Adventures of a Mathematician

Confessions of a math fashion-victim Towards the end of his celebrated autobiography that was published in 1976, mathematician Stanislaw Ulam makes a striking remark about the way mathematics is presented: 'This was more agreeable than the present style of the research papers or books which have so much symbolism and formulae on every page. I am turned off when I see only formulas and symbols, and little text. It is too laborious for me to look at such pages not knowing what to concentrate on. I wonder how many other mathematicians really read them in detail and enjoy them.' To wit, these are the words of someone who really has enjoyed mathematics and has been engaged in the highest ranks of the subject for almost all of his life. For me this is quite a relevant statement, since I started studying mathematics at the University of Leiden (The Netherlands) in the year 1975. And for me it was like Ulam describes. Lectures in mathematics almost entirely involved the stating of theorems and the subsequent proofing of them. Little was said about the meaning of what was proofed, why it would be interesting, or even what the essential idea of a proof was; most of the time no background or context of any kind was given. A semester of Lebesgue integration theory was given without even referring to the problems that had arisen with more basic forms of integration like the Riemann-Stieltjes Integral. It made a lot of the matter less exiting than it could have been. And to be honest, most of the proofs stayed quite unintelligible: one could follow the details but kept missing the big picture. The point however is, that it only now becomes clear to me that I have been a fashion victim, that what I perceived as the way mathematics was done period, was only a relatively new style of writing and teaching, a fashion that had been en vogue for only a few decades yet. This reflection of Stanislaw Ulam is confirmed by Davis & Hersh in their 1981 book The Mathematical Experience. In a section on the philosophy of mathematics they remark: 'The formalist style gradually penetrated downward into undergraduate mathematics teaching and, finally, in the name of the new math, even invaded kindergarten'. (p.344) And they continue with the observation that the formalist style might have had its longest time. Actually I am not sure that such a thing will happen. At least some of the formalism seems to me related to a certain machismo between mathematicians; the shorter and the less intuitive the proof, the better the mathematician. In their section on Teaching and Learning Math, Davis & Hersh give an example of the contrast between a short formal proof and a more elaborate and a more intuitive one. It is about the 'two-pancake problem', the problem of cutting two pancakes in halves by cutting only once in a straight line. And the pancakes are not on top of each other. The example of the two-pancake problem is put in the context of the contrast between what is calle

this is one of the few books i've read twice. i'm fascinated by brilliant minds like ulam, oppenheimer, feynman, and von neumann. it's one of the best science biographies/autobiographies and is very easy to read. lots of time is spent on the atomic and hydrogen bomb projects and the great minds/peculiar personalities involved. it's been 15 years since i read it, but now that i've found it again, i'll reacquaint myself with these great and interesting minds. it's not a math book by any means, but a book about brilliant men that do math. they definitely listen to a different drummer.

Before I start, let me say that, for me at least, this is one of the most fascinating and entertaining books I've ever read. But I'm a special case, as you'll see...Stan Ulam was head of the math department at U. of Colo., Boulder, where I was a doctoral candidate circa 1970. I hardly knew him to speak to, but heard about his participation in the Manhattan Project, and that many of those connected with it considered him to be the "father of the H-bomb" rather than Edward Teller. Having already been put off by the dryness and lack of application of a great deal of the math I'd studied, I was intrigued on hearing that a pure mathematician could have played such a central part in that effort. That, and the book's title, convinced me to buy it, even though I was an impoverished grad student.There are many reasons why I love this story, but I think foremost is the picture of a gregarious, open, and sometimes mischievous man who was also bright enough to hold his own with the leading scientific minds of the 20th century. The sketches of the many famous people he worked with are priceless -- for example, Enrico Fermi, Richard Feynman, George Gamov. And especially John von Neumann, possibly the most brilliant mathematician of that time, certainly the most diverse and prolific (he practically invented the computer industry that I now work in). Having tried to read his work on game theory, it's especially comforting to me to hear Ulam refer to him as "Johnny".My struggles with some of the math mentioned in the book give it special meaning to me, but this is not a technical book at all, and I hope that aspect won't be off-putting to non-mathematicians. Ulam was simply trying to give an honest picture, through the lens of his own experiences and friendships, of how people become mathematicians, of how essential group efforts are to progress in science and math, and of the staggering accomplishments that can result when people push the limits of thought. This book is about history and humankind, by one of the brightest and most thoughtful individuals who ever lived.

Monte Carlo simulation was discovered by Stanislaus Ulam and today is used by millions in all walks of life. It is the basis for planning and decision making in for corporations and in all issues of public and private life.Ulam says "The idea...occurred to me when I was playing solitaire during my illness. I noticed that it may be much more practical to get an idea of the probability of the successful outcome of a solitary game...by laying down the cards, or experimenting with the process merely noticing what proportion comes out successfully..."The advent of computers removed the need for "hiring several hundred Chinese from Taiwan" and made the progress of rational thought ubiquitous.It is the most striking example of the triumph of mathematics in real life.Andrew Vazsonyi, Real-life mathematician

This is a remarkable book of one that excelled in mathematics, physics and engineering. The stories of his youth, when he made mathematics at a "cafe'" in Poland, with, among others, the great Banach, are wonderful. Also, beautiful and moving portraits of Von Neumann and Enrico Fermi. Everything told with a great sense of drama.