David Berlinski has created a marvelous intellectual history focusing on the progression of Newton's epic breakthrough thinking. He does this in a way that is totally accessible to those who are phobic about mathematics. The explanations are achieved through a skillful combination of simple sentences, symbols, pictures, and diagrams. The presentation is so effective that most readers will find their understanding of important mathematical and scientific principles greatly improved. This is a great book!

Newton was a seminal thinker in the areas of mathematics (developing calculus), physics (with his propositions about gravity and motion), and optics (with his conceptualization of light as being comprised of particles moving in parallel). He also did much work in theology and alchemy, which are recounted here.

A key challenge for David Berlinski was presented by Newton's reticence. He was not a very social person, and wrote almost nothing about how he developed his ideas. Berlinksi does a magnificent job of locating and sharing hints and clues about the bases of these intuitive leaps. This result is enhanced by considering the continuing themes in Newton's thinking, and assuming a connection to his intuition. I suspect that Berlinski is right in connecting the dots that way, but we will never know for sure.

The centerpiece of our story turns out to be the tangent to a curve. From that humble beginning, most of our modern understanding of how physical motion takes place follows.

I also enjoyed better understanding how Newton's thinking was aided by the careful observations and conclusions of Kepler.

If the history of science were always this entertaining, this subject would be one of the most popular majors in colleges.

As Berlinksi tells us in the beginning his purpose in the book is "to offer a sense of the man without specifying in details his . . . activities." This allows us to see the other sides of Newton, but without spending too much time on them. Newton was not perfect. We get glimpses of places where he wasted his time, such as his unsuccessful experiments with alchemy. We also see his flirtations and infatuations. Beyond that, we see what could enrage him, and how he took his revenge. This fleshing out of the whole man makes the scientific history all the more compelling.

If you liked David Berlinski's book, The Birth of the Algorithm, you will probably like this one even better. The asides are much more contained and relevant here.

For those who want a little more math with their scientific history, Berlinski has provided supplementary materials that are quite entertaining.

After you have finished enjoying this wonderful romp, I suggest that you think about where everyday events are unexplained in your life. For example, why do the people you meet with act the way they do? Why is progress slow in many areas, and rapid in others? By looking for connections, you, too, may isolate fundamental principles that can expand our own appreciation as a species of how we achieve understanding. The mysteries of how to improve thinking are still mostly unsolved, and many are relatively unexplored. Perhaps you can be the Newton of this important "last frontier" of self-limiting progress for humans.

Think about it!

Berlinski's gift is getting inside the genius that was Newton and explaining (in a narrative readable by non-mathematicians) the beauty of Newton's logical theory of the universe. Not intended as a thorough survey, the text nevertheless covers the highlights of the development of Newton's thought as well as a straightforward exposition of the critical aspects of the Principia. Berlinski is erudite, literate and witty in what could be dry material, though he occasionally puts himself in mind of his protagonist more than his research supports. On balance, though, this is a readable, fascinating and enlightening little volume about a character who most of us haven't thought about since high school physics class, yet who arguably has had more influence on our world than any other scientist/philosopher in history.

In his book Newton's Gift - How Sir Isaac Newton Unlocked the System of the World David Berlinski presents us with an engaging biography of Newton. What I personally liked was the fact that Berlinski avoided the trap of many biographies that merely present names, dates and places. In this book we see the person that Newton was and how it affected his study of mathematics.One of the main reasons that one should study the history of mathematics is to appreciate the human side of its creation. Berlinski presents Newton's human side quite well.

If you are looking for a lot of detailed mathematics, you probably won't find it here. The mathematics is presented at a very readable and understandable level. This is certainly accessible to the average undergraduate math/physics major.

I recommend this book without hesitation.

This book has good potential - explain in a non-technical way the fundamental theorem of calculus, why it is important, and the history of it's development. The mathematicians who discovered and refined calculus are a fascinating lot, and the mathematics itself has proven to be perhaps the most effective engineering tool yet discovered. Sounds like good stuff. Unfortunately, Berlinski choose to shroud this simple theme in page after page of self-important, over-written, pretentious drivel. One of the reviews on the jacket puts this book in the same category as Godel, Escher, Bach - holy smokes! Nothing could be further from the truth. Buy GEB, stay away from this book!

I give him 2 stars instead of one because the material underlying the terrible writing is interesting and worth knowing. Hopefully someone will write a readable book on this material!

David Berlinski has written two popular books on mathematics, the first entitled, "A tour of the Calculus," and second, "The Advent of the Algorithm." The theme of this duo of books is that mathematicians have produced two great ideas of "the great scientific culture of the West." Neither book requires the reader to have more than a high school level of mathematical knowledge. He does present proofs in appendices that a lay-person might find difficult or beyond their ability to follow; however, these are not required in order to understand the major ideas of the books.

The author's thesis, as stated at the beginning and end of both books, is that the analytical thought of Calculus has gone through it's cycle of growth and is now, for the most part, come to a stand-still, while the sort of mathematical logic embodied in the computer's use of the algorithm, has emerged as the succeeding great idea "of the great scientific culture of the West." Yet, the content of both books is not so much an argument in support of this thesis but a guided tour of the essential ideas of both mathematical methods.

Mr Berlinski is an emancipated professor of college mathematics and clearly knows his subject. He also is a sophisticated writer, presenting the reader with plenty of rhetorical devices in an attempt to make the terse matter of mathematical concepts easier to digest. These devices include imaginary reconstructions of plausible scenes and dialog he might have had with the great pioneering mathematicians, past professors and students. He also frequently meanders into metaphysical interpretations of the mathematical ideas, particularly between sections of the book bearing proofs. His choice of vocabulary can be challenging; I recommend having a pocket dictionary on hand.

In his first book, A Tour of the Calculus, Mr. Berlinski traces the evolution of the first great idea of "the great scientific culture of the West": the Calculus. The time was ripe in the 16th century for both Issac Newton and Gottlieb Leibnitz to simultaneously discover the art of reckoning instantaneous rates of change. While Newton is able to use these calculations to write the great Principia, Leibnitz devises an ingenious set of symbols for representing the strange articles of the Calculus. Neither mathematician would have been able to advance upon the work of the ancient Greeks had it not been for the recently deceased Rene Decartes' fortuitous dream whereby geometrical shapes are represented as coordinates along the X-Y axis of a 2-dimensional grid. However, the phenomenon of acceleration is not a mere polygon, but a continuous function of time. To map this on the Cartesian coordinate system, mathematicians conceived continuous functions. For every possible moment in position of a moving object, another moment from the continuous flow of time is required-with no interludes. This was a logical problem that had not been solved since the ancient Greek, Zeno, proposed his famous mathematical riddles about the impossibility of passing over a continuous distance. Yet by the nineteenth century, logicians Richard Dedekind, Karl Weierstrass, and George Cantor, constructed the ideas of Real Numbers and a logically cogent definition of a limit that finally seemed to answer Zeno's riddles to the satisfaction of most modern philosophers of mathematics.

Michael Rolle's theorem of local maximum and minimum points in a curve cleared the way for the important mean-value theorem. This theorem guarantees the existence of a differential value equal to, and somewhere within the two data points that determine the average rate of change in something always changing (such as a car accelerating). This is a hard idea to comprehend and even harder to appreciate; however Mr. Berlinski devotes much of the book to this quintessential theorem. The reader soon sees how it is put to use, proving the other great theorem, the fundamental theorem of calculus, that links together the operations of integration (i.e. finding the area beneath a curve) and differentiation (i.e. finding the instant rate of change of a function). Mr. Berlinski marvels that these two seemingly different quantities are mathematically related.

The first twelve chapters of this book should be required reading for anyone teaching high school mathmatics. There are a great number of intelligent people out there who hated algebra in school. I can't help but wonder if some of these people might have been reached by a few selected readings from this book. It puts a whole different perspective on learning math.

Mr Berlinski has somehow managed to write a book on a very interesting subject which is almost impossible to read . Though he seems to be very knowledgable about the topic at hand, instead of sticking to the objective, concise and entertaining style which is quite common among today's good science history writers, he has chosen to wander into the dark corners of the literary forest. The many diversions Mr. Berlinski jumps into almost every other page makes it nearly impossible to follow the subject matter while his labyrinthic prose complicates the already diffucult task of trying to concentrate on this book beyond a patience level that can be considered reasonable. "The Advent of the Algorithm" would certainly be a "one-star" book if it wasn't for the generous collection of interesting historical facts that are sprinkled throughout. I can't wait until one of the better science authors like Simon Singh or Ivars Peterson chooses to write a book on the same subject.

In a profession, the language used to describe it is very formal and brief, making it difficult for someone to learn from anything written in that style. It is necessary for expository writers to step into this gap, telling stories that entertain as the topic is explained. This type of writing is very difficult, which is why organizations like the Mathematical Association of America give awards on expository writing.
This book is an example of a description that entertains while it explains. Berlinski occasionally takes a couple steps off the main track, but overall the course is true. The algorithm as a set of instructions that will lead to a solution is a simple powerful idea that is in no way original. However, placing it in a formal form so that it can be mechanically executed is.
The main personalities the author uses in his descriptions of algorithms are mathematicians and for some reason, he chooses to cover only the time since Newton and Leibniz. Algorithms existed long before that, as all cultures used them in their mathematical operations. Unfortunately, there is little effort spent in describing the background of algorithms before the inventors of calculus.
While the mathematical achievements of the principals are laid out in detail, so are the elements of their personal lives. Many of the people had strong personality traits, some of which were detrimental to their lives and careers. Berlinski goes into these areas in great detail, so much so that the book becomes as much a set of short biographies of the men as it is a history of the formal algorithm. I did not find this detrimental, but think that it increases the readability of the book. This will certainly increase the appeal to nonprofessionals, although professionals may wish that he stuck a little more to the explanation of the algorithms.
This is a book that tells one major story and several smaller, more personal ones. The major story is about the development of formal algorithms and the minor ones are about the people that created the formal part of their structure. All of them are interesting and this book is one that makes the learning of mathematics entertaining.

David Berlinski has delivered another fascinating tale of an underappreciated topic. What he did for the calculus he now does for the algorithm. The text preserves all of Berlinski's extravagant, quirky and sometimes difficult style, shifting between careful analysis, historical drama, insightful explanation, and obscure fictional aside. Readers will either love it or hate it. (I love it.)

Unfortunately, some readers misunderstand Berlinski's subtlety and insight. For instance, the official trade review of the book complains that Berlinski never really defines "algorithm." This is incorrect. The introduction concludes with an offset definition: "In the logician's voice: an algorithm is a finite procedure, written in a fixed symbolic vocabulary, governed by precise instructions, moving in discrete steps, 1, 2, 3,..., whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end." It doesn't get much clearer than that. But Berlinski doesn't ponder long over what he takes to be obvious, and he doesn't always speak in the logician's voice.

The Advent of the Algorithm demonstrates that a seemingly dull concept can have unimaginably profound implications. Those implications illuminate everything from computing and information technology to the nature of life and the universe. And ultimately (not to spoil the ending) Berlinski argues that the advent of the algorithm foretells the end of scientific materialism, suggesting nothing so much as a world permeated by the marks of intelligence and design. To paraphrase, we are shocked to discover information--something we had assumed was found exclusively in the domain of human activity--flourishing on the alien shores of biology.