Customer Reviews

The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth

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1 star:		(6)

 

 

I very much enjoyed this biography (Hoffman calls it "in large part a work of oral history") of the legendary Hungarian mathematician, Paul Erdös. Hoffman's relaxed style with his attention to detail and concrete expression makes it a pleasure to read. You don't need to know any mathematics. Hoffman mentions the math and occasionally goes lightly into it, but for the most part the focus is on the eccentric and loveable mathematician himself and his many friends and collaborators. In fact, the title is somewhat ironic since Erdös was very much a people person, a man who loved and was loved by others. It is only in the case of "romantic" love that Erdös loved only numbers.

By the way, Hoffman does indeed go into Erdös's sex life in a completely tasteful and PG-13 sort of way. He was a man who dearly loved his mother and children but practiced a deep and abiding celibacy all his life. His friends made many jokes about his uneasiness with "bosses" (his pet name for women) and once made a bet with him that he could not go to a burlesque show. He did however, but took off his glasses so he couldn't see anything.

Erdös was a pure mathematician, a child prodigy who fell in love with numbers at an early age and never lost his love while wandering over the entire globe searching for collaborators. He was himself a caricature of the absent-minded professor, a man who asked others to tie his shoes for him, a man who could not drive, who worked nineteen hours at day at mathematics, often calling his friends up at four in the morning to share an insight. He paid no attention to his appearance, cared nothing for literature, the arts, sports, etc., only for his beloved math. He had a way with children and an ability to impose on his friends, often arriving unannounced at their houses and staying for days or weeks at a time. He freely gave away his money to any number of charities, and sometimes to outright strangers on a whim. He cared nothing for worldly goods. He didn't even like applied mathematics, referring to colleagues who had gone that route, as being "dead." Indeed, only children and pure mathematics delighted him.

There's a child-like simplicity to the man that charms us. Hoffman's book reflects this as a kind of fairy tale life lived in delight in spite of all the horror going on in the world. There is a pristine beauty to living one's life so incredibly focused on one thing. In a sense it is like an addiction and in another it is like an all-consuming love. It is the kind of life few of us could ever live (or would want to live), but it is the kind of life we can admire and read about with pleasure.

Hoffman sometimes slips away from Erdös to write about his family and friends, especially about Ronald Graham, Erdös's long-time friend and collaborator, a very interesting man himself, a world class juggler and a practical as well as theoretical mathematician. Hoffman recalls some Hungarian history, some Cold War history, and relates anecdotes from friends and family. He devotes a chapter to Fermat's Last Theorem, Fibonacci numbers, the Prime Number Theorem, etc., and then part of a chapter to the Monty Hall dilemma and the tussle between Parade magazine columnist Marilyn vos Savant and her detractors. There is also a lot of humor, which is appropriate because Erdös liked witticisms and used humor as a way to deal with the world. "Soon I will be cured of the incurable disease of life," he is quoted as saying on page 173. He adds, a little later, still in a sardonic mood, "Television...is something the Russians invented to destroy American education."

There are some photos, a bibliography and an index. Hoffman does not glorify Erdös as much as some would like, but this is an affectionate and balanced, very interesting portrait of a true original and a great mathematical genius.

This is a disappointing book. Certainly Paul Hoffman should be commended for writing a math book that so many people find lively and informative. Probably it is the only profile of a mathematician that many people will read. But the author makes mistakes of several types. There are what might by typographical errors. For example, on page 252 we find a description of Béla Bolobás who "won Hungary's infamous student math competition..." If the competition is in fact infamous, the reader is never told why.

There are errors of fact. For example, a fainting episode described on pages 244 and 245 as having happened in Boca Raton actually happened in Baton Rouge and was later repeated in Kalamazoo. We learn in this book that Kurt Gödel was an Austrian. This will come as sad news to Czechs and Moravians.

There are less objective examples. For instance Erdös is credited with developing the probabilistic method. While Erdös certainly championed the method and demonstrated its power, it is overreaching to give him all the credit. I would not want to guess as to who first used it, although some attribute it to William Feller. Certainly Tibor Szele used the method in a paper published in 1943. The paper was reviewed by Erdös in Mathematical Reviews. He did not use it until his paper on Ramsey Theory in 1947.

But these sorts of problems are mostly minor and have been perhaps corrected in subsequent printings. There is a deeper problem with the structure of the book. Much of the book is based on the author's 1987 article which appeared in The Atlantic Monthly. Discover Magazine also published some of the book. As magazine articles, I thought they worked very well. But the book has a disjointed impressionistic tone that seems distracting. And while Hoffman gathered enough material for two fine magazine articles, he doesn't seem to have enough for a book. So it is diluted with superfluous, albeit interesting, material. These detract from the story. For example, there are discussions of Fermat's Last Theorem and Andrew Wiles contribution. There is a discussion of infinity and set cardinality similar to what would be found in a discrete math textbook published ten years ago (and sadly missing from most textbooks today). Gödel's incompleteness theorem is presented. But donations by Erdös to these things is given little discussion mostly because, I suppose, his contributions to those topics is tangential.

Hoffman has a fascination with Erdös's brilliance, portraying him as an uncanny wizard. There is no denying he had an incredible mind. It's possible that all of the book's anecdotes are true. But still, they seem to miss the target. This is not how Erdös really was. His mind was human. He could interchange maximums and minimums and mix up quantifiers. He sometimes had trouble (as many great minds do) with arithmetic. I recall once asking him about an important theorem he proved with Endre Szemérdi. He didn't recall the result and seemed surprised by its existence. On one occasion he asked me to reproduce a proof he had previously shown me. We went through it twice when he asked to be left alone for half an hour. On my return he said, "I am sorry for being such a stupid old man. Yes, you are right. This proof is correct." No doubt, part of his success rested on natural talent. But much rests on his passion and dedication to mathematics.

But again, I can forgive these problems. My most serious concern is the way this book reduces a kindhearted loveable human to caricature. While Hoffman interviewed many people, including Erdös, Hoffman's account seems to have missed the flesh and blood and left us with a wacko schematic. Nobody will deny that Erdös was a special man with a special personality. He warmly gave so much to so many; especially to young mathematicians and graduate students who would go on to owe much of their careers to his generosity. But portrayed here is something freakish, something best left to carnival sideshows and wax museums. Fascination with his personality seems to be growing; drawn in grotesque proportions. Time Magazine profiled him under the heading "The Oddball's Oddball." His eccentricities are outlined in "Strange Brains and Genius," Clifford Pickover's book on twisted brilliant minds. One wonders how much responsibility Hoffman's writing has in contributing to this persona. The reduction extends even to the title. Paul Erdös did not love only numbers. He loved history, politics, philosophy, science. He loved ideas in just about any area. But most of all, he loved people

Paul Erdos' position in number theory of the 20th century is pretty much like Miles Davis' in jazz: in some way or another every important figure in number theory has worked with Erdos, much like every influential jazz musician collaborated with Davis at one point in their respective careers. This may explain the number theorists' obsession with calculating their "Erdos number" (a person is said to have Erdos number one if the person wrote a mathematical paper with Erdos; a person with Erdos number 2 is a person who wrote a paper with a person with Erdos number 1, and so on and so forth. For more information on Erdos number visit oakland.edu/~grossman/erdoshp.html). Erdos was a prolific mathematician. According to the statistics compiled in the site just mentioned, he was the one who authored the most papers in the entire history of mathematics, even surpassing Euler.

The book is a collection of anecdotes related to Erdos. I say "anecdotes" because the book does not follow the usual birth-till-death timeline approach for biographies. Each chapter roughly corresponds to a story surrounding important collaborators of Erdos for a certain type of mathematical problem, not necessarily ordered chronologically. Erdos appears in these anecdotes as a person who cared dearly for his mother (he did not have his own family, not to mentioned he that he died a virgin according to his own words), mathematicians of all sorts regardless of their nationalities, children; as a person who despised anything that confined anyone's freedom, including God, or to put it in his words, SF, the "Supreme Fascist"; as a person who did not even have the ability to operate the most basic things, like operating air conditioners or even slicing a grapefruit with the right side of a knife (according to this book Erdos confessed that the first time he applied butter to bread was when he was in his 20s -- before Erdos' mother took care of him, and henceforth his friends/collaborators did); as a person whose earthly interest was zero (he never had a house -- he lived off at friends/collaborators), who gave everything he earned to any charity organization and every person in need (his entire possession fit into two suitcases); as a person whose love towards mathematics none equaled (he traveled incessantly to give lectures and worked 18 hours daily till he died); as a person who nevertheless feared death.

The book's format may have been just right for describing Erdos, whose life perhaps had no other way of being described of other than through mathematical problems. However for 1) the lack of information re. Erdos' "real" accomplishments (omitted most likely for general accessibility), 2) the author's occasional deviation from Erdos (for e.g. an entire chapter devoted to Fermat's last theorem which almost has nothing to do with Erdos; retelling of the most "popular" paradoxes of mathematics) which I felt catering to commercialism, I do not feel that the book depicted Erdos' life the best. The book is at best an entertaining read of one of the most interesting and influential mathematicians of the past century.

Paul Erdos, a giant of twnetieth century mathematics, takes center stage in this biography which discusses the extent of both his brilliance and eccentricities. This is a man who made up his own language, roamed the world to discuss mathematical theory, befriended and frustrated his hosts and collabortators, and in is universally remembered as a loving genius. The book itself is a series of vignettes about Erdos's life woven together with explanations of numberous mathematical problems and theories, as well as stories of other math legends. It is very inclusive of the Erdos's predecessors as well as contemporaries, and shows the evolution of mathematics, within the larger context of a biography.

I loved this book, mainly because of Erdos, who was a wonderful character. I was a poor math student in school, but Hoffman's descriptions made these incredibly complex ideas that Erdos played with understandable and interesting. Also, I learned a lot about the field of mathematics, mathematicians, and about passion. These men and women devote their lives to theorems that may never have any real appication, but they do it because of a love for the subject. It was facsinating and inspiring throughout, and a wonderful book for those who want a good story, great characters, and an understandable lesson in math.

Being something of a 'lapsed' mathematician (long ago math major, long unused), I'm always interested in books that involve numbers and people who love numbers. I'm usually not fond of biographies, but I'd heard good things about this one and decided to give it a try. To my surprise and joy, it turned out to be more about numbers and math in general, than about those irritating details of a person's life that usually get in the way of a good read. I agree with one of the earlier reviews here that trying to write an entire book devoted just to Paul Erdos would probably have been futile -- his entire life was numbers. This book opens doors for people who aren't familiar with the various theories and offers some 'math surprises' for those of us who were familiar with math in a former life. I'm still puzzling over the tiling result. (Sorry, you'll have to read the book to find out what it was.) Loved it. Highly recommend it. Have so far purchased two copies as gifts and will likely purchase at least two more (I have a lot of math-oriented friends).

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.

Paul Hoffman wrote an award-winning article on Erdos many years ago. I have to agree with the New Scientist, which said that his book on Erdos is like a bulked up magazine article. It's a fun read, but sloppy, poorly structured, riddled with "filler"-type digressions, and often rambling and disjointed. The other Erdos Biography, My Brain Is Open: The Mathematical Journeys of Paul Erdos (Simon & Schuster), by Bruce Schechter, is far superior. It has all the fun of Hoffman's book, but Schechter doesn't lose the reader with a lot of puffy digressions and he stays focused on Erdos's life and work rather than boring the reader with inconsequential facts. I also don't like the way Hoffman puts himself into the narrative of his book, telling us in the first person how he (Hoffman) feels about various issues. This was supposed to be a book about Erdos, not Hoffman, and Hoffman wasn't even a bit player in Erdos's life, so why does Hoffman think it's important to tell us about himself throughout the book? It's rather tedious and distracting to hear him say "I" all the time in a book that's not about him in any way (or shouldn't be). I would definitely point the reader to Schechter's book for a far better bio of Erdos, one which doesn't just take a core magazine portrait and bulk it up but which was written from scratch by a fine writer who has mastered the material. In short, Hoffman's book is fun but flawed. Schechter's book is the one to buy and read.

I received this book as a gift, and as a non-mathematician I thought it was both an interesting biography and an engaging overview of some of the key events and themes in modern mathematics.

Fair warning: it won't in particular teach you any mathematics per se; it's more about painting a picture of how mathematicians go about doing the things they do, and what makes them tick.

I would recommend this to those who like to read biographies, or those who are specifically interested in Paul Erdos himself, or those who are interested in the mathematics profession (that is, about what mathematics is like as a pursuit or profession).

If, like me, you want a quick, easy read about this fasinating man, this is the book for you. However, if you want a biography that completly covers Paul Erdos, this book is not for you. The author often wanders to other subjects (Other number thoerists)--not that they are bad, he just often gets away from Erdos. Still though, it was worth my money. I recommend it.

The story of Paul Erdos was fantastic and fascinating. To begin with, he had no home. His entire earthly belongings were in two suitcases; one held a few items of clothing, the other was full of mathematical papers which accompanied him as he traveled around the world going from one mathematics conference to another, pausing long enough only to deposit some works in an archive at the home of Ronald Graham and Fan Chung, a husband-and-wife team of remarkable mathematicians in their own right.

Paul Erdos was known as the greatest of mathematical collaborators; he co-authored far more papers with other mathematicians than did anyone else. The extent of his collaborations with other matheamticians has given rise to what is now known as the 'Erdos number' which is simply this: If you co-authored a paper with Erdos you have an Erdos number of one, if you wrote a paper with someone who wrote a paper with Erdos, your Erdos number is two, and so forth and so on. As far as I know, the highest Erdos number is eight. Approximately five hundred mathematitians have an Erdos number of one, the number having an Erdos number of two or higher is well into the thousands; a compete listing is maintained by Jerry Grossman of Oakland University.

Erdos had virtually his own language, to him the Unites States was 'Sam' (for Uncle Sam) and the Soviet Union was 'Joe' (for its long-time leader Joseph Stalin.) Women were 'bosses' and men were 'slaves'. A person 'died' when he or she ceased doing mathematics; when that same person actually expired, he or she 'left'.

This book gives a good look at what goes on in the mind of a mathematician. While there is plenty of mathematics in this volume, the book is written in such a manner as to be understandable by anyone with a high-school education; little or no specialized training in mathematics is required to reap full enjoyment from it. Even if you are unfamiliar with such concepts as Mersenne or Fermat primes or repunits, this book will be both entertaining and enlightening. I believe this book is a better 'read' than Sylvia Nasar's "A Beautiful Mind;" the major focus of the latter book was not so much about mathematics as it was about schizophrenia.

There is no doubt that Paul Erdos was one of the most extraordinary people you could ever wast to meet. This work belongs in the library of any person who may be even the least bit curious about what goes on on the mind of an extraordinary human being.