapest 16 days before he died. He always remembered out collaboration and asked about the impact of the paper. He never worried about mathematical taste or what the powers-that-be might think of him for collaborating with mathematical inferiors or not exhibiting what some call mathematical taste. It was the quality of the mathematics that mattered to Erdös, not following the latest fads. Both do a good job of showing how Erdös interacted with others, but tend to dwell too much on anecdotes that describe his idiosyncrasies. The latter are accurate in spirit if not always in fact. They do so without patronization, but something is lost when one relies too much on funny stories to describe someone.
Both books are worth while and will bring pleasure and edification to their readers while leaving them with the feeling that these authors fail to describe the "real" Paul Erdös. Their sources of information were chosen from among the readily available which are not always most informative. For a small number of many examples, neither Paul Bateman who was once the person in the mid-west to call if you wanted to learn the whereabouts of Erdös, nor Fritz Herzog, nor George Piranian with whom Erdös collaborated extensively are mentioned. Those whose names appear seem to be mentioned in proportion to their availability. I get more space than I deserve, and each book has a fairly thorough biography of Ronald Graham. Even so, the authors have done a remarkable job in a very short time. I hope, however, that someone will make a deeper and more thorough study of the life of Erdös.
The level of the mathematical exposition in each book is quite high. Both do a very good job of explaining problems in number theory that are easy to state but extremely difficult to solve. Schecter venture even further in trying to explain the Erdös-Selberg contraversey over the elementary proof or the prime number theorem. He goes into dramatis personae and possible skull duggery towards Erdös by various eminent mathematicians he had offended, but the veil of mystery about what really happened stays drawn.
The only serious mathematical error I found is Hoffman's attempted description of the work of Paul Cohen and Kurt Godel on the independence of the axiom of choice and the continuum hypothesis from the Zermelo-Frankel axioms for set theory. Suffice it to say that that the mathematical description is incorrect as is his description of the relationship between these two great mathematicians. The cure is to blue pencil it out altogether. While Erdös made substantial contributions to combinatorial set theory, he was never terribly interested in its axiomatic aspects.
I dislike the title "The Man Who Loved Only Numbers" because it seems to describe Erdös as a cold person unconcerned with human beings. The reverse is true. He liked people of both sexes very much, and especially children whom he called epsilons out of deep affection. His greatest handicap was the failure of his parents, out of a desire to free him for intellectual pursuits, to teach him the little everyday things that we learn easily as children such as tying your own shoe laces, buttering your own toast, dressing properly, or making your way in a kitchen without creating a disaster. Many mathematicians equated his ignorance of things we learn so well in the home that they are second nature by the time we reach adulthood as the behavior of someone who is selfish and boorish. (Indeed, he could be maddening as a house guest.) Those of us who loved him accepted his strange behavior as the result of ignorance. Indeed, he did learn many of the social graces and paid attention if you explained them to him, but he never got much beyond the social intelligence of a teen ager. This, and not issue of priority over the prime number theorem is why he was not re-appointed at the Institute for Advanced Study, and why he spent a half a dozen years exiled from the United States. Yes, Erdös relied on others to take care of him, but his mathematical help to so many others was ample repayment. In summary, these two books are well worth reading, but a deeper biography of Erdös needs to be written.