Reviews (15)

Much more than it seems
This book is brillant in many different ways.Not only does Gamow explain the mysteries of the universe in a way that is easy to understand, but his book covers more ground that even he realized when he wrote it.Much of the book, (the sections on extremely large numbers, the drunkard's walk, the law of entropy, etc) is now being studied from a computer science point of view.I studied much of this material in my computer science classes, only not in an atomic point of view, like Gamow, but in a binary point of view.The theories and proofs are the same, just the application is slightly different.I cannot recomend this book highly enough.It is extremely readable and you don't need a doctorate in physics or math to understand what is being taught.

One, Two, Three .....Infinity
I read this book for the first time when I was in school, almost 26 years ago.

I have been searching this book for the last almost 10 years, and suddenly thought of checking on Amazon.

Not only did I locate the book, but also I received the book within 5 days of ordering. I am re-learning the concepts that Dr. Gamow introduced almost 60 years ago.

Reviews (4)

Good book
This book is a collection of short biographies of notable mathematicians from Euler to von Neumann.It does a good job of explaining both a mathematicians background and the significance of their contributions to mathematics.Great to read through or as a reference to have on the shelf.

Very good historical account of lives
The only reason that this book doesn't get 5 stars is because of the fact that not enough emphasis is placed on the achievements of the mathematicians in terms of their mathematics.

However, this does not take away from the fact that is is exteremely well researched, laid out and presented. We get a meaningful insight into how these geniuses (genii?) lived and that fact that they were quite ordinary people with the same levels of hardship (and in some cases even more) as the rest of us. Perhaps an improvement could be made on further mathematicians, both past and present.

Still recommended reading.

Learn how mathematicians interacted with each other
When reading about the great ones of mathematics, I always enjoy short biographies rather than long ones. If the biographer is required to fill a large section of a book, then they tend to cover more detail than I really care for. While I do enjoy some details about the personal life of a mathematician, anything more than just a few morsels tends to detract from their accomplishments in mathematics.
James strikes the perfect balance in describing the lives of these great historical figures. Each biographical sketch is less than ten pages and he covers their life from birth to death. One valuable thing that he does is give their complete names, which is often omitted from biographies. In fact, despite all of my reading about the people of mathematics, there were some whose full names I had not known until I read this book.
The emphasis is on the lives of the people, and the general concepts of the mathematics that they created, rather than the specifics. No formulas are used in the explanations. Personal and professional interactions are a large part of the life of nearly all mathematicians, and from these biographies, we learn many of the specifics of how contemporaries reacted to each other. As is always the case, the full range of human foibles are displayed as the lives of the mathematicians unfold.
The lives of these sixty mathematicians are described in chronological order according to their birth years. Given that they all began their mathematically productive lives at different ages, this leads to some degree of overlap in both directions. Nevertheless, it is possible to easily trace the development of the major mathematical ideas as they are nurtured from early germs to towering oaks.
Mathematicians are people who find themselves in a social and political environment that they must cope with and sometimes just survive in. In this book, you will learn about sixty of them who made a major contribution, sometimes starting from a point of privilege, and other times only after great struggle. It is well worth reading for pleasure and can also be used as a resource for a course in mathematical history.

Reviews (9)

Well worth the read - some excellent contributors !
At first I was disappointed - the most beautiful equation in the world, e^i.pi = -1, was missing! As I read the book, I looked back at the title : great equations of Modern Science, not of Modern Mathematics. And indeed that is what the book is.
However I do have a few criticisms :
I knew by reputation only 2 of the 12 authors - who were the other people? Long after I had searched out their biographies on the web, I found them at the front of the book - but before the title page rather than after - how strange to put them there, or not at the back of the book ?
I didn't think the Drake equation was that `great' - and in Oliver Morton's chapter he places the Arecibo Radio Telescope in Costa Rica when in fact its in Puerto Rico.
In the opening chapter, Graham Farmelo briefly alludes to `British Astronomers announcing their results' without explaining what it was they were looking for and what they found? Only in the later chapters by Peter Galison & Roger Penrose respectively do they take pains to explain that Sir Arthur Eddington measured the bending of starlight during an eclipse.
I was confused in the chapter on Schrodingers Wave Equation - it didn't describe the form I was familiar with. Then in the notes at the end of the book Arthur Miller explained the more general form - and confessed that the `time' element had been ignored - rather a strange omission in my opinion.
Shannons Equations & the Logistic Map were both new to me - and very interesting they were.

It Must Be beautiful
This book had some of the best insight on equatiion form i have read in the rescent past.I could read larger sections of it without haviong to go grab a bottle of asprin. The insight it gave on the personal lives and how the evolution of the equation came to be from raw base form to what we learn now is amazing. The sections on Diracs eqaution I found the most intresting. I would reccommend this book to anyone intrested in math and not just the text book side. It takes almost and artistic veiw on math which i have never seen before. Very intresting .
DIG IN AND ENJOY

Reviews (1)

Reviews (10)

Good for start
I was very happy reading this book. If you are familiar with the Fourier transform and don't know anything about wavelets, this is a book for you.

Actually, the book has got two parts. In the first part you can learn basic things about Fourier transform (about its usage but also about its limits), what we need wavelets for and what the wavelets are. It is explained in very simple language without any formulas. The second part contains basic formulas related to the topics in the first part. I find that the link between these two parts is very good. Also, the author gives physical explanation whenever it's possible.

If you are a specialist in the wavelets area, you probably know all these things but if you are new (like me!) you will find that this book is quite useful.

It can be done!
I am a math professor,-- and I often wondered if it wouldn't be possible to get some essential math ideas accross to almost anyone, --and with fewer equations. Ideas can be burried in symbolism;-- not always! But it does happen. Many of my colleagues tell me that if it were possible, then it would be done. The author of this lovely little book didn't take math courses (she says!). Professional mathematicians would most likely agree with me that she (the author) did in fact communicate the essential ideas behind wavelets (and did it well!);- and so she must have understood them!! Perhaps, anyone who really wants to, can penetrate a specialized math discipline;-- I would guess. Perhaps it is not even hard!? At least this book proves that it is not impossible to communicate
the beauty of math;--and its uses. Take a look at the book, and judge for yourself!
It is fun too!

Editorial Review

Physics might seem part of an alien culture to most people, but it has touched all our lives, and its byproducts, in the form of nuclear fission, are going to remain with us for many generations to come. It could be argued that the 20th century was the century of theoretical physics. The Genius of Science is, as its subtitle claims, a portrait gallery of 16 of the most interesting and eminent of the international physicists who helped change our view of the world--from Niels Bohr to Eugene Wigner.But the list of characters is much, much larger and interweaves most of the international network of physicists and other prominent scientists of the last century. Author Abraham Pais, an eminent American theoretical physicist and professor at Rockefeller University, has written acclaimed biographies of Albert Einstein and Niels Bohr, two of the greatest scientists of the 20th century. Pais was acquainted with many of the people he writes about, and he often appears in the book as a shadowy figure in the background. Anyone can dip into The Genius of Science anywhere in its pages and be immediately grabbed by both the extraordinary and the ordinary aspects of the lives of these scientists. The author provides plenty of anecdotes, from those about Bohr's pipe-smoking to Robert Oppenheimer's reaction to the first successful atomic bomb test: "... some lines of the Bhagavad Gita went through his mind: I am become Death, the destroyer of worlds."

Reviews (12)

Like a video game walk through for applied quantum theory!
Most "beginner" books on quantum theory I've tried to read take the reader on a chronological tour of who discovered or developed what. I hate that. Just becase B happened before A doesn't mean that it's easiest to understand if you describe B before A!

Well, Johnson doesn't cheat the reader by taking this easy way out. He's distilled all the background necessary to understand the key concepts behind quantum theory and how it can be used in a crazy revolutionary way to compute, boiled it down to the bare minimum required and organized it in such a way as to make things crystal clear.

No oblique anecdotes. No historical "human-interest" segues dumped in for filler. Just applied quantum theory 101, pure and simple.

Reading this very compact book took me all of half a day and after that I felt like I had just climbed a set of stairs from darkness to illumination. Before: "What's quantum theory?" After: "I get it now."

There is some sensationalism, but it's easy to read around that. Besides, hype is engaging! It makes you go "Wow, cool!"

-- Insert Superlative Here --
This guy not only describes quantum computing in a way that should be accessible to nearly everyone, but he does it in a highly entertaining, highly readable way.By appealing to a healthy dose of abstraction, the author is able to seamlessly touch on an amazing array of topics from computational theory to quantum mechanics to cryptography. Occasionally he sinks deeper into the quantum quagmire to examine a few quantum algorithms, but he never loses sight of his intended audience: the scientifically curious layman.

This book does contain a large amount of hype, but to his credit the author includes the opinions of a few noteworthy skeptics to lace all the optimism with a sprinkle of doubt.If you are looking for a quantum appetizer, or to bring yourself up to speed on the buzz behind quantum computing, I couldn't recommend this book more highly.

Reviews (7)

A first!
Where it all began.---The book grew out from an epic scientific paper in 1948, but luckly its author Shannon chose a light touch and a gentle delivery in his presentation. The paper became a book, with a 1949 first edition, which is now a classic, and which has been reprinted a number of times since, ending with the present lovely 1998 edition. It is still the place where readers can learn the essentials, including the two equations of information theory, that are now named after Claude Shannon.

Right from the master
The book about information theory. It is old but contain all the basic concepts. Even better, you can enjoy reading it!

Arguably, the most important paper EVER written!
I think it is fair to say that this book, based on Shannons landmark paper represents what I believe to be, the most important engineering paper ever written in the history of the world (both up to this point, and likely will remain so in the future).In terms of "practical implementation" of theory, it's fair to say that this seminal work has had a far greater contribution to mankind than Einsteins' paper on general and special relativity (just don't say that to a physicists face).

... All to often, famous theorists are relegated to "cult-like" obscurity.Persons like Shannon, Gallager, Forney, Komolgorov may be legendary within a cult-circle of die-hard communication theorists, but are relegated to unfortunate obscurity by the masses.It's rather unfortunate, with todays advanced communication systems, and techniques of coding (Turbo codes, modified LDPC codes, etc..)which push the boundaries to the ultimate limits as defined by Shannon.... that more people (both engineers, and laymen alike) don't recognize the names of early pioneers who started the revolution, and who's theories are the basis for many of our modern luxuries which allow us to download information at such rapid rates.

People often underestimate the deepness of Shannons' work,due to Shannon's writing style.He was one of those rare writers (somewhat like Forney, or Massey) who can actually explain complicated subjects using mere words, without the need for prettying the theory up with fancy math.Comparing the equation filled textbooks of today, versus Shannon's work, one might get the impression that Shannon's work was simplistic. I think it's clear to anyone whos studied his work, that IT WAS NOT SIMPLISTIC. Obviously, there was alot of "behind the scenes" math which Shannon had to go through to actually codify his many theorems. Just because Shannon did not show extensive derivations for each one of his theorems does not mean that he was not a good mathemetician..It merely means that he did not want to write a 1,000 page paper... he wanted to keep it simple (as was the customary writing style in the early to mid 1900's).

Reviews (8)

For the uninitiated!.--Fun too!
For the uninitiated! --The author combines insight with story telling. He has a story to tell, and does it well! Not only does he know the theory inside out, he has the ability to get accross the central points so it (almost) seems easy, in any case entertaining, using pictures (including cartoons), humor, and equations when they are needed. He further make clear the many fascinating links between chaos theory, algorithms, technology, and areas of pure math, such as number theory. Highly recommended!

A comprehensive introduction to chaos in two levels
This book can be read in two different ways:

The first one is intended for the uninitiated who wants to get an introduction to chaos and fractals; the way Schroeder guides you into the chaotic phenomenae that occur everywhere around us is clear, elegant and funny. He plays with chaos and makes the reader part of this game.

The second way to read this book includes a warning for scholars: This is not a textbook! The mathematical background used to explain this game is strong. Shcroeder lets the committed reader to work with the maths by himself, so you must have paper, pencil, and computer near to you in order to enjoy the book's whole potential, in this case Shcroeder has all the experience and knowledge on the matter to guide you through "this infinte paradise" in a very firm way.

The only thing I'd wish from this book was a new hardcover edition, I've read it so many times that my copy is getting very spoiled.

If you are still interested after reading this book, but you want a little help with your maths then I'd recommend "Chaos Theory Tamed" by Garnett P. Williams. It will do the trick. However if you just want to fall in love with chaos without complications, then you should read "Chaos: The Making of a New Science" by James Gleick.

Best book on chaos
This book is a complete guide of all possible situations in science where you may encounter chaos. It provides for every situation an intuitive as well as very formal view of every problem and the corresponding solution. The main drawback concerns its relative inaccessibility for non-scientific people, it requires a quite important scientific background to understand the formal part. Anyway, even for the lay-man, it can be interesting to read, in order to understand the widespread of chaos and non-linearity in real-life situations, not just the purely scientific-related ones.

However, the treatment is terrific, with excellent description and explanations of the how's and why's, at an intuitive level as well as a very rigorous one ! I don't think i've ever read a book of such a high quality...

Reviews (2)

Don't miss it!!
I learned from Rudin's math books when I grew up, starting with
"Baby-Rudin", and I got hooked. Since then I have taught from almost everyone of them.--- Not this one though! This book is different. It does have math though, but at the same time, in the math part[the second half of the book], Rudin surprises you by letting you look behind the curtain.You are let in on how the author, the mathematician Rudin, arrived at some of his theorems. Enlightening!
The early parts of this fascinating book recounts Walter Rudin's childhood in central Europe[Vienna], how he escaped to the US, with his life, as Hitler's armies, and the fire of anti-semitism, engulfed Europe in the years up to the second World War. The last ship sailing, at the eve of WWII, from Europe was like an ark. Mount Ararat was America.
A well meaning reviewer writes on the back-cover to the book as follows:"...Rudin's colorful
history, ... his experiences...".--- Well it is more than that!
Another book,[a somewhat different one, from a slightly earlier period, but still the theme of Europe then, and escape...]starts: ..."This book is to be neither..., and least of all an adventure, for death is not an adventure to those who stand face to face with it..."

Reviews (10)

Feels like a dutiful summary
First, my background: I am not a mathematician, but an academic with fair knowledge of college math and even some advanced materials. I do greatly enjoy reading books about mathematics and mathematicians.

This book is obviously a work of great effort by the author. My difficulty probably came from the work's ambitious premise: offering mathematical and biographical history of Hilbert's problems. There are simply too many ideas and persons (some well known, others a bit obscure to lay reader like myself) to cover in one book.The author dutifully and honestly gives references to his sources. My impression is that the author collected as much material as he could about each problem and solvers, and tried to squeeze the information as compactly as possible into the pages.

The result: the narrative is very methodically told - explanation of the problem, some necessary ideas introduced, who the major solvers were, then a short biography of each solver, when and where they were born, who their parents were, where they went to school, who they married and so on; then another cycle begins. Halfway into the book, I began to get bored.

I can imagine mathematicians enjoying a quick review of and glimpses into their discipline and heroes, but lay readers much beware. I recommend lay readers to check out a few pagescarefully online or at your local library to see whether you like it. I certainly didn't hate it but did not like it as much as I expected.

A great work
Due to rapid development of mathemtics in the last century, now one cannot master all subfects of mathematics. This is also true for those historians. Most of the boods of " History of Mathematics " end in the beginning of 20th century. So we know very little about the conteporary mathematicians. This book can be described as a gap for it. After readiming this book, not only you have a knowledge about the life of the great mathemaitcians, you also get the period in World War II how Nazis forced those mathematicians out of Germany and the reason why U. S. A. is now the leading centre of mathematics.

Useful and insightful
The book is well written with the right mix of anecdote and theory. What I do like about it is the fact that we find out a little more about the lives of mathematicians, and they are portrayed as people rather than idols.

Reviews (1)

Isbn: 981023418X
Sales Rank: 1006879
Subjects:  1. Conic sections    2. Geometry    3. Geometry - General    4. Geometry, Non-Euclidean    5. Mathematical optimization    6. Mathematics    7. Science/Mathematics    8. Theory Of Functions   

Reviews (15)

A physicist's essay on a topic he knows not
I'm wondering why scientists are allowed to give their opinion as scientists about topics they know nothing about as scientists. If you want to understand what Life is just go outside and feel Life instead of reading books full of speculations. This book gives yet another personal view that reduces Life to a scientist's perspective. Science does not understand Life because it reduces Life to an inanimate thing. It is funny to read passages when scientists give their opinion on mystics and philosophers accounts on Life. As scientists pretend that Science is objective, then let it deal with the objective world. And keep silent about subjective phenomena like Life. Life is far larger than what Science will ever know.

Pons Asinorum? It Wasn't Then !
While I was reading the book I thought "this is pretty obvious stuff!" Then I began reminding myself that "If I see further, it's because I stand on the shoulders of giants."
I read the book because J.D.Watson said it was good in his book "DNA The Key To Life." He was right. The first chapter was fascinating.

A Classic
What is Life? is an absolute classic. Schrodinger felt that life must be explainable by physics and chemistry, yet seemed to violate the normal behavior of entropy-- and he understood further that this was a remarkable wedge point to explore. He figured out the explanation: life is the result of evolution of genetic information, which selects for complex processes that by ordinary considerations would be very unlikely. He predicted that there must be a molecule capable of carrying the genetic information (incorrectly thinking it would be a protein.) His beautifully-written book was influential and timely. Within 4 years, Von Neumann elucidated the mechanisms involved in self-reproducing automata (illustrating his abstract discussion with a picture looking remarkably like DNA to the eyes of readers today); and within a decade, Watson and Crick grasped the structure of DNA. You should not read Schrodinger's book today as one of your first sources to understand life-- there has been remarkable progress in the 50 years since Watson and Crick-- but you should read it to gain appreciation for how science can be advanced when the time is ready and a wedge point, an apparent conflict between fundamental ideas, is analyzed.

The volume also includes another lecture by Schrodinger, Mind and Matter, which is historically interesting in another way. In Schrodinger's day, the state of understanding had not advanced to the point where it was possible to make as useful conjectures about the structure of mind as of life, and he accordingly felt "[mind] may well be beyond human understanding."

Reviews (11)

Science as Human Creation
This book provides a still useful account, from 'the horses' mouths', of what Alfred Korzybski called the Newtonian and non-Newtonian views in physics. As Korzybski noted, all human beings form a view of so-called 'reality'. Understanding how scientists do this can have value for the rest of us. In this excellent book, the authors emphasize general formulations and a non-mathematical approach: "Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone" (29). The book includes chapters on "The Rise of the Mechanical View," "The Decline of the Mechanical View," "Field, Relativity," and "Quanta." Readers will be rewarded with clear explanations of some potentially forbidding notions. These are interspersed with useful comments on physico-mathematical method, theory and the goals of science. Einstein's and Infeld's discussion demonstrates their view that "Science is not just a collection of laws, a catalogue of unrelated facts. It is a creation of the human mind, with its freely invented ideas and concepts. Physical theories try to form a picture of reality and to establish its connection with the wide world of sense impressions. Thus the only justification for our mental structures is whether and in what way our theories form such a link" (310).

Science, history, and a bit of philosophy
Physics can be difficult to learn when theories and formulae are thrown at you with no historical context.You begin learning about motion, and then electricity and magnetism, and it's almost impossible to see a coherent connection between the ideas.Many people have heard of relativity and quantum theory, but do not have even a general notion of what they aim to explain.

Like mathematics, you can learn physics without knowing about the people behind its development (though you will encounter many of their names in important expressions), but it never hurts to study how such ideas began, and how they came to be what they are today.Einstein and Infeld's book is aptly titled.They show how and why certain concepts came into being and what significance they hold.Beginning with "The Rise of the Mechanical View," they describe vectors, motion, forces, and energy. With "The Decline of the Mechanical View," they show how the behavior of electricity, magnetism, and light waves poses problems for the mechanical view.

The next two (and most interesting) sections explore field, relativity, and quanta, and how they have proved more accurate in describing physical phenomena than what was previously known.Einstein and Infeld describe everything with a minimum of mathematics so that anyone with an interest in the development of physics can understand the contents.Although such math is necessary for a precise understanding of physics, the aim of the authors, which they frequently repeat throughout, is to give the reader a broad understanding of the general underlying principles.They have succeeded in giving an account of where the human construction of physics started, what has been covered since then, and where it is heading.It is a simply written book, suitable for readers who don't know physics and want to learn, but also helpful for students of physics who want to see a broader picture of its evolution.

A very good book.
This is a really good book which clearly explains the evolution of physics from Newtons laws to Quantum mechanics in a simple and lucid language.

Einstein was not only a genuis mathematician and physicist but also a great author and story-teller and no one else could have told the story of evoultion of physics better than Einstein

Reviews (1)

Editorial Review

Editorial Review

Reviews (17)

Gamma: Exploring Euler's Constant,A Very Good Book
Dr. Julian Havil's book Gamma: Exploring Euler's constant is a marvelous book. With verity and clarity it takes you through Euler's Constant, ... encountering the harmonic series, ... and on through the Riemann Zeta Function, and a lot more -- all done masterfully. Gamma is entertaining as well as edifying. Like other great mathematical works, a few typographical errors crept in, but in nowise diminish from the importance of the book:
1. Page 11, 1st paragraph, 7th line, "that" should be "than."
2. Page 12 at the bottom of the page, the left integral should have a parenthesis around "x+y."
3. Page 13 at the top of the page, in the integral on the right, "x" should be "a."
4. Page 13 in the integral beneath the first sentence, "x" should be "2a" in the integrand, and the upper limit should be "pi," not "2pi."

As an idiot (but not a blithering idiot) I realize I could be mistaken about the above errata.

Nobody's perfect
I recommend this book to anyone who has learned calculus.The book is full of mathematical gems set in historical context.For example, one of the Bernoullis showed that the integral of 1/x^x from x=0 to 1 is the sum of 1/n^n from n=1 to infinity.If you appreciate that result, then this book is for you.I have found only one error in the first 45 pages (which is as far as I have read).On page 13 the author is trying to compute the average distance of a planet from the sun, assuming an elliptical trajectory, and tacitly assuming a uniform distribution in the angle that astronomers call true anomaly.For this distribution,despite the assertion at the top of page 13, it is easy to show that if the ellipse is not a circle, then the average distance from the sun is less than the semimajor axis of the ellipse.So the author is human after all.

Far-reaching, but not "popular math"
I debated for a while whether this book deserved four stars or five. There's a lot of very interesting material here: if there's one thing this book does--perhaps better than any book I've read in quite some time--is show just how interrelated far-flung mathematical concepts can be (how are the prime numbers related to pi, for example?).

My one complaint about the book--and the reason for giving it four stars instead of five--is that there are times when the formulae and notation get so dense that it's extremely difficult to follow the author's train of thought: I can think of a number of places where diagrams would have helped immensely. Likewise, since there's no list of symbols or formulae, it's not a book that you can simply browse through, in the sense that you can browse through, say, "A Brief History of Time."

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• Unabridged

Isbn: 0486421821
Sales Rank: 168442
Subjects:  1. Applied    2. Group Theory    3. Mathematics    4. Physics    5. Science    6. Science/Mathematics    7. Symmetry (Physics)    8. Science / Physics