A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash

Amazon.com

Stories of famously eccentric Princetonians abound--such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up--only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.

Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees). This highly recommended book is indeed "a story about the mystery of the human mind, in three acts: genius, madness, reawakening." --Mary Ellen Curtin

Book Description

How could you, a mathematician, believe that extraterrestrials were sending you messages?" the visitor from Harvard asked the West Virginian with the movie-star looks and Olympian manner.

"Because the ideas I had about supernatural beings came to me the same way my mathematical ideas did," came the answer. "So I took them seriously."

Thus begins the true story of John Nash, the mathematical genius who was a legend by age thirty when he slipped into madness, and who -- thanks to the selflessness of a beautiful woman and the loyalty of the mathematics community -- emerged after decades of ghostlike existence to win a Nobel Prize and world acclaim. The inspiration for a major motion picture, Sylvia Nasar's award-winning biography is a drama about the mystery of the human mind, triumph over incredible adversity, and the healing power of love.

Customer Reviews:

He Saw The World In A Way No One Could Have Imagined: A Tour de Force.......2007-10-06

~A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash~ is Sylvia Nassar's most remarkable biography of the life of mathematician John Forbes Nash, Jr. This is not the most flattering of biographies, but a remarkably intriguing one nonetheless. Nicknamed the Kid Professor, Nash started teaching first at the Massachusetts Institute of Technology at age twenty-three. Nash gained acclaim following after he became a Nobel Laureate in 1994 for his contributions to economics, game theory, and mathematics. But earning this prestigious accolade was marked by a career of alienation and hardship.

He devised the so called Nash equilibrium, and contributed a breathtaking corpus of research to the study of game theory. Game theory concerns itself with the study of strategic interactions between agents. Parties choose strategies which will maximize their return in response to the strategies that other parties choose. Nash transcended the earlier zero-sum game theories, and revolutionized the application of game theory to both economic, political and military strategic questions. Traditionally, game theory applications were primarily were zero-sum in nature, with the winner-take-all approach-- i.e., my win is your loss, or vice versa.

True genius is often thought to meet the edge of insanity by some people. This held true in the life of John Nash. Lamentably, Nash suffered from schizophrenia, and made harrowing descent into mental illness complete with psychotic delusions and bizarre visions. His illness fueled his bizarre obsessions with numerology and other eccentricities.

Nash resigned his post at MIT after his first serious episodes. He took a position with the enigmatic Cold War think tank the RAND Corporation. RAND, the ultra secretive civilian think tank had a casual campus environment in the laid-back Santa Monica, CA of the 1950s, which hosted some of the most brilliant minds in the United States. RAND was enveloped in a melange of detachment, paranoia, and megalomania. His tenure there perhaps fueled his later Cold War paranoia, which came to bloom when his mental illness reached its full blown stage.

After some breakdowns, Nash recouped his bearings and went onto teach at Princeton. There he met his future wife Alicia who was one of his students. She became enamored with his genius. And contrary to popular myth, though schizophrenics are often thought to be devoid of personal attachments, Nash could show empathy and love. Though his illness frequently revisited him, his wife helped him cope with it. Nash scrawled numbers all over Princeton Hall, and became a mysterious ghost-like figure on the campus of Princeton University. His illness ultimately strained their marriage to the point of separation for a while. At one time, he coped with his illness by traveling Europe and became enamored of his delusions of self-importance. When his mental illness became full-blown, it incapacitated him and left him feeling utterly worthless. His wife had him committed to an institution briefly, before reconciling and moving back in with him to care for him. Instead of being relegated to obscurity, Nash eventually overcame his mental illness with age, and with the recommendation of his peers began to earn the recognition he long deserved.

All things considered, this is a most remarkable look at the life of John Nash. Perhaps the eccentric Nash would not have been very well regarded but for his genius. But Nash showed himself capable of compassion, empathy and love in the relationship with his wife Alicia. Nash possessed as his wife Alicia saw--a beautiful mind. Nash's life was dramatized in the 2001 film A Beautiful Mind based on Nassar's book, which renewed interest in the book first published in 1998.

My $.02 worth.......2007-09-30

I read this book long after it was published, and long after it had accumulated more reviews than anyone is likely to wade through. It's tough to think of a fresh approach, but here's a try:
An amusing, minor sub-theme in this book is the fact that John Nash, who ranks at or near the top among American mathematicians of the past century, was a flop at picking stocks. He devoted a tremendous amount of time to looking for patterns and other indicators that might help him beat the market, and he wound up doing worse than your average patzer. He even lost a sizable chunk of his mother's investment funds.
Think about that the next time you are tempted to respond to one of those blaring magazine or TV ads offering to sell you a technical stock-picking system that really works.

Dad's father's day gift.......2007-07-22

Amazon's website wouldn't let me type a zip code; the website defaulted the zip based on city name and zip was incorrect. As a result, package couldn't be delivered and I was issued a full refund.

Good, but sometimes to in-depth.......2007-06-29

Very good story, I could hardly put it down.

though at times Sylvia spent an entire chapter simply talking about a university, She struggled staying with her point, though only at times.

A Beautiful Book.......2007-06-15

In Nasar's biography of the Nobel prize winning mathematician John Forbes Nash, Jr., his descent into irrationality is portrayed by chronicling several experiences in his frenetic childhood and those from his early adulthood to the present.

In the first chapters of the book, Nasar juxtaposes several episodes in Nash's distinguished childhood, displaying his early genius in chemistry and math in conjunction with those that reveal a childishness equally as impressive. As a youngster, Nasar shows his penchant for pulling pranks on his friends, at one time electrocuting a neighbor and even his own sister, who was continually forced by her mother as they grew up to include the younger Nash in her social activities. However, Nash, though not taciturn, preferred reading encyclopedias and most of all, experimenting. His experiments with bomb-making actually killed one of his childhood friends, after which Nash stopped making them for the rest of his life.

The book describes Nash's early discovery of his love for math one day while reading a book about Fermat's Theorem on prime numbers, which he proved by his own self at the age of 12. It also details his spurning Harvard for Princeton University, a less recognized mathematics school then despite Albert Einstein's prominent position in the faculty, upon his graduation from Carnegie Mellon University, then known as the Carnegie Institute of Technology, because he felt they had not tried hard enough to pursue him.

Indeed, his egocentrism is depicted throughout the whole biography, and it is this megalomania which would later develop into full-blown schizophrenia and terrorize his whole constitution for decades, halting his academic production almost completely during that time period.

Nash ascribes his sudden affliction to a number of disappointments: first, though Nash had solved a problem on turbulence in which he was able to devise a mathematical model for notating its sudden changes in motion, he found out when he was about to submit his paper for publication that someone else, an Italian by the name of De Giorgi, had beat him to it and published his paper in the most obscure journal imaginable; secondly, he says in a letter that his attempt to revise quantum theory was "possibly overreaching and psychologically destabilizing."; third, he attributes his failure to win the Fields Medal in 1958--his last chance since it is generally awarded to young mathematicians--as a contributing factor to his disease. The rest of the book focuses on his delusional experiences and the assistance and loving care of his small group of friends, including his wife, which helped him finally regain control of his mind in 1990.

It was at Princeton that Nash became familiar with John von Neumann's famous theory on rational human behavior, The Theory of Games and Economic Behavior, which focused on zero-sum two person games, and which he felt was unrealistic for predicting most economic situations. Concentrating on what to him were gaping flaws in von Neumann's work, he set out to write his epochal dissertation on a theory that could encompass all realistic scenarios, called Non-cooperative Games, which contained the definition of his equilibrium theory, whose name he is now its eponym. His results also inspired the most famous game of strategy in all of social science: The Prisoner's Dilemma. More significantly, it was this work which won him his Nobel prize in Economics in 1994.

Nasar states that his hyper-competitive spirit was fueled by an intense drive to succeed. When he did not receive an assistant professorship offer from Princeton after obtaining his Ph.D at only 22 years of age, despite his seminal paper on algebraic manifolds, he was humiliated deeply and thereafter went to MIT where he was offered a fellowship. At 25, Nasar describes Nash's sudden impulse to solve the embedding problem for manifolds--a problem which had been left unsolved since it was suggested by Riemann--as a way to belittle a colleague at MIT. And he did. This is today one of the most famous works in pure mathematics.

The body of research which Nasar obviously has pored over is impressive, and it shows in the fluidity of his biography, which flows like a novel, and the immense number of sources cited. It is a fascinating book and one which I recommend as an insight into the emergence of a supposedly degenerative disease and its subsequent effects on a man who at the time seemed on the verge of unprecedented success and fame in the scholastic world. It also shows how even the most logical can at times seem most illogical, and vice versa. As Nash says, "the ideas I had about supernatural beings came to me the same way my mathematical ideas did." For me, I was less intrigued by the episodes detailing Nash's battles with schizophrenia than I was with those of his academic achievements. His spirit and motivation is something I wish I possessed much more of.

All in all, this is a book I enjoyed immensely. And for $2 at Deseret Industries, I couldn't have asked for a better way to spend my money!

Logical Dilemmas: The Life and Work of Kurt Godel

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Good Biography, a bit heavy on the math
Excellent.
The definitive biography of Kurt Godel
By a Mathematician for Mathematicians

Logical Dilemmas: The Life and Work of Kurt Godel
John W. Dawson Jr.
Manufacturer: A K Peters, Ltd.
ProductGroup: Book
Binding: Paperback

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ASIN: 1568812566
Release Date: 2005-05-28

Product Description

This authoritative biography of Kurt Gödel relates the life of this most important logician of our time to the development of the field. Gödels seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from turn of the century Austria to the Institute for Advanced Study in Princeton.

Customer Reviews:

Good Biography, a bit heavy on the math.......2005-09-02

This book has a kind of interesting way of doing a biography. The subject, Godel, is one of the pre-eminent mathematicians of the twentieth century. This biography, written by a mathematician spends a good bit of time on the math that Godel was doing as well as the story of his life.

Chapter III, for instance is a capsule history of the development of logic to 1928. This is to give background to the mathematical world as it existed when Godel was starting his work. In particular it discusses the open problems in mathematics that David Hilbert proposed in 1900. Godel resolved the second of these problems.

Coupled with his genius in mathematics, Godel also had serious psychological problems. He eventually died of starvation because he was convinced that the food he was getting had been poisoned and refused to eat. Dr. Dawson has written a compasionate and understanding biography, even if the mathematics gets just a bit deep once in a while.

Excellent........2003-09-20

An excellent biography of Godel. Examines his personal life and mathematical work in an integrated manner. Dawson is thorough, well-researched, and shows a command of the mathematics involved. He provides the most accurate picture available of the real Godel- in contrast to the anecdotal, 'crazy-genius' stories you see elsewhere. This is not a popular account of Godel's work, so the reader will need an understanding of fundamental mathematical logic and Godel's theorem to appreciate much of the book. But Dawson does provide a lot of history of mathematical logic, including a great chapter on developments up to 1928 that could stand by itself. The appendix provides a chronology, genealogy, and "biographical vignettes" of other important logicians.

The definitive biography of Kurt Godel.......2001-08-01

Knowing what went on in the mind of Kurt Godel will forever be unattainable. Nonetheless, John Dawson comes as close as possible to understanding what made Godel click.

Having catalogued Godel's works and personal papers, Dawson saw aspects of Godel's life that perhaps no one short of his wife had seen.

The book is a fascinating jaunt through the through the lives of one of the greatest minds of the 20th century. What is also interesting is Godel's interaction with personalities such as Einstein and Van Neumann.

While the mathematics is often abstract, as can be expected, Logical Dilemmas is a mesmerizing read.

By a Mathematician for Mathematicians.......2001-05-20

Writing a biography of anyone is difficult. How can a writer, no matter how talented, really claim to understand someone well enough to give an overview of his life? When the subject is a genius like Kurt Godel, whose name is known by few and whose work is really understood by even less, the job must be even more difficult. Fortunately, people like Mr. Dawson are will to give it a shot and he succeeds fairly well.

In putting together this biography, Mr. Dawson has the advantage of being mathematician. Additionally, he has the advantage of being the mathematician who catalogued Godel's papers after his death. This gives him a lot of insight into Godel that other writers cannot have and he weaves quotations from these papers into the biography very well. Mr. Dawson's is a well-documented and logical biography that is short on conjecture and long on footnotes. In brief, it is a biography about a mathematician clearly written by a mathematician. This is both its strength and its weakness.

Actually, I like the purely biographical sections of this book very much. The biographical information is clear and informative, though a bit dry in the academic style favored by mathematicians and scientists. Fortunately, having lived and worked among these people, I am comfortable with this style. More importantly, I feel like I have a better idea now of who Godel was and what he was like from reading this book. His focus on his work, his relationship with his family and friends (particularly his wife) and his ultimate decent into mental illness are much more in focus for me now.

Book Description

Paul Adrien Maurice Dirac was one of the founders of quantum theory. He is numbered alongside Newton, Maxwell and Einstein as one of the greatest physicists of all time. Together the lectures in this volume, originally presented on the occasion of the dedication ceremony for a plaque honoring Dirac in Westminster Abbey, give a unique insight into the relationship between Dirac's character and his scientific achievements. The text begins with the dedication address given by Stephen Hawking at the ceremony. Then Abraham Pais describes Dirac as a person and his approach to his work. Maurice Jacob explains how Dirac was led to introduce the concept of antimatter, and its central role in modern particle physics and cosmology. This is followed by David Olive's account of the origin and enduring influence of Dirac's work on magnetic monopoles. Finally, Sir Michael Atiyah explains the deep and widespread significance of the Dirac equation in mathematics.

Customer Reviews:

A Tribute to a Brilliant Man.......2005-11-10

A man Stephen Hawking calls 'probably the greatest British theoretical physicist since Newton,' has got to be a pretty bright man. Paul Dirac wrote the definitive equasion that joined the Theory of Relativity and Quantum Mechanics. Like Einstein before him, his equasion is very simple to express, very complex in its overall impact. It explains things like how television sets or computers work.

This book is not exactly a biography, but more a tribute to him. It is a series of four talks given about Dirac eleven years after his death, upon the dedication of a plack to him in Westminster Abby.

Abraham Pais describes Dirac's character and his approach to his work.

Maurice Jacob explains not only how and why Dirac was led to introduce the concept of antimatter, but also its central role in modern particle physics and cosmology.

David Olive gives an account of Dirac's work on magnetic monopoles and shows how it has had a profound influence in the development of fundamental physics down to the present day.

Sir Michael Atiyah explains the widespread significance of the Dirac equation in mathematics, its roots in algebra and its implications for geometry and topology.

Paul Dirac - The man and his work.......2000-01-19

We were ourselves participating in the inauguration of the Paul Dirac memorial in Westminster Abbey. Especially the speeches of Stephan Hawking and Abraham Pais were very touching as they did not only touch Dirac's work but also his personality and life. He was a very complex person and a great physicist. This book reflects that more than others about him.

An insightful recollection of a nearly invisible genius........1998-11-28

After missing the first collection of essays on this brilliant recluse published soon after his death, I picked up the present version as soon as I was able. It did not disappoint.

The book is a collection of four lectures given in the subject's honor in 1995 on the tenth anniversary of his death. The final lecture and the latter part of the third are highly mathematical and technical and clearly intended for a professional audience.

But for me, the first lecture by Abraham Pais is worth the purchase price alone. Pais was not only a contemporary physicist, but also a close friend and as close to a confidant as was possible with such a reticent man.

Through Pais' eyes, we see a mathematician turned physicist who was very different from the man to whom Dirac is most frequently compared, Albert Einstein. Einstein was a physicist first, mathematician second. Dirac was exactly the opposite. Einstein became a social and political critic, Dirac never strayed far from his study. The two were similar in that both viewed mathematical beauty as primary and both hated the modern remake of quantum mechanics (after the initial theory) for very similar reasons. This last point was interesting as Dirac was the first one to combine all his contemporaries' work on this improved quantum physics into a formal mathematical structure. His resulting equation, called naturally the Dirac equation, is classic Dirac, short and sweet. It combined Einsteinian relativity with the new quantum theory and Dirac considered the result to govern most of physics and all of chemistry. Stephen Hawking, the renowned theoretical physicist, says in his introductory memorial address to the book, "If Dirac had patented the equation ... he would have become one of the richest men in the world. Every television set or computer would have paid him royalties." For this work, Dirac shared the 1933 Nobel Prize with German physicist Erwin Schroedinger. One unexpected consequence of this work was a mathematical conclusion that defined a "negative energy" matter (aka antimatter) solution. Simply put, he had discovered a universe noone had imagined. To this day, we see the effects of this discovery from medical necessities (PET scan imaging-Positron Emission Tomography) to science fiction (Star Trek).

The quotations and anecdotes Pais chooses are well placed and often very funny. They are also supported by the images of Dirac portrayed in the sketch on the cover and in the few photographs scattered through the first two lectures. They reveal his character well. He saw mathematical and physical realities so clearly that he simply could not understand why others did not see them as well. The photo of him "listening" to future Nobel Laureate Richard Feynman in Maurice Jacob's section is one of the most amusing of the collection.

Amazon.com

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

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

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

Book Description

Paul Erd+s was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erd+s would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution.Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erd+s's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erd+s never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erd+s: "A mathematical genius of the first order, Paul Erd+s was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life."The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind.Hoffman, who followed and spoke with Erd+s over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erd+s is no doubt missed. --Therese Littleton

Customer Reviews:

An enjoyable book about an eccentric math genius.......2007-08-20

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

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

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

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

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

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

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

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

Man Who Loved Only Numbers.......2007-01-23

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

a popular math gem.......2007-01-09

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

A very enlighten book for a math novice (like me).......2007-01-05

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

He loved numbers, mathematicians loved him........2006-10-01

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

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

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

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

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

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

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

My Brain is Open: The Mathematical Journeys of Paul Erdos

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The perfect man of knowledge
N is a Number: True Story of the Travelling Mathematician
The hidden magic of math
The Remarkable Saga of a Remarkable Man
Sympathetic insight into the world of mathematicians

My Brain is Open: The Mathematical Journeys of Paul Erdos
Bruce Schechter
Manufacturer: Simon & Schuster
ProductGroup: Book
Binding: Hardcover

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ASIN: 0684846357

Amazon.com

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

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

Schechter spoke with many of Erdös's collaborators to complete this biography, which reveals the odd mathematician as charming, opinionated, and completely dependent upon the kindness of others. Schechter not only tells his fascinating story, but introduces some intriguing mathematics problems (with easy-to-understand explanations) to show readers why Erdös loved the elegance of numbers more than anything else in the world. --Therese Littleton

Book Description

A compelling portrait of the eccentric mathematical wayfarer, Paul Erds.

Customer Reviews:

The perfect man of knowledge.......2007-02-06

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

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

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

N is a Number: True Story of the Travelling Mathematician.......2004-07-12

+++++

The four-word title of this book is "My Brain Is Open." If you keep the first word and form a word from the first letter of the three remaining words, you get "My BIO." And that's exactly what this book is. This ten chapter book, by Dr. Bruce Schechter, is a BIOgraphy of Dr. Paul Erdos (pronounced "Air-dish").

Erdos (1913 to 1996) is said to have been one of the greatest mathematicians of the twentieth century (especially in number theory, the branch of math concerned with the properties of integers) as well as the most eccentric. Throughout this book, we also learn of the many others who collaborated with Erdos on his many published mathematical papers. (He wrote or collaborated on more than 1500 papers with over 450 collaborators.)

This book is also filled with the sorts of mathematical puzzles that intrigued Erdos and continue to fascinate mathematicians today. Schechter does a good job of explaining these puzzles (with the aid of diagrams, tables, and graphs) so the reader does not have to worry that these problems will be too difficult to understand.

The reader is also taken on a tour of mathematics. We are introduced to such people as Pythagoras and his famous theorem, Karl Gauss who, when ten years old, was able to add up the numbers from 1 to 100 in less than half a minute, and Bernhard Reimann and his work on prime numbers.

Erdos was born in Hungry. By age seventeen he had gained international recognition as a prodigy. He eventually left Hungry and went to the Institute of Advanced Study at Princton in the United States. (Einstein was the institutes most famous resident then.) Because of his politics, he was exiled from the U.S. for a decade. From this point beginning in the 1950s, he became "the Bob Hope of mathematics" or "the travelling mathematician."

Since Erdos was constantly travelling, he had no home or job but still managed to meet with math colleagues all over the world. He had all his belongings in a suitcase and his mathematical papers in a bag when he arrived at their homes. Erdos also depended on the generosity of colleagues to sustain him.

The reader is introduced to Erdos' eccentricities throughout the book. For example, he invented a vocabulary where the U.S. was "Sam" or "Samland" (after Uncle Sam) and the Soviet Union was "Joe" or "Joedom" (after Josef Stalin).

There are more than fifteen black and white photographs found in the middle of this book. These photos span a period from 1916 to 1993.

To get the information needed to write this book, Schechter relied "on the memories of the many people" who met Erdos -- his hundreds of collaborators and friends. That is, he "primarily relied on interviews with many of the people who knew Erdos best." Schechter also "drew heavily" from biographical essays as well as magazine articles about Erdos. He also used the information from the over ninety sources listed in this book's bibliography.

Finally, as I said above, this book does contain mathematical puzzles that intrigued Erdos. Personally, I found these interesting but some readers may find that they interfere with the flow of the book. As well, mathematicians who read this book may question the accuracy of a few of the mathematical concepts that are introduced.

In conclusion, this book invites the reader into the wacky world of mathematical genius Paul Erdos. If you're like me, you'll find this book both comical and enlightening!!

+++++

The hidden magic of math.......2004-04-07

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

The Remarkable Saga of a Remarkable Man.......2002-06-20

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

Stories about Erdos abound. It is rumored that he walked into a classroom, saw some writing on a chalkboard and asked if this was mathematics. Upon receiving an affirmative answer, he then asked what the various symbols were. Immediately after the explanations were given, Erdos took chalk in hand and in two lines proved the hypothesis that had baffled other mathematicians for some time, and this was in a field of mathematics that Erdos was largely unfamiliar with! Another story had Erdos taking a train fron Boston to New York; across the aisle sat a beautiful female who said "hello" to him. One thing led to another; by the time the train arrived the two of them had written a paper!

This book covered much of the life and mathematics of Paul Erdos; much of the mathematics in the book is number theory because it is a topic that is easy for anyone to understand yet difficult to prove. A typical example is Goldbach's conjecture, which says: "Any even number greater than 2 can be expressed as the sum of two prime numbers." Sounds simple enough and logical; 4=2+2, 6=3+3, 8=3+5,10=5+5 or 3+7,... The problem has been around for about 300 years but as yet lacks a proof. Other mathematics topics touched upon include Ramsey theory, the division of a square into unequal squares, and Godel's Incompleteness Theory. The book also shows the strange language of Erdos, in which women were 'bosses', men were 'slaves', the United States was 'Sam' (from Uncle Sam), and the Soviet Union was 'Joe' (Stalin), to list a few of his own variations of English.

This book is easy to read, even if the reader has only a high-school background in mathematics. If you are curious about mathematics and/or human nature, you will find this book of great interest. I highly recommend this book.

Sympathetic insight into the world of mathematicians.......2002-04-05

I enjoyed this book and thought that Bruce Schechter did well to get across the humanity of the man and as well as some of his ideas. Inevitably, the mathematics contained in the book will seem a bit hard going for some but Schechter handles it delicately and manages a fair balance.

Book Description

This book contains Thirring's scientific contributions to mathematical physics, statistical physics, general relativity, quantum field theory and elementary particle theory from 1950 onward. The order of the papers within the various sections is chronological and reflects the development of the fields during the second half of this century. In some cases, Thirring returned to problems decades later when the tools for their solution had ripened. Each section contains introductory comments by Thirring, outlining his motivation for the work at that time.

Features:

A complete proof of the divergence of the renormalized perturbation theory in a relativistic quantum field theory and a proof of the divergence of a similar theory

A proof of the stability of matter

An analysis of a dynamical system with negative specific heat

Book Description

Analyzing observed or measured data is an important step in applied sciences. The recent increase in computer capacity has resulted in a revolution both in data collection and data analysis. An increasing number of scientists, researchers and students are venturing into statistical data analysis; hence the need for more guidance in this field, which was previously dominated mainly by statisticians.

This handbook fills the gap in the range of textbooks on data analysis. Written in a dictionary format, it will serve as a comprehensive reference book in a rapidly growing field. However, this book is more structured than an ordinary dictionary, where each entry is a separate, self-contained entity. The authors provide not only definitions and short descriptions, but also offer an overview of the different topics. Therefore, the handbook can also be used as a companion to textbooks for undergraduate or graduate courses.

Book Description

The literature on inequalities is vast-in recent years the number of papers as well as the number of journals devoted to the subject have increased dramatically. At best, locating a particular inequality within the literature can be a cumbersome task. A Dictionary of Inequalities ends the dilemma of where to turn to find a result, a related inequality, or the references to the information you need. It provides a concise, alphabetical listing of each inequality-by its common name or its subject-with a short statement of the result, some comments, references to related inequalities, and a list of sources for further information. The author uses only the most elementary of mathematical terminology and does not offer proofs, thus making an interest in inequalities the only prerequisite for using the text. The author focuses on intuitive, physical forms of inequalities rather than their most general versions, and retains the beauty and importance of original versions rather than listing their later, abstract forms. He presents each in its simplest form with other renditions, such as for complex numbers and vectors, as extensions or under different headings. He has kept the book to a more manageable size by omitting inequalities in areas-such as elementary geometric and trigonometric inequalities-rarely used outside their fields. The end result is a current, concise, reference that puts the essential results on inequalities within easy reach. A Dictionary of Inequalities carries the beauty and attraction of the best and most successful dictionaries: on looking up a given item, the reader is likely to be intrigued and led by interest to others.

Handbook of Feynman Path Integrals (Springer Tracts in Modern Physics)

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Handbook of Feynman Path Integrals (Springer Tracts in Modern Physics)
Christian Grosche , and Frank Steiner
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals.
As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

Customer Reviews:

look here first.......2004-11-27

Feynman path integrals are a beautiful discovery by Richard Feynman. But what you may not realise in the textbooks that describe these is that the examples given where an analytic answer is found are very rare.

Which is the virtue of this book. In many situations, the maths of solving the path integral is difficult, when you have nontrivial problems. All the easy stuff has been done. So if you are tackling a problem, it behooves you to first consult this book. If indeed somone has already solved it, you need to know. So that you can use the answer given here. Or if you are doing research, it indicates that you need to look elsewhere for an unsolved problem.

Hermann Günther Graßmann (1809-1877): Visionary Mathematician, Scientist and Neohumanist Scholar (Boston Studies in the Philosophy of Science)

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Hermann Günther Graßmann (1809-1877): Visionary Mathematician, Scientist and Neohumanist Scholar (Boston Studies in the Philosophy of Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792342615

Book Description

In this volume specialists in mathematics, physics, and linguistics present the first comprehensive analysis of the ideas and influence of Hermann G. Graßmann (1809-1877), the remarkable universalist whose work recast the foundations of these disciplines and shaped the course of their modern development.

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