Amazon.com
Paul Erdös was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdös would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution.

Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdös's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdös never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdös: "A mathematical genius of the first order, Paul Erdös was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life."

The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind.Hoffman, who followed and spoke with Erdös over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdös is no doubt missed. --Therese Littleton ... Read more

Customer Reviews (92)

An enjoyable book about an eccentric math genius
This is a very interesting and enjoyable book about Paul Erdos, an eccentric math genius.

Speaking as a former college "Mathlete" (Kappa Mu Epsilon), I used to (and still do) have an abiding love for mathematical 'truths', and this book gives readers a brief introduction to some of the many ways that a sense of wonder & curiosity, focused on the universe through the prism of mathematics, can fire one's soul on many levels, both intellectual and spiritual.

As for myself - after a promising start, I peaked early back in undergrad school, and eventually left the field after finishing a minor degree, and moved on to other studies. However, my sense of wonder has remained ... and it was this book that helped me to recall some of my old joys, and to relive some of the might-have beens, had I been able to stay with it.

In any case, the book is a fine read. However, I have some nits that I've ranked them from most to least annoying:

1) MISSING PROOFS: The author, during his tale, mentions in passing many interesting mathematical problems and theorems that both Paul Erdos, and other mathematicians, helped to solve ... but in the vast majority of instances, the author anti-climactically fails to include the details of those proofs for the benefit of interested & proficient readers. IMHO, proofs of less than, say, 5 pages, could and should have been included in an appendix, and the author could have referred readers to appropriate AMS publications for those proofs that are longer and more involved. Instead, the author leaves the reader with nadda in all but a few trivial instances. It always irks me off when an author (or editor) dumbs down a book because they think readers can't keep up. Very annoying, and very anti-climactic. I mean come on - what's the point of spending pages and pages telling about the quest for a solution, only to finish lamely that yes, they solved it ... but omit all the details. Feh.

2) FOCUS: The author did a commendable job assembling and integrating a large array of verbal and historical accounts into a fairly coherent whole ... but he also has a mildly irritating tendency to meander around, in his focus, somewhat like a runaway horse cart. First forwards in time, then backwards, then sideways across various topics, then in the middle of nowhere we're talking about Fibonacci, Gödel, Gauss, then back to the present, and then to his childhood again, etc. In other words, the flow of the book is a bit uneven and fractured in places, and IMHO it could have benefited from some additional polishing and a bit of re-organization. I kept wanting to grab the reins and drag the book back on course. It's a fine ride, but it's a bit more rickety and bouncy then it could have been with some better editing.

3) ENDMATTER: The author/editor neglected to tie the "Acknowledgements and Source Notes" section in the rear of the book (p. 269- p.278) into the main text with some helpful endnotes or annotations ... thus rendering the section mostly useless to first time readers. Without notations to clue a reader in that that information is present in the back, then readers are left to finish the book unaware of it's existence until they reach the end ... by which time the information is of little or no value.

Highly enjoyable.Subtract a star if you're a math geek who prefers to see actual proofs, rather than simply taking solutions for granted, sans details.

Man Who Loved Only Numbers
Paul Erdos is presented as a sweet math genius. He loved children & Math, but never had life of his own. He lifed only to futher study of Math.

a popular math gem
I absolutely loved this book. A coworker of mine found this book depressing, but I thought it was a very uplifting story about a truly unique human being. I don't know where the title came from, as it is inappropriate, but everything else about the book was wonderful. Given the petty squabbles between scientists in many disciplines, it was very nice to read a story about collaboration such as that promoted by Erdos.

A very enlighten book for a math novice (like me)
I'm bad in math. Horrible to be correct. But this book is so easy to understand and even entertainning to read. Like some other reviewer said that it has all the things going on besides Erdos's life. This book may not have lots of detail about his accomplishment, which even for some that it has, not really offer a complete or clear explaination about them, but somehow it makes me want to know more and looking for anything deeper and more thorouoghly. Therefore, despite some flaws that it has, I love it. Such an entertaining when you consider it's something about math.

He loved numbers, mathematicians loved him.
Paul Erdös ("Air-dish") really did love numbers, and lived for mathematics. He was well known in maths circles, a legend, but known little outside. The book by Paul Hoffman introduces the work of this prolific numbers man to a new audience. It is at the same time a full of glimpses of the man, and tributes from those working mathematicians that he worked with. For there is no doubt that Erdös was an eccentric of the first magnitude, but Hoffman gives a picture of a well-loved man, who moved and inspired individual and groups of his colleagues worldwide.

Erdös made an enormous contribution in basic number theory, and Hoffman introduces readers to many of the ancient and modern problems of mathematics. Is it possible, for example, to predict the distribution of prime numbers? The relationship of prime numbers with each other is a well-known area of investigation in number theory, and ideas such as perfect numbers (where the sum of the factors equals the number itself - for example the number 6) and friendly numbers are well explored. Friendly numbers are where the sum of the factors of one number equals a second number, and the sum of the factors of that number equal the first number; the lowest friendly numbers are 220 and 284.

What has made Erdös so special is his relationship with so many of the world mathematics community; he co-authored papers with 485 individuals, and in some cases was a joint author with the same individual of 15 or more papers. His output was immense, even though he was working in basic number theory, an area where much work is done by young men. Yet he continued to make significant contributions almost right up until his death in 1996.

Erdös's brain was "always open" for mathematics. He even made group maths possible, or even `invented' it,, often with several different groups in the same room, with the aged Hungarian as the lynch pin, flitting between groups engaged on different subjects. The affectionate guide by Hoffman to his life and achievements is infectious, for those with an interest in mathematics. And so was Erdös, who wanted to prove theorems, and to prove them elegantly, but was very actively engaged in encouraging and nurturing others in his obsession. Erdös had no passions in life, maths was his life.

Individuals who had written a paper with the Hungarian are said to have an Erdös numbers of 1, and to have achieved this distinction is a great accolade. Even Einstein only achieved an Erdös number of 2, having written a paper with a person who had written a paper with Erdös.

Hoffman gives a good view of the man, a glimpse of how he worked, but comparatively little about his achievements, probably because non-mathematicians would not understand it. What he does show is that without Erdös, the world is a poorer place, both mathematically, and because of his unique ways.

Peter Morgan, Bath, UK [...].
... Read more

Book Description
This rather unique book is a guided tour through number theory.While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors havechosen instead to illustrate the many varied subjects by associating recent discoveries, interesting method, and unsolved problems.In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös.Janos Suranyi's vast teaching experience successfully complements Paul Erdös' ability to initiate new directions of research by suggesting new problems and approaches.This book will surely arouse the interest of the student and the teacher alike.Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers.While his papers contributed to almost every area ofmathematics, his main research interest was in the area of combinatorics, graph theory, and number theory.He is most famous for proposing problems to the mathematical community which were exquisitely simple to understand yet difficult to solve.He was awarded numerous prestigious prizes including the Frank Nelson Cole prize of the AMS.Professor Janos Suranyi is a leading personality in Hungary, not just within the mathematical community, but also in the planning and conducting of different educational projects whiich have led to a new secondary school curriculum.His activity has been recognized by, amongst others, the Middle Cross of the Hungarian Decoration and the Erdös Award of the World Federation of National Mathematical Competitions. rian Decoration and the Erdös Award of the World Federation of National Mathematical Competitions. ... Read more

Amazon.com
Physicist and science writer Bruce Schechter's biography of legendary Hungarian mathematician Paul Erdös is an engaging portrait, warm and intimate, bringing this strange, happy man to life. Schechter's focus is quite a bit tighter, and more traditionally biographical, than Paul Hoffman's in The Man Who Loved Only Numbers. Here, we get to see Erdös's brief childhood transform quickly into a carefree adolescence of solving difficult math problems with his circle of brilliant friends--uniquely encouraged by a country that valued the contributions of mathematics in a way that has never been equaled. Fleeing the Holocaust, Erdös never settled down, instead traveling from place to place, showing up on the doorsteps of other mathematicians with his few possessions and an open mind. During his career, Erdös published more papers than any other mathematician in history. Most of the papers were collaborations:

For Erdös, the mathematics that consumed most of his waking hours was not a solitary pursuit but a social activity. One of the great mathematical discoveries of the twentieth century was the simple equation that two heads are better than one.... That radical transformation of how mathematics is created is the result of many factors, not the least of which was the infectious example set by Erdös.

... Read more

Customer Reviews (33)

The perfect man of knowledge
If one has to define a perfect man of knowledge, one would come up with someone who is a genius, has done pioneering work in several areas of his domain, is friendly and sociable towards all (especially 'epsilons' or children), finds material possessions as a hassle and spends all his time doing what he loves best. In other words, someone just like Paul Erdos.

In this short and engaging biography, the author manages to inform and entertain at the same time. Apart from the life-story of Erdos himself which is fascinating, what I also enjoyed are the anecdotes on other greats like Gauss and Ramanujan. And there is just enough math in the book (explained very well) to interest us so that we get a glimpse of what lies at the heart of it all.

I cannot think of a better gift than this book to be given to any child to provide inspiration as well as a 'cool' introduction to mathematics. Highly recommended.

N is a Number: True Story of the Travelling Mathematician
+++++

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!!

+++++

The hidden magic of math
Bruce Schechter's book is exceptional.In telling this fascinating story of the eccentric mathematician Paul Erdos, the author manages to convey the recent history of math and capture the magic of this unique art/science.Quite an accomplishment for a book that is so enjoyable to read!

The Remarkable Saga of a Remarkable Man
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.

Sympathetic insight into the world of mathematicians
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! ... Read more

Book Description
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics in this century, with over 1200 papers on number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some fifty outstanding unsolved problems, together with their "values." ... Read more

Book Description
This volume contains a collection of papers in Analytic andElementary Number Theory in memory of Professor Paul Erdös, oneof the greatest mathematicians of this century. Written by manyleading researchers, the papers deal with the most recent advances ina wide variety of topics, including arithmetical functions, primenumbers, the Riemann zeta function, probabilistic number theory,properties of integer sequences, modular forms, partitions, andq-series.
Audience: Researchers and students of number theory, analysis,combinatorics and modular forms will find this volume to bestimulating. ... Read more

Book Description

A man with no home and no job, Paul Erdös was the most prolific mathematician who ever lived. A wandering genius, Erdös, who died in 1996 at the age of 83, spent his life engaged in a cosmic struggle to uncover truths hidden by a stubborn adversary - God. In N is a Number he describes this metaphysical duel with the same wry humor he applied to politics, relationships and death. The documentary follows him through four countries to discover what makes mathematicians tick. N is a Number presents Erdös' mathematical quest, its personal and philosophical dimensions, and the tragic historical events that molded his life. Two animated sequences illustrate the kinds of problems Erdös pursued throughout his life. N is a Number is a one-hour documentary film made with support from the American Mathematical Society, Films Arts Foundation, the Heineman Foundation, the Mathematical Association of America and the National Science Foundations' Information Science Education Program. For the DVD additional scenes with Paul Erdös have been added.

Book Description
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdös, one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdös' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 900 pages, arranged into two volumes. These volumes contain both high level research articles as well as "key" articles which survey some of the cornerstones of Erdös' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdös complement this striking collection. A unique contribution is the bibliography on Erdös' publications: the most comprehensive ever published. ... Read more

Book Description
This collection of surveys and research papers on recent topics of interest in combinatorics is dedicated to Paul Erdös, who attended the conference and who is represented by two articles in the collection, including one, unfinished, which he was writing on the eve of his sudden death. Erdös was one of the greatest mathematicians of his century and often the subject of anecdotes about his somewhat unusual lifestyle. A new preface, written by friends and colleagues, gives a flavor of his life, including many such stories, and also describes the broad outline and importance of his work in combinatorics and other related fields. ... Read more

Book Description
A tribute to Paul Erdos, the wandering mathematician once described as the prince of problem solvers & the absolute monarch of problem posers,examines within the context of his personality & lifestyle the legacy ofopen problems he left to the world of mathematics after his death in 1996. DLC: Graph theory. ... Read more

Customer Reviews (2)

Immediate throw away for non-professional Mathematicians
I got a book by Ron Graham and Fan Chung.
It is amazingly bad.
It is a book on graphs without one graph diagram
or graph matrix.
I buy these books for learning.
I'm left with not being able to give an honest review
because it would be politically suicide in Mathematics to
cross Ron Graham who has been president of both Mathematics societies.
The book is a very badly written one, too,
with a few mostly ancient( from as far back as the 1930's )
problems in graph theory.
I have to go to MathWorld to get an idea of what the graphs might look like!

Since it appears that the graphs are the dog that wags the matrices,
I thought I might get further with some better understanding.
It appears this book is the wrong place to get it.

One reason as I see it that Fan Chung and Ron Graham
don't answer emails much is that they really aren't all that nice, good or smart:
their "meal ticket" was Erdos and he is dead now.
That's not a "pretty" conclusion or one I wanted, you know?
Tattle tale stories about the great man aren't going to save this one.

Even for me this may take years to get my money's worth out of.
I looked at the review by Charles Ashbacher and I had to set the record straight.
He is a friend of a friend who is also into integer sequences.
Somebody has to be honest here.

Only one of many such books that could be written
What is incredible about this book is not that there are over one hundred pages of unsolved problems posed all or in part by Paul Erdos. The amazing thing is that the word graphs could be replaced by several other mathematical words or phrases and a similar book could be written. Erdos was an expert in so many areas of mathematics and perhaps his greatest ability was in putting forward just the right questions to just the right people. There is very little explanation of the problem proposals, the authors rely on a great deal of the listing of references to fill in the details. Therefore, anyone interested in exploring the problems in greater detail should be prepared to spend some time and effort in tracking down the relevant articles. Fortunately, the authors themselves did a great deal of that, as there are complete references for every problem that appears.
The range of problems is a demonstration of the depth of his understanding of graph theory, and also a demonstration of how little is still unresolved. I put forward no pretense to understanding any more than a few of the problems in this book. However, that did not alter my interest in the problems, as I was able to understand the fundamentals of almost all of them. Reading this book is one of the most educational experiences that I have had in the past year and I encourage all mathematicians at the level of slightest interest in graph theory and above to read it.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Book Description
Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul Erdös. From July 4 to 11, 1999, the conference "Paul Erdös and his Mathematics" was held in Budapest, with the ambitious goal of showing the whole range of Erdös' work - a difficult task in view of Erdös' versatility and his broad scope of interest in mathematics. According to this goal, the topics of lectures, given by the leading specialists of the subjects, included number theory, combinatorics, analysis, set theory, probability, geometry and areas connecting them, like ergodic theory. The conference has contributed to changing the common view that Erdös worked only in combinatorics and combinatorial number theory. In the present two volumes, the editors have collected, besides some personal reminiscences by Paul's old friends, mainly survey articles on his work, and on areas he initiated or worked in. ... Read more