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My Brain is Open: The Mathematical Journeys of Paul Erdos

Bruce Schechter
Simon & Schuster
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Keith Devlin
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What makes a book a bestseller? Here's my list: Luck, reputation or name recognition of the author, marketing (including the launch), title, and topic, probably in that order. Quality of writing is rarely a factor, as far as I can see.

Of the first two of what might be a small flood of Erdös biographies to appear after Erdös's death in 1996, the clear bestseller was The Man Who Loved Only Numbers, by Paul Hoffman. I liked Hoffman's book, and said so in my review in MAA Online, published earlier this year. But in many ways, Schechter's is a much better biography. Where Hoffman strayed away from Erdös too often for my taste, Schechter has crafted a much tighter and better focused account of mathematics' famous wayfarer.

To my mind, the advantages of Hoffman's book are these. First, Hoffman chose a much more catchy title having wide appeal, whereas the phrase "my brain is open" really only works for people who recognize it as one of Erdös's modes of greeting when he turned up unexpectedly on a colleague's doorstep. Second, as former editor of Discover magazine, current editor of Encyclopedia Britannica, and a frequent guest on television and radio talk shows, Hoffman has name recognition and media credentials. Third, The Man Who Loved Only Numbers seems to have been carefully released and well promoted -- I became aware of it well before it was published -- whereas Schechter's version just seemed to appear on the bookstore shelves unannounced one day. Fourth, Hoffman knew Erdös personally, which I think shows in his book (Schechter admits he never met his subject). Fifth, Hoffman provided more details on Erdös's early life in Hungary, much of which was new to me. Sixth, Hoffman included far more snippets of Erdös-related gossip. And finally, Hoffman was lucky; his book took off and climbed high on the non fiction bestseller lists.

Since a non mathematician is surely only going to read one Erdös biography, one consequence of the observations I have just made is that Schechter's book is likely to be read only by mathematicians. They will not be disappointed. The two books provide different views of Erdös. Whereas Hoffman's book is more like a series of magazine profiles strung together, providing the reader a series of snapshots of Erdös, Schechter's account gives a well-crafted, coherent overview of Erdös's life and his development as a mathematician.

Mathematicians who read Schechter's biography -- and I have already remarked that I suspect that will account for the majority of his readers -- are likely to be annoyed at a number of inaccuracies that could have been avoided by getting a mathematician to check through the manuscript. On page 53, the author states that trial division is "the only surefire way of determining whether a number is prime," which is false. On pages 76 to 78, Schechter screws up the logic in the proof of Esther Klein's theorem that if five points are drawn at random on a plane, with no three collinear, then four of them will determine a convex quadrilateral. On page 81, it is stated that Frank Ramsey's younger brother "was the Archbishop of Canterbury," whereas it should have read "was to become the Archbishop of Canterbury." Finally, on page 155, Jingrun's theorem on the Goldbach conjecture is mis-stated as: "every even number [can] be expressed as the sum of a prime and a number that has two prime factors." What it should say is "exactly two prime factors." The distinction matters. It is clear from the context that Schechter understood the result correctly. But as mathematics instructors tell their students every year, theorems should be stated precisely, especially results such as Jingrun's that are inching their way toward a particular goal.

Errata aside, however, I enjoyed the book and can recommend it. It's worth reading, even if you have already read Hoffman's version of the tale.






Keith Devlin ( is Dean of Science at Saint Mary's College of California, in Moraga, California, and a Senior Researcher at Stanford University. He has an Erdös number of 2 (i.e., he wrote a paper with someone who wrote a paper with Erdös). His most recent book is The Language of Mathematics: Making the Invisible Visible, published by W. H. Freeman.


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