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Adventures of a Mathematician

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For its greatest part, the book is about Ulam's encounter with other scientists. It's thus a must-have for all historian of science, with great details about the three important Ulam's acquaintances: Banach, Von Neumann and Fermi. However, it's not what is making this book an invaluable document.

Ulam was a pure mathematician, like Banach or ErdĆs, not like Dirac or Einstein. Yet he had the ability to escape from formal abstract considerations to think about how other sciences could show him a path to new mathematical considerations. In this regard, the Monte Carlo method and all his proposals to non-linear systems and usage of computers for exploring them may be are his greatest achievements (his H-bomb papers are classified, and I like to think Monte Carlo is still more useful).

For that matter, this book is of the greatest interest for he who wish to deepen his understanding of links between mathematics and physics, that are usually discussed by physicists often having very poor idea of what mathematics really are about. The chapter "random reflections" is a jewel which by itself makes worth buying the book, explaining for instance how practical problems can lead to new mathematical concepts, how mathematic theories link altogether, or advocating the use of computers to help mathematicians view new spaces of new objects. Many aside jokes or peculiar reflections--like how mathematics change according to what language one is exploring them with (English, Russian, French, German...)--make the book very entertaining, seldom boring. This "mathematician's mathematician"'s overview of this century's science (he also had some contributions to biology) is thus highly recommended.

(caution to purists: the book has been edited by Ulam's wife from recorded tapes, he didn't write it.)

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.

The very first time I heared from Stanislaw Ulam was reading a book by Otto Robert Frisch (What little I remember). In this book he said that a polish mathematician called Ulam was doing mathematics for the Hydrogen Bomb but his maths were deviating so much from abstract that he even used numbers with decimals in his formulas. This funny comment opened my curiosity to know more about this guy doing maths. Well, years later I bought this book and surprisingly he mentioned the comment by O.R Frisch. What a coincidence! I liked the book. He details his life and other genius lives: John von Neuman, Paul Erdos, Fermi, etc. No necessity to know maths. No formula within the book. Easy to read. Stan Ulam was co-father of the Hydrogen Bomb but everybody knows Edward Teller but not him. He makes especial emphasis in Alamos times (Ulamos times). Enjoyable book.

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 called 'the logic of scientific discovery' and that of 'the logic of scientific justification'. The latter being a streamlined version of the former, a logically tight presentation with all hurdles and frustrations left out. It is a linear 'success only' story, told in a highly stylized language, ideally that of formal logic.

Now such a linear success story has only one goal, and that is to bring home the message of success. Formal proofs do that, but with the same price paid as with other success stories: because of the lack of drama it is difficult to get engaged by them and the insights that the storyteller gained in his struggles are not the focal point of the story, only the message of success is.

So I think there is something to say for a math education (if not math itself) where insights from storytelling are used to bring home the insights of the great mathematicians.

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.

Surprisingly easy to read. It is an interesting perspective on the communitiy of scientists working at Los Alamos before and after the development of The Bomb. Ulam deftly considers all aspects of his life juxtaposed with those around him; sociological, philosophical and even poignant glimpses into the theological.

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 very easy to read book about the life and work of one of the great modern mathematicians. Especially interesting are the sections relating to the development of the atomic and hydrogen bombs.

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.

I read this in 1982 or 83; now it's 2010. That's plenty of time to forget many books and their content, and I'm a heavy reader, but this one stands out especially in my memory, even though the details have faded. Among autobiographies and memoirs of scientists, this was outstanding. The inside look at how mathematicians think was helpful to me as a grad student later on.