Book Description

Customer Reviews (5)

Excellent overview by two outstanding mathematicians
The audience for ths book is people with background in mathematics. They teach many branches briefly with their examples in Chapter 1, but the presentation is at a fairly sophisticated level.

I found the historical and philosophical remarks very valuable, coming from authorities like these two men. Examples (slightly edited by me):

The great analysts of the 18th and 19th centuries (e.g., Newton, Leibniz, Bernoulli, Euler, Lagrange ...) had an almost unerring instinct for presenting valid results and plausible proofs without a firm basis in formal systems and without strict adherence to standards of logical rigor... Mathematical intuition in the hands of people of genius has such a clarity and unity that it anticipates special formalisms.

Mathematics is a science; it is also an art. The criteria of judgment in mathematics are always aesthetic, at least in part... One looks for `usefulness,' for `interest,' and also for `beauty.' Beauty is subjective, yet it is surprising that there is usually considerable agreement among mathematicians concerning aesthetic values.

It is a distinctive feature of mathematics that it can operate effectively and efficiently without defining its objects. Points, straight lines and planes are not defined... One need not know what things are so long as one knows what statements about them one is allowed to make [the axioms]... Other statements involving these undefined words can then be deduced by logic alone. This permits geometry to be taught to a blind man and even to a computer!

A Classic of Popular Mathematics
With new mathematics growing wild in the trees in the new century, one should review those things that have givenmodern mathematics direction and flavor. This classic little book sits along side of Sawyer's " Prelude to Mathematics" as the go to books for basic understanding. To these books I have added an unlikely candidate " Elliptical Curves" by McKean and Moll.If one has these three books, he will have a crack in the damof mathematics...

Important and Useful but not Engaging
The book shows what the power of mathematics is, how it changes, and how it expands to new areas. Unlike books that aim to popularize math, the book does not pontificate a mystic view of the meaning of mathematics; rather, it gives a sober perspective of what has happened in mathematics and what can be expected of the field.

The book requires somewhat serious mathematical thinking.

A great strength of the book is the diverse mathematical concepts that it presents: homology groups, group theory, Turing machines, undecidability, Monte Carlo method.In a compact book, you learn a little about some important ideas in advanced mathematics.

Important!! This book is not written to popularize its subject matter, so it is different and definitely less entertaining than most popular science books.

why math is interesting, written for laypeople
Kac and Ulam were both strong mathematicians; this encyclopedia articlewhich they coauthored provides a nice counterweightto the answers-without-questions view of mathwhich can result from a little indifferentcoursework.

Easy and lively reading, written for everyone.

A bargain indeed
Just read the editorial review (Book News).It's all true (except for the publishing date,which is 1968, not 1986...) ... Read more

Book Description
The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects.
With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality. ... Read more

Customer Reviews (9)

math autobiography and atomic bomb history
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.

An examined life
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 Monte Carlo method
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

A Mathematician in Physics
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 Neumannand Fermi. However, it's not what is making this book an invaluabledocument.

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

Forthat matter, this book is of the greatest interest for he who wish todeepen his understanding of links between mathematics and physics, that areusually discussed by physicists often having very poor idea of whatmathematics really are about. The chapter "random reflections" isa jewel which by itself makes worth buying the book, explaining forinstance how practical problems can lead to new mathematical concepts, howmathematic theories link altogether, or advocating the use of computers tohelp mathematicians view new spaces of new objects. Many aside jokes orpeculiar reflections--like how mathematics change according to whatlanguage 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'sscience (he also had some contributions to biology) is thus highlyrecommended.

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

Stanislaw Ulam and other mathematician lives.
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 HydrogenBomb but his maths were deviating so much from abstract that he even usednumbers with decimals in his formulas. This funny comment opened mycuriosity to know more about this guy doing maths. Well, years later Ibought 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 geniuslives: 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 theHydrogen Bomb but everybody knows Edward Teller but not him. He makesespecial emphasis in Alamos times (Ulamos times). Enjoyable book. ... Read more

Book Description