My Brain is Open: The Mathematical Journeys of Paul Erdos [Paperback]

The four-word title of this book is "My Brain Is Open." If you keep the first word and form a word from the first letter of the three remaining words, you get "My BIO." And that's exactly what this book is. This ten chapter book, by Dr. Bruce Schechter, is a BIOgraphy of Dr. Paul Erdos (pronounced "Air-dish").

Erdos (1913 to 1996) is said to have been one of the greatest mathematicians of the twentieth century (especially in number theory, the branch of math concerned with the properties of integers) as well as the most eccentric. Throughout this book, we also learn of the many others who collaborated with Erdos on his many published mathematical papers. (He wrote or collaborated on more than 1500 papers with over 450 collaborators.)

This book is also filled with the sorts of mathematical puzzles that intrigued Erdos and continue to fascinate mathematicians today. Schechter does a good job of explaining these puzzles (with the aid of diagrams, tables, and graphs) so the reader does not have to worry that these problems will be too difficult to understand.

The reader is also taken on a tour of mathematics. We are introduced to such people as Pythagoras and his famous theorem, Karl Gauss who, when ten years old, was able to add up the numbers from 1 to 100 in less than half a minute, and Bernhard Reimann and his work on prime numbers.

Erdos was born in Hungry. By age seventeen he had gained international recognition as a prodigy. He eventually left Hungry and went to the Institute of Advanced Study at Princton in the United States. (Einstein was the institutes most famous resident then.) Because of his politics, he was exiled from the U.S. for a decade. From this point beginning in the 1950s, he became "the Bob Hope of mathematics" or "the travelling mathematician."

Since Erdos was constantly travelling, he had no home or job but still managed to meet with math colleagues all over the world. He had all his belongings in a suitcase and his mathematical papers in a bag when he arrived at their homes. Erdos also depended on the generosity of colleagues to sustain him.

The reader is introduced to Erdos' eccentricities throughout the book. For example, he invented a vocabulary where the U.S. was "Sam" or "Samland" (after Uncle Sam) and the Soviet Union was "Joe" or "Joedom" (after Josef Stalin).

There are more than fifteen black and white photographs found in the middle of this book. These photos span a period from 1916 to 1993.

To get the information needed to write this book, Schechter relied "on the memories of the many people" who met Erdos -- his hundreds of collaborators and friends. That is, he "primarily relied on interviews with many of the people who knew Erdos best." Schechter also "drew heavily" from biographical essays as well as magazine articles about Erdos. He also used the information from the over ninety sources listed in this book's bibliography.

Finally, as I said above, this book does contain mathematical puzzles that intrigued Erdos. Personally, I found these interesting but some readers may find that they interfere with the flow of the book. As well, mathematicians who read this book may question the accuracy of a few of the mathematical concepts that are introduced.

In conclusion, this book invites the reader into the wacky world of mathematical genius Paul Erdos. If you're like me, you'll find this book both comical and enlightening!!

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Stories about Erdos abound. It is rumored that he walked into a classroom, saw some writing on a chalkboard and asked if this was mathematics. Upon receiving an affirmative answer, he then asked what the various symbols were. Immediately after the explanations were given, Erdos took chalk in hand and in two lines proved the hypothesis that had baffled other mathematicians for some time, and this was in a field of mathematics that Erdos was largely unfamiliar with! Another story had Erdos taking a train fron Boston to New York; across the aisle sat a beautiful female who said "hello" to him. One thing led to another; by the time the train arrived the two of them had written a paper!

This book covered much of the life and mathematics of Paul Erdos; much of the mathematics in the book is number theory because it is a topic that is easy for anyone to understand yet difficult to prove. A typical example is Goldbach's conjecture, which says: "Any even number greater than 2 can be expressed as the sum of two prime numbers." Sounds simple enough and logical; 4=2+2, 6=3+3, 8=3+5,10=5+5 or 3+7,... The problem has been around for about 300 years but as yet lacks a proof. Other mathematics topics touched upon include Ramsey theory, the division of a square into unequal squares, and Godel's Incompleteness Theory. The book also shows the strange language of Erdos, in which women were 'bosses', men were 'slaves', the United States was 'Sam' (from Uncle Sam), and the Soviet Union was 'Joe' (Stalin), to list a few of his own variations of English.

This book is easy to read, even if the reader has only a high-school background in mathematics. If you are curious about mathematics and/or human nature, you will find this book of great interest. I highly recommend this book.