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4.7 out of 5 stars
MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos
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32 of 33 people found the following review helpful
on March 18, 1999
Format: HardcoverVerified Purchase
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
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26 of 28 people found the following review helpful
on September 22, 2001
Format: PaperbackVerified Purchase
I read this book after reading the one by Paul Hoffman. I would say that this one by Schechter is a little easier to read, flows better and is better organized. There is a great deal of overlap, but I was glad I read both. I liked reading about the Monty Hall problem and about Erdos' getting water all over in the Hoffman book, but Schechter had the conflict with Selberg in his book, which was meaningful to me. I guess I would recommend reading both.
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11 of 11 people found the following review helpful
on June 20, 2002
Format: Paperback
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.
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16 of 18 people found the following review helpful
on November 16, 1998
Format: Hardcover
I liked the other bio of Erdos by Paul Hoffman, "The Man Who Loved Only Numbers," but Schechter's bio presents a fuller picture, showing that Erdos loved a lot more than just numbers. There is a new review of Schechter's book from the Mathematical Association of America (MAA) by a fellow who also reviewed the Hoffman book, and I think he hit the nail on the head when he said that he liked Hoffman's book, "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." Why has Hoffman's book gotten more attention? The MAA reviewer says "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." It's a shame that Schechter's book wasn't promoted more heavily, though the book did reach the Amazon top 50 after it was called "better" than Hoffman's book in the Wall Street Journal. This is the one to buy, in my opinion. Don't let accidents of hype lead you to read the wrong book. "My Brain Is Open" is the better book by far.
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4 of 4 people found the following review helpful
on April 5, 2002
Format: Paperback
I enjoyed this book and thought that Bruce Schechter did well to get across the humanity of the man and as well as some of his ideas. Inevitably, the mathematics contained in the book will seem a bit hard going for some but Schechter handles it delicately and manages a fair balance.
The book is written in an approachable style and has a deliberately non-critical and inspirational tone. I recommend that it should be put in the hands of any teenager who is thinking of studying mathematics at university. If she/he does not like the ideas and characters described, he might be happier choosing another major!
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8 of 10 people found the following review helpful
Format: 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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3 of 3 people found the following review helpful
on March 31, 2008
Format: PaperbackVerified Purchase
Shurik, a friend of mine I used to share student dorm with, was a mathematician. Algebraist, to be precise. We talked a lot discussing multitude of topics, not necessarily mathematical ones. In those days hot water was customarily shut off across campus during summer season so students could prepare for exams without such a distraction as hot showers. That fact prompted me to comment that our lifestyle, while notably different, still somewhat resembles what a lifestyle in Upper Paleolithic might look like. Shurik was digesting my remark for a few moments with the stamp of intense thinking on his face (his Calculus test was next day), then said excitedly:

- Dude, you know why there was no hot water in Upper Paleolithic? That's because the water pressure was not strong enough in the Lower Paleolithic!

That insignificant episode from my student years characterizes true mathematicians very eloquently. They are quite unusual breed of humankind with extraordinary abilities to locate not very obvious properties and relations in seemingly regular objects and notions. Having been exposed to interaction with mathematicians for sometime I, by the time the book of Mr. Schechter was read through, felt I knew Paul Erdos almost personally. Very light and elegant writing style of the author was a contributing factor as well.

Mathematicians rarely can be aggressive. Usually, they are very sensitive and kind people. In this regard the portrait of Paul Erdos by Mr. Schechter goes along quite naturally with my experience of dealing with them. At the same time that portrait leaves a very sad impression of the true inner nature of Erdos - depressingly lonely person, with no family and no home. The deep tragedy of the Erdos family with Paul's siblings gone by disease, father's suffering in Russian exile, terrible WWII ordeals - all that makes you wonder how Paul and his parents can continue "to prove and conjecture" so successfully under such horrendous circumstances? Author partly explains this phenomenon very brightly describing the scientific and especially educational traditions in Hungary before the war. Indeed, the density of incredible talents generated in this small central European country somewhat shocking. It underscores how important the role of truly good teacher in elementary school can be. Taking into account all that and also the fact that both parents of Erdos were superior math teachers in high school themselves a reader can see the roots of the enormous productivity of Erdos, who published more math papers in multiple branches of it than any other scientist in history. But it also can be a city of Budapest whose streets, as per Mr. Schechter, are very inviting for any kind or scientific reasoning - although not a scientist myself, I did experience the same when I was roaming with friends along Duna shores in Buda one summer.

The mathematical content of the book is very engaging for non-mathematicians. It is explained almost with no formulas but Mr. Schechter manages to convey the depth of the mathematical ideas very well without them. It is especially applicable to the chapter about prime numbers. The primes, although endless in the set of integers, do have very strange properties. Take the theorem proved by Chebychev first and re-proved by Erdos by elementary means - between N and 2N there is always a prime. At the same time we know that the intervals without primes can be as long as one would wish. At first glance two facts seems to contradict to each other but they do not. Facts like that are abundant in the Numbers Theory with most enigmatic one as a problem of primes distribution and Riemann function. Mr. Schechter does a good job providing historical background of the Numbers Theory, its evolution, contributions of Paul Erdos and controversy of Erdos and Selberg.

I have to admit the author did a brilliant homework researching all kinds of details pertinent to mathematics and its origins. I did enjoy pages about clay table Plimpton 322 with its incredible content of Pythagorean triplets as well as multitude of other stories like most bizarre "application" of Numbers Theory when close collaborator of Erdos avoided deportation to Gulag just because he happened to have his publication on the subject in Russian mathematical magazine with him. In this regard, the book of Mr. Schechter can be considered as not so much as biography of Paul Erdos but as biography of mathematics as a scientific discipline. Humor, albeit sometimes very dark (for example, about math students, who were "studying" Jordan theorem being confined to "inner area", id est being imprisoned) sparking the text regularly and appropriately.

Mathematics is somewhat similar to soccer. While everybody can perceive the beauty of ball handling by say Riquelme or Robinho, very few of us can do the same on the soccer field. In math, formulation of the conjecture can be deceptively simple and elegant, and most of us can understand it well. At the same time, it is very different story once you start thinking about trying to prove that conjecture. In many cases it might require years of learning and tons of exercises. But even that no guarantee to success. The inclination to a special way of thinking is required. In this regard, magic of Riquelme on the stadium is direct equivalent of wizardry of Erdos in Numbers Theory. The books similar to Mr. Schechter facilitate our comprehension of the conjecture beyond mere formulation, opening the curtain after which the proof is hidden.

On the other note, I can't stop thinking of what kind of future European science might have should its development was not brutally aborted by sad realities of Second World War. True, many of bright Hungarian (and other) minds escaped from the inferno of warfare and extermination campaigns; true, many of them intensified their research in military related directions and achieved significant results. Still so many perished needlessly making a good number of famous European scientific centers empty and forgotten for a very long time. It seems incredible that one person's paranoia can mercilessly terminate so much in such a short period of time. Let's us hope the future Erdoses will never be forced to travel so intensively against their wills even with theirs brains open so widely.
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3 of 3 people found the following review helpful
on December 15, 2001
Format: PaperbackVerified Purchase
Every time I picked up this book and read a few pages, it made my day. Who would have thunk I would read a book about a number theorist? Not I! Too arcane! But the story is delightful, the mathematics accessible and stimulating. Altogether an easier and far more delightful read than one would imagine. You will recommend it to others. I bought it for my 13-year-old son's Christmas. It will be his favorite gift.
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2 of 2 people found the following review helpful
on June 29, 2011
Format: Paperback
My Brain Is Open, by Bruce Schechter, takes us on a journey through the life of one of the most creative mathematicians, Paul Erdos, and certainly one of the most productive, of the twentieth century (and quite possibly of any century). Schechter provides an interesting portrait of Erdos, through his struggles early in life, and then later in a period, following the 1950s, when numerous mathematicians began to collaborate with him, and his work became widely respected and admired. His dedication to mathematics was remarkable, but using some simple, and illustrative examples, Schechter is able to convey something of the appeal that mathematics held for Erdos, and one can only say, the "magical" world of mathematics that surrounded his youth in Hungary. One cannot help feeling, after reading the biography, that Erdos was somehow able to preserve this magical world of his childhood, and that in some important respects, he did not grow up. It is unlikely that many other mathematicians were both as gregarious as Erdos, and traveled as much. There is certainly a sense that is conveyed in this biography of his "elementary" style of doing mathematics, his originality, the quickness of his mind, and his ability to delve deeply into mathematics through examining specific problems, rather than constructing whole theoretical edifices. Conventional thinking would fault his focus on problems and conjectures, and interdisciplinary work, for producing much of minor significance. However, it is clear that, while Erdos was open to an enormous variety of problems, he had an "instinct" for problems of central importance. Interdisciplinary work can be of great value to people. One must focus on work that is deep, to offer a challenge, but not so deep that the challenge goes into specializations beyond the level of the investigators. In addition, the research must be "hot", i.e. of much current interest, and something that the important aspects of the research can be comprehended in small chunks rather quickly. Erdos was something of an expert at finding such problems and conjectures. His world was an exciting one of engagement with mathematics that draws all of us into its domain of attraction even today after much of the currency of the problems he considered has worn off. However, his world of mathematics was merely a tiny part of the vast world that he encountered. This greater world was very troubled by both fascism and communism during much of his life and this is in evidence in this biography. Despite his "charm" (many would say "eccentricity"), his life seemed to have an edge of sadness about it, certainly not so surprising when one considers the horrors of WWII, and its immediate precursors and aftermath in history. This book treats this larger world to some extent, and gives us Erdos' life with much sympathy and warmth. The biography itself is enlightening, in helping us to see something of one of the great mathematicians of the twentieth century in human terms, rather than as a mere caricature from his eccentricities. We come away affected by his passion for mathematics and his openness to other people and the world, or at least I did, feeling a great excitement for the world of mathematics.
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2 of 2 people found the following review helpful
on February 9, 2002
Format: Paperback
What would be your answer if somebody asks you the meaning of life?Here is the story of a man who says it lies in just two words "Prove and conjecture".True to this,Paul Erdos spent close to 80 years of his life just proving theorms and formulating his own theorems and proofs and conjectures.Bruce Shechter gives a wonderful picture of the 'MATHMAN'.More specifically ,this is a lucid account of a genius who taught *How to count*.The author is also successful in giving a good portrayal of the Humane Erdos and the Westernised Mathematician.
Here is a man who would spend 18 hours each day doing mathematics.For those Math-fearers,here is the story of a successful man who loved maths and lived with it all through his life through days and nights.
This book also introduces readers to the wonderful concept of numbers,the prime number theories and combinatorics.And Bruce Shechter has also been quite succesful in not touching upon the other facet of the man-his unusual behaviours as known in the Mathematics Circle.
In the process of reading this you also get acquainted with many mathematicians of his times and their realted works.Paul erdos dwelled in the Kingdom of infinity with an unquestionable Kingship and that shows his genius that was pronounced since his childhood.
What a way to point Hungary on the atlas!
Read this book and you will know.
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