My Brain Is Open: The Mathematical Journeys of Paul Erdos

Paul Erdos was a unique individual. He never had a permanent residence; instead, he traveled from one mathematics conference to another with his few earthly belongings in two suitcases, one which held a few changes of clothes, the other a treasure of mathematics papers. He collaborated with mathematicians everywhere; the extent of these collaborations is so immense it gave rise to the Erdos number, which is this: You have an Erdos number of 1 if you co-authored a paper with Erdos, your Erdos number is 2 if you co-authored a paper with someone who jointly wrote a paper with Erdos, etc. About 500 people have an Erdos number of 1 and well over 5000 hold the Erdos number of 2. Erdos numbers go as high as 16 and the number of people with an Erdos number is said to be well above 100,000.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.

This beautiful book is an intellectually rich biography of one of the world's most prolific mathematicians. Amusingly, inoffensively and highly idiosyncratic, Erdos worked on hard problems in apparently simple fields, taking rather easily explained concepts and forging powerful new results and tools with a speed which astounded professional colleagues. Bruce Schechter does a magnificent job of clearly explaining what Erdos did and the many connections between his work and other areas of mathematics and, more generally, science. Through frequent digressions he paints both a humane portrait of a uniquely caring individual and a thumbnail sketch of western political oppression around the world during the first sixty years of this century. This book also will introduce readers, in a gentle and interesting manner, to the world of numbers and mathematics. The nature of prime numbers and how they are distributed, famous conjectures such as Goldbach's, topics in graph theory and combinatorial mathematics, and more are made accessible to the reader. The account of the controversy surrounding the "elementary" proof of the Prime Number Theorem benefits from the author's access to newly available material, and will be of interest to both laypeople and mathematicians. Other topics, introduced through natural association with the subject at hand, include Godel's Theorem, Russell's paradox, the Monty Hall problem (made famous by Marilyn vos Savant), the nature of infinity, proving theorems by contradiction, and the normal distribution. Though Erdos is known to many for his unusual life style and behavior, this book does not dwell on the bizarre but weaves such facets of his life into the more exciting mathematical development of the person. This biography ranks among the very best of the numerous works about mathematicians which I have read over the past 45 years. Arguably, more has been written about Erdos in the past decade or two than about any other mathematician. Despite this, Schechter's new contribution is an outstanding addition to the literature

Wonderful book. The authors brings the mathematical genius of Erdos very much alive. The complex theories are presented in way that even laypersons can appreciate.

Schechter takes you by the hand and walks you through some stunning yet simple mathematical proofs that are real eye-openers for a layman like myself. He doesn't just talk about math, though. For example, one chapter has Paul Erdos explaining a simple proof to the non-math-literate wife of a colleague. You get to see the proof (which was nifty) as well as the way Erdos interacted on a human level. It's the kind of thing this biography does fantastically well, i.e., math in a thoroughly human context. Erdos is a very charming and unusual person who comes alive along with the math. The book is written in stories, anecdotes, and observations about math in general and Erdos's contribution in particular. It could be understood by a tenth grader who is bad at math but it's still written in an adult and intelligent tone, not one that talks down to the reader. One of the best popular math or science books I have ever read. I liked it better than Gleick's book, Chaos, and Gleick's bio of Feynman (though these were also very fine books, in my opinion).