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螣 维谓胃蟻蠅蟺慰蟼 蟺慰蠀 伪纬伪蟺慰蠉蟽蔚 蟿慰蠀蟼 伪蟻喂胃渭慰蠉蟼
螚 喂蟽蟿慰蟻委伪 蟿慰蠀 螤慰位 螆蟻谓蟿慰蟼 魏伪喂 蟿畏蟼 伪谓伪味萎蟿畏蟽畏蟼 纬喂伪 蟿畏 渭伪胃畏渭伪蟿喂魏萎 伪位萎胃蔚喂伪.
螕喂伪 谓伪 伪谓伪魏伪位蠉蠄蔚喂 魏伪谓蔚委蟼 蟽蟿慰谓 伪喂蠋谓伪 渭伪蟼 魏维蟺慰喂慰谓 维位位慰 维谓胃蟻蠅蟺慰 蟺慰蠀 谓伪 苇蠂蔚喂 伪蠁喂蔚蟻蠋蟽蔚喂 蟿蠈蟽慰 伪蟺蠈位蠀蟿伪 蟿畏 味蠅萎 蟿慰蠀 蟽蟿畏谓 伪蠁畏蟻畏渭苇谓畏 蟽魏苇蠄畏 胃伪 苇蟺蟻蔚蟺蔚 谓伪 伪谓伪蟿蟻苇尉蔚喂 蟽蟿慰 螞慰蠉谓蟿尾喂蠂 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 (1889-1951) 蟺慰蠀 伪蟺慰纬蠉渭谓蠅蟽蔚 蟿畏 味蠅萎 蟿慰蠀 纬喂伪 蠂维蟻畏 蟿畏蟼 蠁喂位慰蟽慰蠁委伪蟼. 螘谓蠋 蠈渭蠅蟼 慰 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 蟽魏蠈蟻蟺喂蟽蔚 蟿畏谓 慰喂魏慰纬蔚谓蔚喂伪魏萎 蟿慰蠀 蟺蔚蟻喂慰蠀蟽委伪 蠅蟼 苇谓伪 蔚委未慰蟼 伪蠀蟿慰蟿喂渭蠅蟻委伪蟼, 慰 螆蟻谓蟿慰蟼 蟽魏蠈蟻蟺喂味蔚 蟿伪 蟺蔚蟻喂蟽蟽蠈蟿蔚蟻伪 伪蟺蠈 蟿伪 蠂蟻萎渭伪蟿伪 蟺慰蠀 魏苇蟻未喂味蔚 伪蟺位蠋蟼 蔚蟺蔚喂未萎 未蔚谓 蟿伪 蠂蟻蔚喂伪味蠈蟿伪谓... 螝伪喂 蔚谓蠋 慰 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 蟺慰蟻蔚蠀蠈蟿伪谓 渭蔚 蟽蠂蔚未蠈谓 伪蠀蟿慰魏蟿慰谓喂魏苇蟼 蟺伪蟻慰蟻渭萎蟽蔚喂蟼, 慰 螆蟻谓蟿慰蟼 慰喂魏慰未蠈渭畏蟽蔚 蟿畏 味蠅萎 蟿慰蠀 苇蟿蟽喂 蠋蟽蟿蔚 谓伪 蟿畏蟼 伪蟺慰蟽蟺维蟽蔚喂 蠈蟽慰 蟿慰 未蠀谓伪蟿蠈谓 蟺蔚蟻喂蟽蟽蠈蟿蔚蟻畏 蔚蠀蟿蠀蠂委伪.
螕喂伪 谓伪 伪谓伪魏伪位蠉蠄蔚喂 魏伪谓蔚委蟼 蟽蟿慰谓 伪喂蠋谓伪 渭伪蟼 魏维蟺慰喂慰谓 维位位慰 维谓胃蟻蠅蟺慰 蟺慰蠀 谓伪 苇蠂蔚喂 伪蠁喂蔚蟻蠋蟽蔚喂 蟿蠈蟽慰 伪蟺蠈位蠀蟿伪 蟿畏 味蠅萎 蟿慰蠀 蟽蟿畏谓 伪蠁畏蟻畏渭苇谓畏 蟽魏苇蠄畏 胃伪 苇蟺蟻蔚蟺蔚 谓伪 伪谓伪蟿蟻苇尉蔚喂 蟽蟿慰 螞慰蠉谓蟿尾喂蠂 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 (1889-1951) 蟺慰蠀 伪蟺慰纬蠉渭谓蠅蟽蔚 蟿畏 味蠅萎 蟿慰蠀 纬喂伪 蠂维蟻畏 蟿畏蟼 蠁喂位慰蟽慰蠁委伪蟼. 螘谓蠋 蠈渭蠅蟼 慰 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 蟽魏蠈蟻蟺喂蟽蔚 蟿畏谓 慰喂魏慰纬蔚谓蔚喂伪魏萎 蟿慰蠀 蟺蔚蟻喂慰蠀蟽委伪 蠅蟼 苇谓伪 蔚委未慰蟼 伪蠀蟿慰蟿喂渭蠅蟻委伪蟼, 慰 螆蟻谓蟿慰蟼 蟽魏蠈蟻蟺喂味蔚 蟿伪 蟺蔚蟻喂蟽蟽蠈蟿蔚蟻伪 伪蟺蠈 蟿伪 蠂蟻萎渭伪蟿伪 蟺慰蠀 魏苇蟻未喂味蔚 伪蟺位蠋蟼 蔚蟺蔚喂未萎 未蔚谓 蟿伪 蠂蟻蔚喂伪味蠈蟿伪谓... 螝伪喂 蔚谓蠋 慰 螔委蟿纬魏蔚谓蟽蟿伪蠆谓 蟺慰蟻蔚蠀蠈蟿伪谓 渭蔚 蟽蠂蔚未蠈谓 伪蠀蟿慰魏蟿慰谓喂魏苇蟼 蟺伪蟻慰蟻渭萎蟽蔚喂蟼, 慰 螆蟻谓蟿慰蟼 慰喂魏慰未蠈渭畏蟽蔚 蟿畏 味蠅萎 蟿慰蠀 苇蟿蟽喂 蠋蟽蟿蔚 谓伪 蟿畏蟼 伪蟺慰蟽蟺维蟽蔚喂 蠈蟽慰 蟿慰 未蠀谓伪蟿蠈谓 蟺蔚蟻喂蟽蟽蠈蟿蔚蟻畏 蔚蠀蟿蠀蠂委伪.
368 pages, Paperback
First published January 1, 1998
281 people are currently reading
16757 people want to read
About the author
Paul Hoffman
134听books88听followersPaul Hoffman (born 1956) is a prominent author and host of the PBS television series Great Minds of Science. He was president and editor in chief of Discover, in a ten-year tenure with that magazine, and served as president and publisher of Encyclopaedia Britannica before returning full-time to writing and consulting work.
He lives in Woodstock, New York. Author of at least ten books, he has appeared on CBS This Morning and The NewsHour with Jim Lehrer as a correspondent. Hoffman is also a puzzlemaster using the pseudonym Dr. Crypton. He designed the puzzle in the 1984 book Treasure: In Search of the Golden Horse. He also designed the treasure map in the 1984 film, Romancing the Stone, starring Michael Douglas, Kathleen Turner, and Danny DeVito.
Hoffman holds a B.A. degree summa cum laude from Harvard. He is the winner of the first National Magazine Award for Feature Writing and is a member of the American Academy of Arts and Sciences.
He lives in Woodstock, New York. Author of at least ten books, he has appeared on CBS This Morning and The NewsHour with Jim Lehrer as a correspondent. Hoffman is also a puzzlemaster using the pseudonym Dr. Crypton. He designed the puzzle in the 1984 book Treasure: In Search of the Golden Horse. He also designed the treasure map in the 1984 film, Romancing the Stone, starring Michael Douglas, Kathleen Turner, and Danny DeVito.
Hoffman holds a B.A. degree summa cum laude from Harvard. He is the winner of the first National Magazine Award for Feature Writing and is a member of the American Academy of Arts and Sciences.
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Displaying 1 - 30 of 518 reviews
March 10, 2009
I originally wanted to be a mathematician, and I'm still enough of one that I am completely in awe of Erd枚s. He was the Saint Francis of Mathematics; he had no possessions, and just wandered around the world doing math research with like-minded people. I see that another reviewer has called him a "hanger-on". Friend, you completely miss the point. He might turn up on someone's doorstep and expect them to feed him and give him a place to sleep for a few nights. He'd often reward them with a couple of ideas so brilliant that their whole careers would be revitalized, or pushed in some exciting new direction they hadn't even suspected might exist. I'm afraid you don't understand mathematicians' priorities.
As the title says, Erd枚s loved only numbers, and he wanted to share that love with the whole world. He collaborated with over 500 different people on over 1400 published papers, and every researcher now talks about their "Erd枚s number". If you published a joint paper with him, your number is 1. If you published a paper with a person who's a 1, you're a 2, and so on. Low numbers are much sought after; if you're wondering, I'm a 5, which is so-so. I keep trying to find a 3 who wants to write a joint paper with me, but so far unsuccessfully.
Like many mathematicians, Erd枚s had an unusual way of talking, and liked making up his own names for things. He was in particular famous for his habit of calling God "The Supreme Fascist", or "The S.F." for short. I don't think he meant any harm by this: it's just the kind of thing mathematicians think is funny. If there is a God, I'm sure He has some equally insulting pet name for Erd枚s. The world of mathematics still misses him badly; it would be nice to think that he was up there in the Heavenly Math Institute, publishing joint papers with Pythagoras and Gauss.
This is a fine book about Erd枚s, sympathetically written by someone who understood well what an amazing, unique person he was. If you're any kind of mathematician, and by some mischance you haven't already come across it, you should put it on your list without further delay!
As the title says, Erd枚s loved only numbers, and he wanted to share that love with the whole world. He collaborated with over 500 different people on over 1400 published papers, and every researcher now talks about their "Erd枚s number". If you published a joint paper with him, your number is 1. If you published a paper with a person who's a 1, you're a 2, and so on. Low numbers are much sought after; if you're wondering, I'm a 5, which is so-so. I keep trying to find a 3 who wants to write a joint paper with me, but so far unsuccessfully.
Like many mathematicians, Erd枚s had an unusual way of talking, and liked making up his own names for things. He was in particular famous for his habit of calling God "The Supreme Fascist", or "The S.F." for short. I don't think he meant any harm by this: it's just the kind of thing mathematicians think is funny. If there is a God, I'm sure He has some equally insulting pet name for Erd枚s. The world of mathematics still misses him badly; it would be nice to think that he was up there in the Heavenly Math Institute, publishing joint papers with Pythagoras and Gauss.
This is a fine book about Erd枚s, sympathetically written by someone who understood well what an amazing, unique person he was. If you're any kind of mathematician, and by some mischance you haven't already come across it, you should put it on your list without further delay!
April 14, 2019
Authentic Living
Child prodigy, adult genius, benefactor to anyone in need, eccentric professor, persona non grata in the USA, the Soviet Union and several European states, amphetamine addict, lifelong virgin of no fixed address, Paul Erdos had one passion, one religion, and one goal in his life: the solving of mathematical problems. He was a singular human being, incomparable even among other singular men like Albert Einstein, and William Teller, and Andrew Wiles who were his friends.
Paul Erdos wrote more mathematics than any other mathematician except the 18th century Leonhard Euler. But Erdos, by choice, never held a permanent academic position of significance. He was a competent teacher but could not tolerate the distraction that teaching implied for his problem-solving.
He lived primarily from the kindness of fellow-mathematicians with whom he collaborated constantly during a sort of royal progress from continent to continent. After the age of 50, he was accompanied in his travels by his aged and sickly mother who ate every meal with him and insisted on sleeping in the same room.
Perhaps, however, the most remarkable aspect of Erdos's life was the demonstration that knowledge neither requires nor necessarily results in power. At no point did his global intellectual eminence lead to material wealth and influence. He simply wouldn't allow it.
Like a medieval monk, or better said a Galacian rabbi, Erdos lived solely for the infinite cause of mathematical understanding. He was never seduced by his 'earning potential', the prestige of his reputation, or even by the politics rampant during his lifetime to engage in anything but more and more mathematics.
For me it is this persistent, consistent expression of who and what he was, in opposition to virtually every kind of modern 'value' that is not only the most admirable but also the most inspiring thing about this truly authentic person.
Child prodigy, adult genius, benefactor to anyone in need, eccentric professor, persona non grata in the USA, the Soviet Union and several European states, amphetamine addict, lifelong virgin of no fixed address, Paul Erdos had one passion, one religion, and one goal in his life: the solving of mathematical problems. He was a singular human being, incomparable even among other singular men like Albert Einstein, and William Teller, and Andrew Wiles who were his friends.
Paul Erdos wrote more mathematics than any other mathematician except the 18th century Leonhard Euler. But Erdos, by choice, never held a permanent academic position of significance. He was a competent teacher but could not tolerate the distraction that teaching implied for his problem-solving.
He lived primarily from the kindness of fellow-mathematicians with whom he collaborated constantly during a sort of royal progress from continent to continent. After the age of 50, he was accompanied in his travels by his aged and sickly mother who ate every meal with him and insisted on sleeping in the same room.
Perhaps, however, the most remarkable aspect of Erdos's life was the demonstration that knowledge neither requires nor necessarily results in power. At no point did his global intellectual eminence lead to material wealth and influence. He simply wouldn't allow it.
Like a medieval monk, or better said a Galacian rabbi, Erdos lived solely for the infinite cause of mathematical understanding. He was never seduced by his 'earning potential', the prestige of his reputation, or even by the politics rampant during his lifetime to engage in anything but more and more mathematics.
For me it is this persistent, consistent expression of who and what he was, in opposition to virtually every kind of modern 'value' that is not only the most admirable but also the most inspiring thing about this truly authentic person.
May 28, 2015
"V茅gre nem butulok tov谩bb."
"Finally I am becoming stupider no more."
The epitaph Paul Erd艖s wrote for himself.
Paul Erd艖s was the embodiment of mathematics. His brain was finely tuned to think about mathematics constantly -- for as much as 18 hours a day, if not more. Every moment of his waking life appears to have been spent thinking about theorems, conjectures, problems, and solutions. He was one of the most influential mathematicians of the 20th century, and collaborated with more than 500 other mathematicians. Indeed, because of his extremely productive output, there now exists an Erd艖s number. An Erd艖s number is simply a number which indicates how 'close' person X is in terms of collaborating with Erd艖s: i.e. if your number is 1, you collaborated directly with him; if your number is 2, you collaborated with someone who collaborated with him, and so on. Reading on Wikipedia, it tells me that as many as 200 000 mathematicians have an Erd艖s number.
He had what I think is the essential ingredient for genius, and that is what Einstein called being 'passionately curious". Add to this passionate curiousity an extremely eccentric and interesting personality, and you have yourself a person that is well-worth reading about. He was a mathematical nomad, traveling hither and thither in search of mathematical prodigies that he could help foster and mathematical problems he could help solve. He called children "epsilons", as epsilon is used to represent small quantities in math; he was fond of calling everything disagreeable "fascist", and God is known in his vocabulary as the SF, the "supreme fascist", and once, when waking up a mathematician friend early in the morning, unsure if his friend was awake or not, he opened the door carefully and asked, "Ralph, do you exist?" Isn't that just the cutest thing?
This book does a good job(and I say this as a non-mathematician) of showing us both Erd艖s the mathematician, and the personality of Erd艖s (although the two are arguably inseparable, as the book stresses). But at the same time, it is an extremely interesting book about the world of mathematics. I struggled with math in school: I never had any encouragement, and my teachers were horrible, one of them going as far as insulting me repeatingly for struggling. I distinctly recall sitting over problems that everyone else could solve, and I couldn't. To this day, I am in awe of mathematics and wish I was better at it, but I dread it at the same time. My inability to do mathematics has always made me feel stupid, and it does so to a somewhat smaller degree today as well.
Somehow, though, this book made the math understandable and incredibly exciting. I won't pretend like I got all of it, but I did get enough to feel enormous satisfaction from reading the book. It was very exhilarating to read about all the (unsolved and solved) problems that exist in mathematics, and to learn about the minds that wrestled with them. More than just talking about Erd艖s, Hoffman mentions Cantor, Poincare, Fermat, and a whole host of other mathematicians and things they discovered and struggled with.
Indeed, this book has made me so interested in mathematics that I have just ordered a number of more books dealing with math: John Derbyshire's Prime Obsession, Marcus du Sautoy's The Music of the Primes, and Donal O'Shea's The Poincare Conjecture. So thanks to Paul Hoffman for writing such a wonderful book on mathematics and on such an interesting character as Paul Erd艖s, and last but not least, thanks for opening my brain!
* Here is a very interesting youtube documentary on Paul, although I don't like that the title mentions "mathematical aspergers." As far as I know, Paul did not have aspergers. Regardless, it is a wonderful video.
** I also find it interesting that this thing with constantly thinking about math, as Erd艖s evidently did, is something you find again and again in most geniuses. An interesting example is world chess champion and world #1, Magnus Carlsen. He also always stresses that he is constantly thinking about chess, always replaying games or thinking of ideas. I also think of Mark Knopfler, the guitarist, who says that guitars are "magnetic objects" for him. And for me as a footballer, it's hard to pass by a football without touching it, even though I put my boots away many years ago. As Richard Feynman said, "There are no miracle people. It just happens. They got interested in this thing, and they learned all this stuff. They're just people. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and study..." And paraphrased, geniuses fall in love with some activity and then do it constantly. Just interesting how genius works. Erd艖s certainly was one!
"Finally I am becoming stupider no more."
The epitaph Paul Erd艖s wrote for himself.
Paul Erd艖s was the embodiment of mathematics. His brain was finely tuned to think about mathematics constantly -- for as much as 18 hours a day, if not more. Every moment of his waking life appears to have been spent thinking about theorems, conjectures, problems, and solutions. He was one of the most influential mathematicians of the 20th century, and collaborated with more than 500 other mathematicians. Indeed, because of his extremely productive output, there now exists an Erd艖s number. An Erd艖s number is simply a number which indicates how 'close' person X is in terms of collaborating with Erd艖s: i.e. if your number is 1, you collaborated directly with him; if your number is 2, you collaborated with someone who collaborated with him, and so on. Reading on Wikipedia, it tells me that as many as 200 000 mathematicians have an Erd艖s number.
He had what I think is the essential ingredient for genius, and that is what Einstein called being 'passionately curious". Add to this passionate curiousity an extremely eccentric and interesting personality, and you have yourself a person that is well-worth reading about. He was a mathematical nomad, traveling hither and thither in search of mathematical prodigies that he could help foster and mathematical problems he could help solve. He called children "epsilons", as epsilon is used to represent small quantities in math; he was fond of calling everything disagreeable "fascist", and God is known in his vocabulary as the SF, the "supreme fascist", and once, when waking up a mathematician friend early in the morning, unsure if his friend was awake or not, he opened the door carefully and asked, "Ralph, do you exist?" Isn't that just the cutest thing?
This book does a good job(and I say this as a non-mathematician) of showing us both Erd艖s the mathematician, and the personality of Erd艖s (although the two are arguably inseparable, as the book stresses). But at the same time, it is an extremely interesting book about the world of mathematics. I struggled with math in school: I never had any encouragement, and my teachers were horrible, one of them going as far as insulting me repeatingly for struggling. I distinctly recall sitting over problems that everyone else could solve, and I couldn't. To this day, I am in awe of mathematics and wish I was better at it, but I dread it at the same time. My inability to do mathematics has always made me feel stupid, and it does so to a somewhat smaller degree today as well.
Somehow, though, this book made the math understandable and incredibly exciting. I won't pretend like I got all of it, but I did get enough to feel enormous satisfaction from reading the book. It was very exhilarating to read about all the (unsolved and solved) problems that exist in mathematics, and to learn about the minds that wrestled with them. More than just talking about Erd艖s, Hoffman mentions Cantor, Poincare, Fermat, and a whole host of other mathematicians and things they discovered and struggled with.
Indeed, this book has made me so interested in mathematics that I have just ordered a number of more books dealing with math: John Derbyshire's Prime Obsession, Marcus du Sautoy's The Music of the Primes, and Donal O'Shea's The Poincare Conjecture. So thanks to Paul Hoffman for writing such a wonderful book on mathematics and on such an interesting character as Paul Erd艖s, and last but not least, thanks for opening my brain!
* Here is a very interesting youtube documentary on Paul, although I don't like that the title mentions "mathematical aspergers." As far as I know, Paul did not have aspergers. Regardless, it is a wonderful video.
** I also find it interesting that this thing with constantly thinking about math, as Erd艖s evidently did, is something you find again and again in most geniuses. An interesting example is world chess champion and world #1, Magnus Carlsen. He also always stresses that he is constantly thinking about chess, always replaying games or thinking of ideas. I also think of Mark Knopfler, the guitarist, who says that guitars are "magnetic objects" for him. And for me as a footballer, it's hard to pass by a football without touching it, even though I put my boots away many years ago. As Richard Feynman said, "There are no miracle people. It just happens. They got interested in this thing, and they learned all this stuff. They're just people. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and study..." And paraphrased, geniuses fall in love with some activity and then do it constantly. Just interesting how genius works. Erd艖s certainly was one!
November 22, 2020
This is a lovely biography of a child prodigy, Hungarian mathematician who had been doing maths for 70 years, with 144 published papers with the best other mathematicians. It鈥檚 so encouraging for people who should learn maths, you can look at this field with a different perspective
October 8, 2013
A human look at the Hungarian mathematician Paul Erdos who loved numbers more than anything. Instead of being a cold analytic, Erdos was a compassionate person who shared the best part of himself with others. Making money off his talent was not important to him but sharing math was. He had selflessly paired his talents with countless others who seek to solve mathematical conundrums and traveled where he was needed. A wandering monk of mathematics, he gave away what he earned to charities, living on little except what he needed to continue his work. He鈥檚 had so many collaborators that a term 鈥淓rdos number鈥� pertained to him. Someone who had co-authored with Erdos is assigned number 1. This is an enjoyable read for those who are interested in mathematics. Mathematical references and anecdotes abound, such as the Four Color Map Theorem, or that if 鈥渁 mathematician tells you that you're a 220 to her 284 (et vice versa), or a 17,296 to her 18,416 (v.v.), then you're pals, since they are proper divisors of each other鈥�, and a "minimal guest list needed to guarantee a foursome of friends or a fivesome of strangers" is 25.
March 7, 2020
"What would you say to Jesus if you saw him on the street?"
Erd艖s said he'd ask Jesus if the Continuum Hypothesis was true. "And there would be three possible answers for Jesus," Erd艖s said. "He could say, 'Godel and Cohen already taught you everything which is to be known about it.' The second answer would be, 'Yes, there is an answer but unfortunately your brain isn't sufficiently developed yet to know the answer.' And Jesus could give a third answer: 'The Father, the Holy Ghost, and I have been thinking about that long before creation, but we haven't yet come to a conclusion.'
A life of a saint. Not in the sense of a moral paragon - though he was very kind when he wasn't being stubborn - but in the sense of a man devoted to, possessed by one thing, a high and rare thing that sets him some way beyond society. No money, no fixed abode, no lovers, no children, no religion. 80% of his family eaten by Nazi Germany. And yet , hilarious life. A champion moocher, eternal couchsurfer, generous and ascetic, witty and worldly. We are lucky to have had him.
I [Hoffman] slept where he slept and stayed up nineteen hours a day, watching him prove and conjecture. I felt silly not being able, at the age of thirty, to keep up with a sickly looking seventy-three-year-old man. I suppose I could have shared his pills, but the only stimulant I took was caffeine.
He abhorred discussions of sex as much as he disliked the act itself... In the late 1940s, during the Chinese civil war, Erd艖s took part in a food drive for the Communist Chinese. "I remember walking into a big room in Los Angeles, at UCLA, I think," said Vazsonyi, "and there was Erd艖s and all these people making packages of food. Some mischief-makers who knew of his disgust at naked women offered to make a $100 donation if he'd go with them to a burlesque show." To their astonishment, he immediately took them up on the offer. Afterwards, when they forked over the $100, he revealed the secret of his victory: "See! I tricked you, you trivial beings! I took off my glasses and did not see a thing!"
Unlike Perelman, the other late-C20th-century mathematical saint, Erd艖s had a wicked sense of fun and style. Like him, Erd艖s let himself be completely dependent on others for housing and logistics, and demanded much of them.
he expected his hosts to lodge him, feed him, and do his laundry, along with anything else he needed, as well as arrange for him to get to his next destination.
Erdos started developing his private language... referring to Communists as people "on the long wave-length," because in the electromagnetic spectrum the red waves were long. He said that Horthy supporters and other Fascist sympathizers were "on the short wavelength." That's also when he started calling children and other small things "epsilons," grandchildren "epsilons squared," alcohol "poison," music "noise," and women "bosses," an inversion of what Hungarian women often called their husbands. "Give me an epsilon of poison," Erdos would say when he wanted a sip of wine. "Wine, women, and song" became "Poison, bosses, and noise."
He then had a huge argument with the surgeon about why, since only one eye was being deadened [during his cornea transplant], he couldn't read a mathematics journal with the other, good eye. The surgeon made a series of frantic calls to the Memphis math department. "Can you send a mathematician over here at once so that Erdos can talk math during surgery?" The department obliged, and the operation went smoothly.
Unfortunately only half of this is anecdotes about Erd艖s, the rest being the usual potted-history of quirky mathematicians (Archimedes the oblivious, Fermat the executioner, Gauss the crabbed, Hardy the dry eccentric, Ramanujan the sublime, Wiles the Stakhanovite) with the usual stories. I skimmed these bits to get more of the good stuff.
February 2, 2013
Paul Erdos was a prolific, well-known mathematician. He wrote over 1400 journal articles in various mathematical publications, many of them collaborations. Those people who collaborated with him earned an Erdos "number 1". Those who collaborated with someone who collaborated with him earned a "number 2", and so on.
To say that Erdos was "eccentric" would be an understatement. He had no home--he carried a suitcase with a single change of clothes in it, and traveled the world, visiting one mathematician after another. He would stay at a mathematician's home until he became unwelcome--and that was not long at all. Erdos only slept a few hours at night, so he kept his hosts pretty busy! He was physically inept, so help left trails and messes in his wake. The collection of anecdotes about his life are amusing, and usually center on his single-mindedness about mathematics.
Erdos' main area of expertise was number theory. Paul Hoffman has written a very readable book, expertly interleaving chapters about number theory with Erdos' biography. This gives a layman some understanding about the sorts of problems that Erdos solved. I learned some interesting things about mathematics, and also about the psychology of mathematicians. This was a fun book to read, and I can recommend it to anybody.
By the way, baseball great Hank Aaron earned an "Erdos number 1"--read the book if you are curious to find out why!
To say that Erdos was "eccentric" would be an understatement. He had no home--he carried a suitcase with a single change of clothes in it, and traveled the world, visiting one mathematician after another. He would stay at a mathematician's home until he became unwelcome--and that was not long at all. Erdos only slept a few hours at night, so he kept his hosts pretty busy! He was physically inept, so help left trails and messes in his wake. The collection of anecdotes about his life are amusing, and usually center on his single-mindedness about mathematics.
Erdos' main area of expertise was number theory. Paul Hoffman has written a very readable book, expertly interleaving chapters about number theory with Erdos' biography. This gives a layman some understanding about the sorts of problems that Erdos solved. I learned some interesting things about mathematics, and also about the psychology of mathematicians. This was a fun book to read, and I can recommend it to anybody.
By the way, baseball great Hank Aaron earned an "Erdos number 1"--read the book if you are curious to find out why!
March 20, 2016
A good book over the life of Paul Erdos in his histhorical and mathematical context,a life wholly devoted to his only love :the mathematics,with the exception of his mother,the beautifull mathematics and proofs,those he said were written in "The Book" a book owned by God,at what the men can only get glimpses.
Erdos was a eccentric man,a sort of monk for whom the maths were almost a religion,perpetually itinerant whose only private properties were two suitcases and that said that the private property was a nuissance,he also had a human side ,compasionate and friend of children.
For him the mathematics were a social activity and was a prolific publisher at the level of Euler in quantity of works, allmost all in collaboration with others;he invented the Erdos number according the more near or far relation in the collaborations.
The book is full of fun anecdotes in his life and plainly explains interesting facts and concepts of number theory one of his main fields of work.
A easy,pleasant and entertaining read for all with some interes in maths and its men
Erdos was a eccentric man,a sort of monk for whom the maths were almost a religion,perpetually itinerant whose only private properties were two suitcases and that said that the private property was a nuissance,he also had a human side ,compasionate and friend of children.
For him the mathematics were a social activity and was a prolific publisher at the level of Euler in quantity of works, allmost all in collaboration with others;he invented the Erdos number according the more near or far relation in the collaborations.
The book is full of fun anecdotes in his life and plainly explains interesting facts and concepts of number theory one of his main fields of work.
A easy,pleasant and entertaining read for all with some interes in maths and its men
March 9, 2009
Paul Erdos, the famously eccentric mathematician, spent twenty hours a day, every day hopped-up on amphetamines, working through mathematical proofs, to the exclusion of any sort of normal social life. He had his own language (to 鈥渄ie鈥� meant to leave the field of mathematics, children were 鈥渆psilons鈥�, women 鈥渂osses鈥�, God was the 鈥淪F鈥� or 鈥淪upreme Fascist鈥�). Admittedly asexual, he lived alone with his mother until she died, and then he wandered the U.S. and Europe, staying for a few weeks at a time in the homes of math colleagues, working long hours on math proofs and then moving on. Erdos was so prolific and is still so revered in the field of mathematics that mathematicians often refer to a person鈥檚 鈥淓rdos Number鈥�. An Erdos Number of 1 means you鈥檝e co-authored a paper with Erdos himself. An Erdos Number of 2 means you鈥檝e co-authored a paper with someone with an Erdos Number of 1, and so on.
If you鈥檙e familiar with Erdos, you've probably already heard much of the lore contained here, but what鈥檚 really unique about the portrait we get in this book is that it humanizes Erdos. He related well to children. From his meager income, he gave generously to charities, friends, and panhandlers. He cared for sick colleagues, often prodding them back to health with math. And he wasn鈥檛 actually that unworldly after all.
Unfortunately, this book and its account of Erdos鈥� life is entirely too brief, made shorter yet by large sections of text with almost no relation to Erdos. Fermat鈥檚 Last Theorem and Andrew Wiles鈥� 1995 solution of this long-standing problem gets particularly detailed treatment, and possibly the only connection to Erdos here is that Wiles solved FLT in isolation and secrecy, an approach to mathematics that is antithetical to Erdos. Quibbles aside, this book is an entertaining sketch of one very fascinating man. Even for those with no interest in math, it鈥檚 well worth picking up.
If you鈥檙e familiar with Erdos, you've probably already heard much of the lore contained here, but what鈥檚 really unique about the portrait we get in this book is that it humanizes Erdos. He related well to children. From his meager income, he gave generously to charities, friends, and panhandlers. He cared for sick colleagues, often prodding them back to health with math. And he wasn鈥檛 actually that unworldly after all.
Unfortunately, this book and its account of Erdos鈥� life is entirely too brief, made shorter yet by large sections of text with almost no relation to Erdos. Fermat鈥檚 Last Theorem and Andrew Wiles鈥� 1995 solution of this long-standing problem gets particularly detailed treatment, and possibly the only connection to Erdos here is that Wiles solved FLT in isolation and secrecy, an approach to mathematics that is antithetical to Erdos. Quibbles aside, this book is an entertaining sketch of one very fascinating man. Even for those with no interest in math, it鈥檚 well worth picking up.
August 12, 2017
A very engaging read about one of the most prolific minds of the 20th century. Highly recommended.
February 18, 2013
I enjoyed this book a lot. Within a humanized story of the colourful life of Hungarian maths genius Paul Erd艖s and the people associated with him in various ways, this book gives a fascinating insight into the world of pure mathematics, its historical background and the lives and psychology of many famous mathematicians.
I was particularly interested in the real-life applications of the maths concept as well as the psychological aspect. I found it surprising that, despite their talent for finding logical solutions for mathematical problems, professional mathematicians may suffer illogical or unjustified fears and bouts of insecurity just like the rest of us. On the other hand, the manner in which Erd艖s used his talent to help him find a balance, even under difficult circumstances, was worth admiring. Thanks to an engaging and occasionally humorous manner in which the maths concepts are approached, I also learned quite a bit about Number Theory.
I give this book 4 stars instead of 5 because the very beginning could turn some readers off making them think it's only a collection of anectodes and a caricatured biography of an eccentric mathematician and the manner in which life stories of Erd艖s and other people are scattered around makes it a little difficult to follow at times. I'd also like the book has tried to explain the connections of the geometry of elliptic curves, the algebra of Diophantine equations and the Wiles's proof of the Fermat's Last Theorem.
Last but not least, I have a serious issue with the title of this book since Erd艖s was shown to be a caring person, generous to a fault and interested in many things, not only numbers.
I recommend this book for non-mathematicians like me, with a word of advice to push ahead softly and try to appreciate the mathematicians' work without need to understand each and every thing.
I was particularly interested in the real-life applications of the maths concept as well as the psychological aspect. I found it surprising that, despite their talent for finding logical solutions for mathematical problems, professional mathematicians may suffer illogical or unjustified fears and bouts of insecurity just like the rest of us. On the other hand, the manner in which Erd艖s used his talent to help him find a balance, even under difficult circumstances, was worth admiring. Thanks to an engaging and occasionally humorous manner in which the maths concepts are approached, I also learned quite a bit about Number Theory.
I give this book 4 stars instead of 5 because the very beginning could turn some readers off making them think it's only a collection of anectodes and a caricatured biography of an eccentric mathematician and the manner in which life stories of Erd艖s and other people are scattered around makes it a little difficult to follow at times. I'd also like the book has tried to explain the connections of the geometry of elliptic curves, the algebra of Diophantine equations and the Wiles's proof of the Fermat's Last Theorem.
Last but not least, I have a serious issue with the title of this book since Erd艖s was shown to be a caring person, generous to a fault and interested in many things, not only numbers.
I recommend this book for non-mathematicians like me, with a word of advice to push ahead softly and try to appreciate the mathematicians' work without need to understand each and every thing.
June 20, 2014
A book that made me very happy, this one details the life of Paul Erd艖s (with two thingies on the o), arguably the most important mathematician of the 20th century, his works & achievements, and his more than, um, quirky lifestyle. He had little possessions and like a world-citizen he travelled from collaborator to collaborator's couch, staying at each house for a few weeks until another theorem was proven.
Since it's a book about an influential mathematician, pretty much all of the greats of mathematics show up, so the book doubles as a history of modern mathematics, starting with Gauss. If you're into maths some parts of the books might bore you, as the book often sidesteps to explain the background of a particular proof or problem, which you'll probably have heard of already. If you're not into maths, the book might kindle a new love for you, who knows. The author clearly works to make the proofs and conundrums understandable for 'ordinary' people.
Erd艖s was clearly full of love, always visiting mathematicians' mothers, looking after other peoples' children, never very caring about the order or status of collaborations on papers' authors [1], eschewing wealth and stability for a life of doing what he loved, often donating what money he had to a particular cause he read about in the newspaper, or sending it to struggling mathematicians. In that regard, the book's title isn't that well-chosen, it's probably based on his lack of romantic and sexual love - the book hints towards a severe phimosis or something similar, and a general lack of understanding of women.
The book shines in fun anecdotes about Erd艖s' life - he buttered his first bread at the ripe old age of 21, he never had a driver's license, he was extremely dependent on his mother, he usually gave away what little money he had, he got lost on a 5-minutes walk, on seeing the solution for the Monty Hall Problem he got angry and didn't understand it for a few days (that made me feel better - that particular solution is so counter-intuitive, I'm still not sure I understood it), he called children epsilons, God the Supreme Fascist, women bosses, he read only one fiction novel in his life (Flatland, what else?) and more..
Recommended for: People who like interesting people.
Not recommended for: Heartless robots.
[1] I can talk for hours how picky scientists can get about that, entire projects with hundreds of scientists have been severely delayed because some ego insisted on being author Nr. 12 instead of 13. It's one of the more annoying aspects of scientific work.
P.S.: I want to steal his epitaph: 'Finally, I am becoming stupider no more'
Since it's a book about an influential mathematician, pretty much all of the greats of mathematics show up, so the book doubles as a history of modern mathematics, starting with Gauss. If you're into maths some parts of the books might bore you, as the book often sidesteps to explain the background of a particular proof or problem, which you'll probably have heard of already. If you're not into maths, the book might kindle a new love for you, who knows. The author clearly works to make the proofs and conundrums understandable for 'ordinary' people.
Erd艖s was clearly full of love, always visiting mathematicians' mothers, looking after other peoples' children, never very caring about the order or status of collaborations on papers' authors [1], eschewing wealth and stability for a life of doing what he loved, often donating what money he had to a particular cause he read about in the newspaper, or sending it to struggling mathematicians. In that regard, the book's title isn't that well-chosen, it's probably based on his lack of romantic and sexual love - the book hints towards a severe phimosis or something similar, and a general lack of understanding of women.
The book shines in fun anecdotes about Erd艖s' life - he buttered his first bread at the ripe old age of 21, he never had a driver's license, he was extremely dependent on his mother, he usually gave away what little money he had, he got lost on a 5-minutes walk, on seeing the solution for the Monty Hall Problem he got angry and didn't understand it for a few days (that made me feel better - that particular solution is so counter-intuitive, I'm still not sure I understood it), he called children epsilons, God the Supreme Fascist, women bosses, he read only one fiction novel in his life (Flatland, what else?) and more..
Recommended for: People who like interesting people.
Not recommended for: Heartless robots.
[1] I can talk for hours how picky scientists can get about that, entire projects with hundreds of scientists have been severely delayed because some ego insisted on being author Nr. 12 instead of 13. It's one of the more annoying aspects of scientific work.
P.S.: I want to steal his epitaph: 'Finally, I am becoming stupider no more'
April 24, 2007
I sat by one of the math faculty at a new faculty dinner, and when we started talking about math he told me I should read this book. I enjoyed it! Paul Erdos was a very unique individual (as mathematicians are) - more than anything I enjoyed his made up vocabulary - God = S.F. (Supreme Fascist), children=epsilons, women=masters, men=slaves, Americans=Sam, Soviets=Joe. A lot of math is sprinkled in there as well, including information about numbers bigger than infinity (ha! proven at last!) and many many mathematical theories.
February 19, 2022
Una vida bastante peculiar, la de Paul Erd枚s y la gente que lo rodeaba. Un libro bien escrito, f谩cil de leer. Aunque no s茅 qu茅 tan f谩cil sea llevar el hilo de las ideas matem谩ticas que se explican para alguien no matem谩tico. Aprend铆 mucho con este libro.
October 23, 2016
When Paul Erd艖s died in 1996 Paul Hoffman had known him for about 10 years and interviewed him a number of times. Hoffman had also known and interviewed many of Erd艖s' friends and associates. So it's fair to say that Hoffman had a lot more knowledge of the subject of his biography than most biographers (unless they're family or close friends) ever do. The biography is indeed quite good, and provides a clear and informative portrait of the very unique, appealing, and colorful individual that Erd艖s was.
However, what defined Paul Erd艖s even more than his idiosyncrasies and his humanity was that he was quintessentially a mathematician 鈥� a singularly talented and prolific one. Another biography of Erd艖s, by PhD physicist Bruce Schechter (), was published at almost the same time as Hoffman's. (I have reviewed that as well, and I'll try not to duplicate much from that other review.) Hoffman freely concedes that he is not a mathematician. While Schechter isn't a professional mathematician, he is more able to give a complete and accurate account of Erd艖s' work than Hoffman.
The picture of Erd艖s that comes across in both biographies is much the same, since both books are based on a lot of the same source material. Hoffman's book has the advantage that the source of all Erd艖s quotes (except those Hoffman got directly) are documented in footnotes. But because Hoffman also can report many anecdotes from his interviews with Erd艖s himself and with his associates, this biography offers a somewhat clearer picture of the subject as a person, apart from his work.
One anecdote is especially revealing. On an occasion in the late 1960s Erd艖s (who was about 55 at the time) was staying with an old friend from Hungary in southern California, very near the beach. One day Erd艖s went out to walk on an esplanade above the beach. Only ten minutes later his hosts received a phone call, from someone who lived close to the esplanade about five blocks away, to report that Erd艖s turned up on their doorstep saying he was lost and needed help finding his way back to his friend's place. So Erd艖s, in spite of his prodigious memory for details of his mathematics and his mathematical collaborators, couldn't even remember how to retrace his steps. The natural explanation is that he was so absorbed in his mathematical thoughts that no vestige of his short walk had registered in his memory.
As other anecdotes made clear, Erd艖s was fully capable of recalling details of mathematical conversations he'd engaged in years before, and he could also keep track of more or less simultaneous conversations he carried on with several different mathematicians at the same meeting. He could also recall details of perhaps thousands of technical papers he'd read decades before. It seems reasonable to conclude that his ability to concentrate and to recall mathematical detail had a great deal to do with his singular power as a mathematician 鈥� as exemplified by his ability either to solve quickly new mathematical problems or at least to judge accurately their level of difficulty almost effortlessly.
In contrast to this clear portrait of Erd艖s as a person, Hoffman's lack of mathematical background means he must rely on the testimony of others he interviewed to describe Erd艖s' mathematics. The result is a somewhat less satisfactory account. One example is what Hoffman calls "". He says this means a pair of numbers (a and b) where the sum of proper divisors of a is equal to b and the sum of proper divisors of b is equal to a. This is actually the definition of "". The example given is the pair 220 and 284, which was known to Pythagoras. Those are indeed "amicable numbers". The accepted definition of "friendly numbers" is numbers that have the same ratio between themselves and their own sum of divisors. By this definition, 220 and 284 aren't "friendly".
An even more serious problem is the discussion of Bernhard Riemann's non-Euclidean geometry. Hoffman writes "He [Riemann] builds a seemingly ridiculous assumption that it's not possible to draw two lines parallel to each other. His non-Euclidean geometry replaces Euclid's plane with a bizarre abstraction called curved space." It's not actually bizarre at all, since the surface of any sphere is one example. Straight lines on the surface of a sphere are "great circles" (which are by definition the largest circles that can be drawn on a sphere, like the Earth's equator). Great circles are never "parallel", since they always intersect.
Apart from these and a few other mathematical glitches, Hoffman's book is almost free of trivial proofreading errors. But there's one glaring exception (at least in the paperback edition). Sixteen pages of pictures are included in the middle of the book, and given appropriate page numbers. However, the footnotes at the end of the book are all keyed to page numbers, and they haven't been corrected to account for the picture pages, so that all references to pages after the pictures are off by 16 鈥� a very annoying problem if one wants to actually check these references.
In spite of these problems, Hoffman's book provides a fine portrait, based on personal experiences, of Erd艖s the man.
However, what defined Paul Erd艖s even more than his idiosyncrasies and his humanity was that he was quintessentially a mathematician 鈥� a singularly talented and prolific one. Another biography of Erd艖s, by PhD physicist Bruce Schechter (), was published at almost the same time as Hoffman's. (I have reviewed that as well, and I'll try not to duplicate much from that other review.) Hoffman freely concedes that he is not a mathematician. While Schechter isn't a professional mathematician, he is more able to give a complete and accurate account of Erd艖s' work than Hoffman.
The picture of Erd艖s that comes across in both biographies is much the same, since both books are based on a lot of the same source material. Hoffman's book has the advantage that the source of all Erd艖s quotes (except those Hoffman got directly) are documented in footnotes. But because Hoffman also can report many anecdotes from his interviews with Erd艖s himself and with his associates, this biography offers a somewhat clearer picture of the subject as a person, apart from his work.
One anecdote is especially revealing. On an occasion in the late 1960s Erd艖s (who was about 55 at the time) was staying with an old friend from Hungary in southern California, very near the beach. One day Erd艖s went out to walk on an esplanade above the beach. Only ten minutes later his hosts received a phone call, from someone who lived close to the esplanade about five blocks away, to report that Erd艖s turned up on their doorstep saying he was lost and needed help finding his way back to his friend's place. So Erd艖s, in spite of his prodigious memory for details of his mathematics and his mathematical collaborators, couldn't even remember how to retrace his steps. The natural explanation is that he was so absorbed in his mathematical thoughts that no vestige of his short walk had registered in his memory.
As other anecdotes made clear, Erd艖s was fully capable of recalling details of mathematical conversations he'd engaged in years before, and he could also keep track of more or less simultaneous conversations he carried on with several different mathematicians at the same meeting. He could also recall details of perhaps thousands of technical papers he'd read decades before. It seems reasonable to conclude that his ability to concentrate and to recall mathematical detail had a great deal to do with his singular power as a mathematician 鈥� as exemplified by his ability either to solve quickly new mathematical problems or at least to judge accurately their level of difficulty almost effortlessly.
In contrast to this clear portrait of Erd艖s as a person, Hoffman's lack of mathematical background means he must rely on the testimony of others he interviewed to describe Erd艖s' mathematics. The result is a somewhat less satisfactory account. One example is what Hoffman calls "". He says this means a pair of numbers (a and b) where the sum of proper divisors of a is equal to b and the sum of proper divisors of b is equal to a. This is actually the definition of "". The example given is the pair 220 and 284, which was known to Pythagoras. Those are indeed "amicable numbers". The accepted definition of "friendly numbers" is numbers that have the same ratio between themselves and their own sum of divisors. By this definition, 220 and 284 aren't "friendly".
An even more serious problem is the discussion of Bernhard Riemann's non-Euclidean geometry. Hoffman writes "He [Riemann] builds a seemingly ridiculous assumption that it's not possible to draw two lines parallel to each other. His non-Euclidean geometry replaces Euclid's plane with a bizarre abstraction called curved space." It's not actually bizarre at all, since the surface of any sphere is one example. Straight lines on the surface of a sphere are "great circles" (which are by definition the largest circles that can be drawn on a sphere, like the Earth's equator). Great circles are never "parallel", since they always intersect.
Apart from these and a few other mathematical glitches, Hoffman's book is almost free of trivial proofreading errors. But there's one glaring exception (at least in the paperback edition). Sixteen pages of pictures are included in the middle of the book, and given appropriate page numbers. However, the footnotes at the end of the book are all keyed to page numbers, and they haven't been corrected to account for the picture pages, so that all references to pages after the pictures are off by 16 鈥� a very annoying problem if one wants to actually check these references.
In spite of these problems, Hoffman's book provides a fine portrait, based on personal experiences, of Erd艖s the man.
May 12, 2020
I like Math, some people love math, Paul Erdos lived math. This biography of the most prolific mathematician of the 20th century is insightful. It's jammed full of mathematical history, solved and unsolved problems - accessibly explained, and the lifestory and aphorisms of a genius. 5* for content, 4* for story organisation. (4+5)/2 = 4.5 (unless all of our axioms are wrong)
April 30, 2022
I was disappointed in this book. There was not enough on Erd艖s himself. In fact it could have been retitled: The Man Who Loved only Numbers, The Story of Paul Erd艖s and Ron Graham and his Wife, Fan. For this reason, I'm of the view that a biography should only be written about someone who is dead and who has been dead long enough that the lives of all those who intersected with his have terminated as well. (I am under the impression that this idea used to underlie the canon of literary works for study at Oxford.)
Able though he certainly is, Ron Graham is not as interesting a figure as Erd艖s. Graham sounds pretty much like a Bell Labs type of guy--capable, professional, personable and bland. So why does he figure so prominently in this book? My guess is it's because Hoffman is caught up in the modern journalistic obsession with reality and thus he probably believes we must make things alive by providing real, live people, just like you and me to make it relevant; like they do in recent documentaries as a genus of reality TV. But I digress.
Erd艖s was, by all accounts, a transcendent figure. He was kind of like St. Francis of Assisi, giving up all worldly life--even sexual life--for mathematics. The author only scratches the surface of this surprising quality and then only manages to appreciate its eccentric or comic aspects. I was left wanting to know more about how someone could be not only so dedicated, but seemingly religiously so. Surely, it was not sheer mental horsepower because, smart as mathematicians are, his kind is unique even among them?
That there might have been a religious aspect to his endeavors is in evidence because Erd艖s said he did his mathematics in contest with an entity he called the Supreme Fascist (SF), almost as Jacob wrestled with God. Indeed, reading Hoffman's book one can almost hear Erd艖s cry, in his struggle to wrest theorems from what he called The Book, I will not let thee go, except thou bless me. However, this seems to have had no more than passing significance to the author and so Erd艖s' religious beliefs are never seriously explored; under the assumption, no doubt, that simple atheism combined with, perhaps, the atavistic tendrils of Jewish tradition sufficiently accounts for them. Otherwise, the SF is a figure of Erd艖s' whimsy.
I for one wanted to ask the Erd艖s, "Paul, how it is that the SF could have taken the trouble to create The Book with its splendid theorems? Just to make a capricious game with lowly humans?" I suspect he would have answered no to the last question. Such might be the Pagan view, but I don't think it is the Jewish one. Even Jewish atheists do not look at the God of their ancestors as being Zeus. Unfortunately, we'll never know. Indeed, Erd艖s himself may not have fully known, so it would have been nice if Hoffman, who spent a lot of time with Erd艖s on his roadshow of 25+ countries, could have devised a way to pursue this line of inquiry with him. Again, such questions are particularly important in the case of Erd艖s because of the extraordinary way he lived--a way that might have usefully illuminated our own lives.
Not only could the book have been more thoughtful in this regard, but it also could have provided a better sample of Erd艖s' mathematical contributions. I did not find, for example, Ramsey Theory all that compelling, even though Erd艖s spent time developing it. I suspect Hoffman, as a layman, was drawn to it mainly by its esoteric quality. Yet Erd艖s did work on a number of mathematical topics that had (have) profound philosophical and physical implications and which, when combined with his non-mathematical views, might have provided an important clue as to how a man was able to live as an itinerant while eschewing all of the comfy accoutrements of modern life--especially a stable berth as a tenured professor or researcher.
Then he might have been able to shed light on the question--often assumed by most moderns to be answered in the negative--of whether there is anything to the good life more than fun and amusement to the clever like Ron Graham, cool experiences to the thrill seeker or, sadly, easy livin' as most in our day would certainly prefer it--in short, whether life is more than just a hedonistic exercise.
Able though he certainly is, Ron Graham is not as interesting a figure as Erd艖s. Graham sounds pretty much like a Bell Labs type of guy--capable, professional, personable and bland. So why does he figure so prominently in this book? My guess is it's because Hoffman is caught up in the modern journalistic obsession with reality and thus he probably believes we must make things alive by providing real, live people, just like you and me to make it relevant; like they do in recent documentaries as a genus of reality TV. But I digress.
Erd艖s was, by all accounts, a transcendent figure. He was kind of like St. Francis of Assisi, giving up all worldly life--even sexual life--for mathematics. The author only scratches the surface of this surprising quality and then only manages to appreciate its eccentric or comic aspects. I was left wanting to know more about how someone could be not only so dedicated, but seemingly religiously so. Surely, it was not sheer mental horsepower because, smart as mathematicians are, his kind is unique even among them?
That there might have been a religious aspect to his endeavors is in evidence because Erd艖s said he did his mathematics in contest with an entity he called the Supreme Fascist (SF), almost as Jacob wrestled with God. Indeed, reading Hoffman's book one can almost hear Erd艖s cry, in his struggle to wrest theorems from what he called The Book, I will not let thee go, except thou bless me. However, this seems to have had no more than passing significance to the author and so Erd艖s' religious beliefs are never seriously explored; under the assumption, no doubt, that simple atheism combined with, perhaps, the atavistic tendrils of Jewish tradition sufficiently accounts for them. Otherwise, the SF is a figure of Erd艖s' whimsy.
I for one wanted to ask the Erd艖s, "Paul, how it is that the SF could have taken the trouble to create The Book with its splendid theorems? Just to make a capricious game with lowly humans?" I suspect he would have answered no to the last question. Such might be the Pagan view, but I don't think it is the Jewish one. Even Jewish atheists do not look at the God of their ancestors as being Zeus. Unfortunately, we'll never know. Indeed, Erd艖s himself may not have fully known, so it would have been nice if Hoffman, who spent a lot of time with Erd艖s on his roadshow of 25+ countries, could have devised a way to pursue this line of inquiry with him. Again, such questions are particularly important in the case of Erd艖s because of the extraordinary way he lived--a way that might have usefully illuminated our own lives.
Not only could the book have been more thoughtful in this regard, but it also could have provided a better sample of Erd艖s' mathematical contributions. I did not find, for example, Ramsey Theory all that compelling, even though Erd艖s spent time developing it. I suspect Hoffman, as a layman, was drawn to it mainly by its esoteric quality. Yet Erd艖s did work on a number of mathematical topics that had (have) profound philosophical and physical implications and which, when combined with his non-mathematical views, might have provided an important clue as to how a man was able to live as an itinerant while eschewing all of the comfy accoutrements of modern life--especially a stable berth as a tenured professor or researcher.
Then he might have been able to shed light on the question--often assumed by most moderns to be answered in the negative--of whether there is anything to the good life more than fun and amusement to the clever like Ron Graham, cool experiences to the thrill seeker or, sadly, easy livin' as most in our day would certainly prefer it--in short, whether life is more than just a hedonistic exercise.
June 18, 2020
"Mathematics is about finding connections, between specific problems and more general results, and between one concept and another seemingly unrelated concept that really is related. "
Yes, I agree. For me, the epigraph gives the best characterizations of mathematics. This is precisely why I love math. I teach mathematics at a university, but I am just an applied mathematician and don't know very much about real math, such as number theory, topology, or abstract algebra. Yet I do love math passionately for the connections it uncovers between seemingly disjoint fields like, say, probability and number theory:
Paul Erd枚s was one of the most famous mathematicians of the 20th century and one of the most prolific in history. He published 1525 papers, mostly with co-authors. His collaborative working style was notorious. There exists such a thing as Erd枚s Number: Erd枚s himself has number 0, mathematicians who co-wrote papers with him have number 1, mathematicians who co-wrote papers with those who have number 1 have number 2, etc. Thanks to my friend in the math department, who published with someone who has number 2, thus getting number 3, I have Erd枚s number 4 (not very convincingly, though, our paper only tangentially touches math).
I have found Paul Hoffman's The Man Who Loved Only Numbers biography of Paul Erd枚s an interesting, solid read. I hope that readers who know even less about math than I do will share my opinion. There is a lot in the biography about Paul Erd枚s himself, about his unconventional behavior, quirks, and eccentricities, like his special words for men, women, children, music, etc. or the fact that "he was twenty-one when he buttered his first piece of bread." The reader will also learn a lot about things that may seem extraneous to the topic - like, for instance, a captivating account of 20th-century history of Hungary, where Paul Erd枚s comes from (along with von Neumann, Teller, Szilard, Wigner, and several others -- see my review of The Martian's Daughter. A Memoir by Marina von Neumann Whitman.)
While there is a lot in the book about mathematics itself the text should be accessible to most readers, not only people who have connections with math. The long story of Fermat's Last Theorem and Dr. Wiles' proof of it is captivating. Because of my fascination with probability I read the account of the famous story about Monty Hall Problem posed and solved by Marilyn vos Savant in the Parade magazine: several PhD-titled math professors disagreed with her solution and were wrong. I like the general tone of the biography, full of sympathy, admiration, and deep respect for the great mathematician.
Of course the author shows the most beautiful equation in mathematics:
I am really curious whether the non-math readers will appreciate the biography more or less than I do. For me it is not quite a four-star work, but not far from it.
Three-and-a-half stars.
Yes, I agree. For me, the epigraph gives the best characterizations of mathematics. This is precisely why I love math. I teach mathematics at a university, but I am just an applied mathematician and don't know very much about real math, such as number theory, topology, or abstract algebra. Yet I do love math passionately for the connections it uncovers between seemingly disjoint fields like, say, probability and number theory:
"Erd枚s, working with Mark Kac, [...] would find a deep connection between a number's roundness and that workhorse of probability theory the bell-shaped curve, or normal distribution."Yes, I also love math for the exquisite elegance of its constructs and maybe even for the certainties it provides, but connections are first and foremost.
Paul Erd枚s was one of the most famous mathematicians of the 20th century and one of the most prolific in history. He published 1525 papers, mostly with co-authors. His collaborative working style was notorious. There exists such a thing as Erd枚s Number: Erd枚s himself has number 0, mathematicians who co-wrote papers with him have number 1, mathematicians who co-wrote papers with those who have number 1 have number 2, etc. Thanks to my friend in the math department, who published with someone who has number 2, thus getting number 3, I have Erd枚s number 4 (not very convincingly, though, our paper only tangentially touches math).
I have found Paul Hoffman's The Man Who Loved Only Numbers biography of Paul Erd枚s an interesting, solid read. I hope that readers who know even less about math than I do will share my opinion. There is a lot in the biography about Paul Erd枚s himself, about his unconventional behavior, quirks, and eccentricities, like his special words for men, women, children, music, etc. or the fact that "he was twenty-one when he buttered his first piece of bread." The reader will also learn a lot about things that may seem extraneous to the topic - like, for instance, a captivating account of 20th-century history of Hungary, where Paul Erd枚s comes from (along with von Neumann, Teller, Szilard, Wigner, and several others -- see my review of The Martian's Daughter. A Memoir by Marina von Neumann Whitman.)
While there is a lot in the book about mathematics itself the text should be accessible to most readers, not only people who have connections with math. The long story of Fermat's Last Theorem and Dr. Wiles' proof of it is captivating. Because of my fascination with probability I read the account of the famous story about Monty Hall Problem posed and solved by Marilyn vos Savant in the Parade magazine: several PhD-titled math professors disagreed with her solution and were wrong. I like the general tone of the biography, full of sympathy, admiration, and deep respect for the great mathematician.
Of course the author shows the most beautiful equation in mathematics:
e to the power (pi times i) + 1 = 0which connects the five most important objects in math - the constants e, pi, 0, 1, and i.
I am really curious whether the non-math readers will appreciate the biography more or less than I do. For me it is not quite a four-star work, but not far from it.
Three-and-a-half stars.
February 10, 2013
The Man Who Loved Only Numbers is an interesting read from multiple aspects. It mostly concentrates on the life story of Paul Erd枚s, an incredible genius who took on an occupation of traveling mathematician, all for one goal: getting more knowledge from the Book. (It was Erd枚s' opinion that the Supreme Fascist up there had a Book filled with elegant mathematical equations, but people weren't allowed to read it. Instead, people could only catch glimpses of the Book's pages, by means of flashes of inspirations mathematicians may have.) The book is basically an expose of the quirks of a man who led a life of a nomad, working a 19 hours a day and collaborating with numerous other people to produce a staggering number of publications. A man who was concentrated on lowering the SF's score by doing kind things, like giving money to charity, finding child prodigies and visiting the mothers and widows of deceased colleagues.
But it doesn't stop on the life and, perhaps less so, work of the prolific mathematician. We're also granted insight into the lives of mathematicians Erd枚s worked with (like G.H. Hardy, Ron Graham and Stan Ulem) or held in high regard (like Ramanujan), as well as tidbits about famous mathematicians from the past (Gauss, Fermat, Fibonacci, Sophie Germain...). Even though the author didn't focus on mathematical problems - usually he would describe a problem significant for the mathematician mentioned - that didn't detract from my enjoyment of the book.
Last but not least, the book also deals with the times in which Erd枚s lived. As an expatriate stemming from a country with troubled history, he was affected in different ways by the political workings of the centers of power. I'm referring to the fact that Paul Erd枚s was born into a Jewish family in a time Jews weren't very popular (and their popularity dwindled down even further during WWII). His father spent a long time in a gulag far aways from home, thanks to the democratic regime in Hungary after the collapse of the Austro-Hungarian monarchy, and his family was severely decimated in WWII. After the rise of communism in Hungary, Erd枚s was regarded with suspicion in the USA (also known as Sam in Erd枚sese :P), and had trouble traveling freely between countries as was his habit.
My final verdict: The book probably won't be appealing to trivial beings, but curious bosses and slaves (and epsilons, for that matter) who would like to learn more about the Book, what Erd枚s numbers signify, what it means to preach, what it means to die, and what it means to leave will find The Man Who Loved Only Numbers interesting.
But it doesn't stop on the life and, perhaps less so, work of the prolific mathematician. We're also granted insight into the lives of mathematicians Erd枚s worked with (like G.H. Hardy, Ron Graham and Stan Ulem) or held in high regard (like Ramanujan), as well as tidbits about famous mathematicians from the past (Gauss, Fermat, Fibonacci, Sophie Germain...). Even though the author didn't focus on mathematical problems - usually he would describe a problem significant for the mathematician mentioned - that didn't detract from my enjoyment of the book.
Last but not least, the book also deals with the times in which Erd枚s lived. As an expatriate stemming from a country with troubled history, he was affected in different ways by the political workings of the centers of power. I'm referring to the fact that Paul Erd枚s was born into a Jewish family in a time Jews weren't very popular (and their popularity dwindled down even further during WWII). His father spent a long time in a gulag far aways from home, thanks to the democratic regime in Hungary after the collapse of the Austro-Hungarian monarchy, and his family was severely decimated in WWII. After the rise of communism in Hungary, Erd枚s was regarded with suspicion in the USA (also known as Sam in Erd枚sese :P), and had trouble traveling freely between countries as was his habit.
My final verdict: The book probably won't be appealing to trivial beings, but curious bosses and slaves (and epsilons, for that matter) who would like to learn more about the Book, what Erd枚s numbers signify, what it means to preach, what it means to die, and what it means to leave will find The Man Who Loved Only Numbers interesting.
August 17, 2017
As a book of somewhat random anecdotes, some about mathematics and some about people who knew Paul Erd艖s or Ron Graham, this is an interesting book; as a book about Paul Erd艖s or about 鈥渢he Search for Mathematical Truth鈥� it鈥檚 severely lacking.
Paul Erd艖s (pronounced air-dish, you鈥檙e on your own with 鈥淕raham鈥�) was 鈥渁 traveling mathematician.鈥� He turned down a permanent position at N么tre Dame at about forty (if I鈥檓 reading Hoffman right) because 鈥渉e didn鈥檛 want to be pinned down.鈥�
This book focuses on the weird things Erd艖s did. Which is okay; that is half the joy in reading about trickster geniuses like Erd艖s or Feynman. But the other half is learning about the philosophy they lived by and what it was about them that both drove them to discover so much in such different ways, and made them so successful at it. How did their deviation from the norm help (or hurt) their scientific or mathematical work?
Someone reading about Feynman may not be able to become the genius that he was, but they will be able to apply the scientific method along with a critical curiosity to what they see, what they are told, and even what they would otherwise assume.
Erd艖s was smart about some things and not about others, rude at some times but not others. But I never got a sense of why or how.
Hoffman goes off on many long tangents about the people Erd艖s knew鈥攁nd sometimes about people the people Erd艖s knew knew, especially Ron Graham. But they are not really tangents, I don鈥檛 think. I think they鈥檙e the real point of the book. 鈥淓rd艖s more than anyone else was responsible for turning mathematics into a social activity.鈥�
I didn鈥檛 get any real sense from this book about what that means about Paul Erd艖s, though.
The chapters weren鈥檛 numbered solely with integers, but rather 1, 2, e, 3, 蟺, 4, 5, 6, 7, and, for the final chapter, 鈭�. It鈥檚 possible that this was a series of unconnected essays; especially in the final chapter bits seemed to be repeated with no sense that it was a repetition.
Paul Erd艖s (pronounced air-dish, you鈥檙e on your own with 鈥淕raham鈥�) was 鈥渁 traveling mathematician.鈥� He turned down a permanent position at N么tre Dame at about forty (if I鈥檓 reading Hoffman right) because 鈥渉e didn鈥檛 want to be pinned down.鈥�
This book focuses on the weird things Erd艖s did. Which is okay; that is half the joy in reading about trickster geniuses like Erd艖s or Feynman. But the other half is learning about the philosophy they lived by and what it was about them that both drove them to discover so much in such different ways, and made them so successful at it. How did their deviation from the norm help (or hurt) their scientific or mathematical work?
Someone reading about Feynman may not be able to become the genius that he was, but they will be able to apply the scientific method along with a critical curiosity to what they see, what they are told, and even what they would otherwise assume.
Erd艖s was smart about some things and not about others, rude at some times but not others. But I never got a sense of why or how.
Hoffman goes off on many long tangents about the people Erd艖s knew鈥攁nd sometimes about people the people Erd艖s knew knew, especially Ron Graham. But they are not really tangents, I don鈥檛 think. I think they鈥檙e the real point of the book. 鈥淓rd艖s more than anyone else was responsible for turning mathematics into a social activity.鈥�
I didn鈥檛 get any real sense from this book about what that means about Paul Erd艖s, though.
The chapters weren鈥檛 numbered solely with integers, but rather 1, 2, e, 3, 蟺, 4, 5, 6, 7, and, for the final chapter, 鈭�. It鈥檚 possible that this was a series of unconnected essays; especially in the final chapter bits seemed to be repeated with no sense that it was a repetition.
April 1, 2013
A very fun read and often extremely interesting and exciting. My only comment is that it's not strictly a biography of Erdos, at times going nearly a whole chapter without mentioning him. Rather it's reminiscences about him and the lives of many other famous mathematicians that intersected with his. (If you've read a few books on mathematics then you've probably heard a lot of the anecdotes before.) Very inspiring.
January 5, 2009
Erdos was a Hungarian who only did math. Never had sex, kept an apartment, or buttered his own toast (though he said he thought he could do it (the butter, not the sex)).
But he did manage to knock on the door of anyone who would put up with him, to do math 20 hours a day with the assistance of coffee and amphetamines (till he was 80-something). You'll think his shenanigans are made up.
But he did manage to knock on the door of anyone who would put up with him, to do math 20 hours a day with the assistance of coffee and amphetamines (till he was 80-something). You'll think his shenanigans are made up.
April 29, 2013
This is a well written biography of paul erdos, a prolific hungarian mathematician who spends over 19 hours a day doing mathematics and has published over 1400 papers. He was a man who had no home and had travelled around the world giving lectures and staying at his friends place's.
To anyone who is interested in mathematics, this book is great and very fun to read.
To anyone who is interested in mathematics, this book is great and very fun to read.
September 1, 2017
I don't generally like maths or have much of an interest in mathematicians but I made an exception for the story of Paul Erdos. He was a very interesting (eccentric) human being whose story is well worth reading and enjoying.
April 22, 2023
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March 8, 2025
3.5 rounded up bc it鈥檚 hard to make someone giggle while reading about how theorems are proved but i did. enjoyed! good biography and general historical overview of 20th century mathematics. would save excerpts to give to future students
August 10, 2016
I wish there were more people like Paul Erd枚s. I was only ever decent at math in high school, and terrible at math after that, so his exploits make me jealous in a good way. I think for many people, and certainly frequently for me, math beyond a certain point is a dense, lightless thicket of symbols. Maybe everyone is born with a certain amount of math facility, and once you learn up to the point where your returns have diminished to uselessness, you have no choice but to forget about it and move on to something else. I made it through calculus and still remember some of what I learned, but I wouldn't want to bet anyone's life on me being able to integrate anything more complicated than a sine function very quickly. That's why it's so cool to read an account of a genuine math genius at work - even though I know that this guy who published over 1,500 papers in his lifetime is on another plane entirely when it comes to mathematics, he's so dedicated to the wonders of the subject that it gradually infected me through the pages and I came away wishing I had stuck with my math classes.
I often wonder to what extent being good at math is simply an innate quality, a gift that you either have or you don't. One of the things that struck me when I was reading G枚del Escher Bach is that Douglas Hofstader's explanations of complicated mathematical issues were much more comprehensible than that same explanation from a textbook (or even Wikipedia), and a large part of it was due to the fact that he gave a lot of history and narrative behind the various problems instead of just laying out symbols and variables. Humans naturally learn through narratives and stories, and it takes a rare kind of person to be able to strip away all of the scene-setting and background and get straight to the abstract symbol-manipulation. Probably some people are just born with the potential to understand things like Russell's paradox and some aren't, but I would really like to know exactly why that is, what separates the neurology of an Erd枚s from that of a mere mortal. I like that the book doesn't make Erd枚s - a fairly weird guy even by the relaxed standards of mathematicians - out to be some kind of freak, which I've frequently seen done to some of the more singular characters in science history like Newton.
Instead it's filled with plenty of testimonials about his kindness, his many friendships, and of course his unbelievable gift for probing the relationships between numbers. Explaining higher-level mathematics to a lay audience is one of the toughest tasks a writer can undertake, and Hoffman does a good job of giving the reader a brief tour of some of the many areas of math that Erd枚s influenced or revolutionized in some way. It's almost comforting to realize that even many professional mathematicians were baffled by what he was doing, and really the way he was able to find patterns in numbers is one of those things that just got more and more impressive with each page. I don't know what kind of mental circuitry lies behind mathematical talent, but I wish I had it, because many of the problems Erd枚s struggled with are extremely interesting in their own right, if you're curious at all at the mysterious relationships behind the world that we see. There are just so many weird things about prime numbers that you can forgive Erd枚s' monastic devotion to the subject. I wish I had read this when I was struggling with differential equations, it might have given me some inspiration and fortitude to remember that mathematics is an infinite field. No one can know everything, and that leaves plenty of room for even the most meager contributor to make a mark.
I often wonder to what extent being good at math is simply an innate quality, a gift that you either have or you don't. One of the things that struck me when I was reading G枚del Escher Bach is that Douglas Hofstader's explanations of complicated mathematical issues were much more comprehensible than that same explanation from a textbook (or even Wikipedia), and a large part of it was due to the fact that he gave a lot of history and narrative behind the various problems instead of just laying out symbols and variables. Humans naturally learn through narratives and stories, and it takes a rare kind of person to be able to strip away all of the scene-setting and background and get straight to the abstract symbol-manipulation. Probably some people are just born with the potential to understand things like Russell's paradox and some aren't, but I would really like to know exactly why that is, what separates the neurology of an Erd枚s from that of a mere mortal. I like that the book doesn't make Erd枚s - a fairly weird guy even by the relaxed standards of mathematicians - out to be some kind of freak, which I've frequently seen done to some of the more singular characters in science history like Newton.
Instead it's filled with plenty of testimonials about his kindness, his many friendships, and of course his unbelievable gift for probing the relationships between numbers. Explaining higher-level mathematics to a lay audience is one of the toughest tasks a writer can undertake, and Hoffman does a good job of giving the reader a brief tour of some of the many areas of math that Erd枚s influenced or revolutionized in some way. It's almost comforting to realize that even many professional mathematicians were baffled by what he was doing, and really the way he was able to find patterns in numbers is one of those things that just got more and more impressive with each page. I don't know what kind of mental circuitry lies behind mathematical talent, but I wish I had it, because many of the problems Erd枚s struggled with are extremely interesting in their own right, if you're curious at all at the mysterious relationships behind the world that we see. There are just so many weird things about prime numbers that you can forgive Erd枚s' monastic devotion to the subject. I wish I had read this when I was struggling with differential equations, it might have given me some inspiration and fortitude to remember that mathematics is an infinite field. No one can know everything, and that leaves plenty of room for even the most meager contributor to make a mark.
June 25, 2021
A highly enjoyable read, which skilfully weaves together an amusing and touching account of the life of Paul Erdos with a fascinating exploration of the branch of mathematics he loved.
Erdos lived for numbers, his obsession with them knowing no bounds. Even other mathematicians, like Michael Jacobson, struggled to keep up with him. "It was 1983 when he came [to visit] for the first time," Jacobson recalls in the book. "The first day we did mathematics until one in the morning. I was completely drained. I went upstairs to bed, and he stayed downstairs in the guest room. At 4.30am I heard pots banging in the kitchen. He kept banging them. It was his way of telling me to get up. I stumbled downstairs about six. What were the first words out of his mouth? Not 'Good morning' or 'How'd you sleep?' but 'Let n be an integer. Suppose k is...' I was half-naked, with just a bathrobe on and my eyes blurry and partially shut. I drew the line there. I told him I couldn't do mathematics before I took a shower."
There's a more endearing side to Erdos, though. A Hungarian Jew who fled anti-Semitism in the 1930s, he never married or had a romantic relationship, but he loved children, or "epsilons" as he called them (after the mathematical term for a small positive infinitesimal quantity). He had a genius for setting each person - child, student or expert - just the right problem, one that would intrigue and stretch without frustrating them. Even the demands he made on others, obvious from Jacobson's account, reflected his zeal for collaboration and desire to see people reach their potential. Hoffman draws a telling contrast between Erdos and Andrew Wiles, who slaved away for seven years in his attic to produce a proof of Fermat's Last Theorem. For Erdos, mathematics was always a social activity - far from jealously guarding his ideas, he was singularly generous with them. "He would share his conjectures because his goal was not to be the first to prove something," said one of Erdos's collaborators, Alexander Soifer: "Rather his goal was to see that somebody proved it - with him or without him."
Where this book really succeeds is in getting across something of the fascination of the kind of mathematics Erdos loved, without which we would struggle to understand his life. Erdos was driven by pure maths - he didn't care much about the applications, and when a friend had a paper published in a physics journal, he sent him a postcard saying "I pray for your soul". He worked mainly with recognisable numbers, eschewing imaginary numbers such as the square root of minus one. Like many pure mathematicians, he was drawn to prime numbers, which had an almost mystical appeal for him. At the age of 20, he announced that he was going to produce an elementary proof of the Prime Number Theorem - which provides a good approximation for how prime numbers are distributed. Twenty years later, he did just that.
The book touches on dozens of other mathematicians besides Erdos: some who worked closely with him, like Ron Graham; others because their ideas had an impact on his work, like Georg Cantor. Hoffman journeys through set theory, transfinite numbers, unit fractions, worst-case analysis, infinite series and Fibonacci numbers - all with a ringing clarity and a lightness of touch - there was barely a paragraph I had to read twice to make sure I'd understood it. If this book doesn't give you a glimpse of the mystery and beauty that Erdos saw in numbers, nothing will.
Erdos lived for numbers, his obsession with them knowing no bounds. Even other mathematicians, like Michael Jacobson, struggled to keep up with him. "It was 1983 when he came [to visit] for the first time," Jacobson recalls in the book. "The first day we did mathematics until one in the morning. I was completely drained. I went upstairs to bed, and he stayed downstairs in the guest room. At 4.30am I heard pots banging in the kitchen. He kept banging them. It was his way of telling me to get up. I stumbled downstairs about six. What were the first words out of his mouth? Not 'Good morning' or 'How'd you sleep?' but 'Let n be an integer. Suppose k is...' I was half-naked, with just a bathrobe on and my eyes blurry and partially shut. I drew the line there. I told him I couldn't do mathematics before I took a shower."
There's a more endearing side to Erdos, though. A Hungarian Jew who fled anti-Semitism in the 1930s, he never married or had a romantic relationship, but he loved children, or "epsilons" as he called them (after the mathematical term for a small positive infinitesimal quantity). He had a genius for setting each person - child, student or expert - just the right problem, one that would intrigue and stretch without frustrating them. Even the demands he made on others, obvious from Jacobson's account, reflected his zeal for collaboration and desire to see people reach their potential. Hoffman draws a telling contrast between Erdos and Andrew Wiles, who slaved away for seven years in his attic to produce a proof of Fermat's Last Theorem. For Erdos, mathematics was always a social activity - far from jealously guarding his ideas, he was singularly generous with them. "He would share his conjectures because his goal was not to be the first to prove something," said one of Erdos's collaborators, Alexander Soifer: "Rather his goal was to see that somebody proved it - with him or without him."
Where this book really succeeds is in getting across something of the fascination of the kind of mathematics Erdos loved, without which we would struggle to understand his life. Erdos was driven by pure maths - he didn't care much about the applications, and when a friend had a paper published in a physics journal, he sent him a postcard saying "I pray for your soul". He worked mainly with recognisable numbers, eschewing imaginary numbers such as the square root of minus one. Like many pure mathematicians, he was drawn to prime numbers, which had an almost mystical appeal for him. At the age of 20, he announced that he was going to produce an elementary proof of the Prime Number Theorem - which provides a good approximation for how prime numbers are distributed. Twenty years later, he did just that.
The book touches on dozens of other mathematicians besides Erdos: some who worked closely with him, like Ron Graham; others because their ideas had an impact on his work, like Georg Cantor. Hoffman journeys through set theory, transfinite numbers, unit fractions, worst-case analysis, infinite series and Fibonacci numbers - all with a ringing clarity and a lightness of touch - there was barely a paragraph I had to read twice to make sure I'd understood it. If this book doesn't give you a glimpse of the mystery and beauty that Erdos saw in numbers, nothing will.
September 24, 2011
Paul Hoffman strikes the perfect balance between math and biography, technicality and heart-felt sentiments for a life worthy of remembering. I'm a little surprised I had never heard of Paul Erdos before having this book recommended to me, but I'm kind of glad I hadn't. It let me experience the world of math through his eyes and the eyes of those who knew him, without a single shred of foreknowledge. I let Hoffman carry me through the life and math (though I'd argue they are hardly separable) of Erdos one fascinating chapter at a time, with the sense of slowly coming to know a stranger and gaining a world of respect and admiration for him along the way.
Having much of the story told through the perspectives of those whose lives and careers Erdos came to touch in his decades of academic nomadery added to its depth, and certainly to its meaning. He had an impact on many, many people, and the joy of discovery that he shared with each of them comes across infectiously throughout the book. What an absolute inspiration to scientists, creators, and curious minds everywhere. The world was lucky to have had him walk it, and I am lucky to have been introduced to what little of him I could ever hope to know, through this book.
Having much of the story told through the perspectives of those whose lives and careers Erdos came to touch in his decades of academic nomadery added to its depth, and certainly to its meaning. He had an impact on many, many people, and the joy of discovery that he shared with each of them comes across infectiously throughout the book. What an absolute inspiration to scientists, creators, and curious minds everywhere. The world was lucky to have had him walk it, and I am lucky to have been introduced to what little of him I could ever hope to know, through this book.
February 27, 2013
This book is about a mathematician and his life with numbers, an idea so esoteric mere humans such as myself cannot comprehend it. This particular mathematician had a special code language for many things. Men were slaves, women were bosses, children were epsilons, etc. This mathematician was generous to a fault but also relied on the kindness of strangers, like Blanche DuBois in "A Streetcar Named Desire." He was a difficult person but so brilliant and so kind that people put up with his many eccentricities.
This book is very funny and keeps you interested throughout. I was intrigued with the idea of the Erdos number which derives from whether or not you collaborated with Mr. Erdos in any way. I even went online to look at the visualizations of the Erdos Collaboration Graphs that other mathematicians have developed to show the correlation of the Erdos numbers.
Finally, this book is not only about Paul Erdos but is also about the great society of mathematicians and their camaraderie, as well as the very idea of humanity and relationships. If you are interested in any of that, whether you know anything about math or not, you should read this book.
This book is very funny and keeps you interested throughout. I was intrigued with the idea of the Erdos number which derives from whether or not you collaborated with Mr. Erdos in any way. I even went online to look at the visualizations of the Erdos Collaboration Graphs that other mathematicians have developed to show the correlation of the Erdos numbers.
Finally, this book is not only about Paul Erdos but is also about the great society of mathematicians and their camaraderie, as well as the very idea of humanity and relationships. If you are interested in any of that, whether you know anything about math or not, you should read this book.
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