David Berlinski

Infinite Ascent

Infinite Ascent: a short history of mathematics by David Berlinski takes the reader through ten significant topics in the development of mathematics. Starting with the Greeks and Euclidean geometry, Berlinski goes on to describe the origins of complex numbers, calculus and analytic geometry. He then looks at some of the mathematics which originated in the nineteeth centrury - group theory, noneuclidean geometry and set theory - and this leads up to Gödel's incompleteness theorem. The final chapter is a look at some of the current areas of mathematical research.

The trouble is that I'm not entirely sure who the book is for. Although it is claimed to be aimed at the novice, I'm not convinced that writing in a somewhat quirky style is the way to achieve this - my feeling is that it's more likely to confuse the uninitiated. Those with more experience of the subject are unlikely to find much which is new to them, although they might enjoy the book as a bit of light reading. I think that the most suitable reaership is those who are currently studying the subjects involved - advanced school students or beginning undergraduates - who will benefit from learning a bit of the history of the subject and from a different 'take' on what they are studying.

Amazon.com info

Hardcover 224 pages
ISBN: 067964234X
Salesrank: 813508
Weight:0.7 lbs

Published: 2005 Modern Library

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Amazon.co.uk info

Paperback 192 pages
ISBN: 0297848518
Salesrank: 398380
Weight:0.71 lbs

Published: 2006 Weidenfeld & Nicolson

Amazon price £14.24

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Amazon.ca info

Hardcover 224 pages
ISBN: 067964234X
Salesrank: 262037
Weight:0.7 lbs

Published: 2005 Modern Library

Marketplace:New from CDN$ 14.37:Used from CDN$ 7.91

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Product Description
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.

Product Description

In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure.

Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt.

The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.

A God send *****
In this book David Berlinski takes you on a trip through the ages into the hidden mystical history of mathematics. The book is relatively short so Berlinski gets right to the point using Biblical like precision and compactness in the array of language he chooses to employ. This book is for anyone who wants to know and understand the history of mathematics from a deep intuitive perspective but doesn't want or need to learn mathematics itself. Belinski does the finest job here of simplifying the concepts of advanced mathematics to such a degree that any high school graduate (with a dictionary handy) can ascertain their meaning and importance. A concise history of mathematics is this book. For the more "self declared" intelligent and learned out there, this book does an excellent job describing in poetic detail the significance of the story imbedded in the enigmatic history of mathematics, as well as explaining the significance of math itself. Berlinski uses a wonderful bouquet of words that will help to titillate even the brainiest and experienced of readers. If you are looking for a little mathematical enlightenment and wouldn't mind a transcending journey, be prepared for the expierence of Infinite Ascent!

A God send *****

In this book David Berlinski takes you on a trip through the ages into the hidden mystical history of mathematics. The book is relatively short so Berlinski gets right to the point using Biblical like precision and compactness in the array of language he chooses to employ. This book is for anyone who wants to know and understand the history of mathematics from a deep intuitive perspective but doesn't want or need to learn mathematics itself. Belinski does the finest job here of simplifying the concepts of advanced mathematics to such a degree that any high school graduate (with a dictionary handy) can ascertain their meaning and importance. A concise history of mathematics is this book.

For the more "self declared" intelligent and learned out there, this book does an excellent job describing in poetic detail the significance of the story imbedded in the enigmatic history of mathematics, as well as explaining the significance of math itself. Berlinski uses a wonderful bouquet of words that will help to titillate even the brainiest and experienced of readers. If you are looking for a little mathematical enlightenment and wouldn't mind a transcending journey, be prepared for the expierence of Infinite Ascent!

The author tries to do two diametrically opposite things simultaneously and he largely fails at both ***
To the extent that this book is mathematical there is no depth and to the extent that it is lyrical, it is sometimes over the top. There is some mathematics presented, but it is often surrounded by extended symbolism, metaphors and occasionally colorful language. For example, on page 128, which is in a section covering set theory, there is the following segment. "The sac itself is not fruit, but how else to collect apples, pears, and peaches without the satisfying rip, the tense tingle between thumb and forefinger, and thereafter the safely bagged pineapple swinging from the scrotum of its sac? " On page 157, which is a section covering incompleteness, there is the following segment. "The same movie is spinning over the sprockets of the very same hideously expensive cutting-room contraption, but the scene revealed is different somehow, and where before there was only black, white, and gray, there are now all sorts of subtle colors, the director, Pedro or Fedro, murmuring with satisfaction as those drab symbols of his first cut come to vibrate, and just look at that remarkable fuchsia!" Finally, on page 91, which is a section on group theory, there is the following segment. "For reasons that I cannot explain, I have always found it helpful to imagine these rather formal statements being uttered by a stout and somewhat disheveled Mexican army officer in one of those movies of the late 1940's in which the Alamo was forever about to be overrun. `Huy senor, there is thees collective. They have thees guns bah only one operation . . .'" The mathematical topics covered are: ) Number ) Proof ) Analytic geometry ) The calculus ) Complex numbers ) Groups ) Non-Euclidean geometry ) Sets ) Incompleteness ) The present Given that the book is only 180 pages long, none of these topics is covered in any depth. Add in the colorful nonmathematical language and the book is more of a historical novel than a history text. There two diametrically opposed concepts are hard to combine and Berlinski does not succeed in doing it here.

The author tries to do two diametrically opposite things simultaneously and he largely fails at both ***

To the extent that this book is mathematical there is no depth and to the extent that it is lyrical, it is sometimes over the top. There is some mathematics presented, but it is often surrounded by extended symbolism, metaphors and occasionally colorful language. For example, on page 128, which is in a section covering set theory, there is the following segment.

"The sac itself is not fruit, but how else to collect apples, pears, and peaches without the satisfying rip, the tense tingle between thumb and forefinger, and thereafter the safely bagged pineapple swinging from the scrotum of its sac? "

On page 157, which is a section covering incompleteness, there is the following segment.

"The same movie is spinning over the sprockets of the very same hideously expensive cutting-room contraption, but the scene revealed is different somehow, and where before there was only black, white, and gray, there are now all sorts of subtle colors, the director, Pedro or Fedro, murmuring with satisfaction as those drab symbols of his first cut come to vibrate, and just look at that remarkable fuchsia!"

Finally, on page 91, which is a section on group theory, there is the following segment.

"For reasons that I cannot explain, I have always found it helpful to imagine these rather formal statements being uttered by a stout and somewhat disheveled Mexican army officer in one of those movies of the late 1940's in which the Alamo was forever about to be overrun.

`Huy senor, there is thees collective. They have thees guns bah only one operation . . .'"

The mathematical topics covered are:

*) Number
*) Proof
*) Analytic geometry
*) The calculus
*) Complex numbers
*) Groups
*) Non-Euclidean geometry
*) Sets
*) Incompleteness
*) The present

Given that the book is only 180 pages long, none of these topics is covered in any depth. Add in the colorful nonmathematical language and the book is more of a historical novel than a history text. There two diametrically opposed concepts are hard to combine and Berlinski does not succeed in doing it here.

Egregious historical error. *
Just for the record, Paul Dirac was British, not French as asserted by Berlinski on page 8. Dirac was born in Bristol and held the Lucasian Chair of Mathematics at Cambridge and built the mathematical foundation for quantum electrodynamics. Dirac has been written about extensively. It is amazing that a book that purports to be "a short history of mathematics" doesn't have anyone checking facts, proof reading, or editing. One loses interest after encountering a major flub so early in the book.

Egregious historical error. *

Just for the record, Paul Dirac was British, not French as asserted by Berlinski on page 8. Dirac was born in Bristol and held the Lucasian Chair of Mathematics at Cambridge and built the mathematical foundation for quantum electrodynamics. Dirac has been written about extensively. It is amazing that a book that purports to be "a short history of mathematics" doesn't have anyone checking facts, proof reading, or editing. One loses interest after encountering a major flub so early in the book.

Wonderfully readable Math major events from 400BC to now *****
I recall "sipping from the fire hydrant of knowledge" during my University days and have felt for decades that I missed some of the big ideas in Mathematics. I wanted a chronological mental map. This enjoyable 181 page book covers the big topics from Pythagoras to Galois through Gauss to Mandelbrot in sufficient detail to allow me to understand who did what when and why it matters. David did a much better job explaining Galois's group theory ideas for proving the quintic unsolvable by radicals than the recent book "The Equation that couldn't be solved". Somehow I never understood the infinitesimals versus limit method proofs of Calculus but David made it clear. I am much indebted for this book, it has cleared up many long standing gaps in my admittedly meager grasp of mathematics.

Wonderfully readable Math major events from 400BC to now *****

I recall "sipping from the fire hydrant of knowledge" during my University days and have felt for decades that I missed some of the big ideas in Mathematics. I wanted a chronological mental map. This enjoyable 181 page book covers the big topics from Pythagoras to Galois through Gauss to Mandelbrot in sufficient detail to allow me to understand who did what when and why it matters. David did a much better job explaining Galois's group theory ideas for proving the quintic unsolvable by radicals than the recent book "The Equation that couldn't be solved". Somehow I never understood the infinitesimals versus limit method proofs of Calculus but David made it clear. I am much indebted for this book, it has cleared up many long standing gaps in my admittedly meager grasp of mathematics.

A 4 for content...a 2 for usefulness ***
This book has bouts of brilliance but was short on usefulness. I found myself time and again asking what the point of this book was. I wasn't sure if Berlinski was happy that math has taken the turns that it did or if he is waiting for the next mathematical revolution. I'm not sure that I would recommend this book to anyone because I don't know what type of person would find it remotely intriguing.

A 4 for content...a 2 for usefulness ***

This book has bouts of brilliance but was short on usefulness. I found myself time and again asking what the point of this book was. I wasn't sure if Berlinski was happy that math has taken the turns that it did or if he is waiting for the next mathematical revolution.

I'm not sure that I would recommend this book to anyone because I don't know what type of person would find it remotely intriguing.

Good overview but painfully over-written **
The chef Berlinski stands before the amassed ingredients. One by one he beckons to his accomplices: Pythagoras walks forward, newly laundered toga draped gracefully, and adds Number to the mixing bowl; next Euclid, calculating his best angle of approach, drops freshly squeezed axioms into the mix and pens a proof of the eventual shape of the cake; Descartes sprinkles analytic geometry; Newton and Liebniz, staring suspiciously at each other reluctantly drip calculus into the bowl, nearly tipping its contents in their eagerness to squeeze out the first drop. Cardano, with an Italian flare, takes the dish into a new dimension with his spicy, complex addition. By now Galois is not at all happy with the look of things and starts trying to group the ingredients appropriately. Gauss wonders if the cake will still preserve its shape in a non-Euclidean space and Cantor considers the possibility that the flour grains are not countable. Finally Gödel speculates that the cake will never be complete no matter how long they continue, so stopping now is as good a time as any. The cake is baked and emerges from the oven as a fine example, perfectly formed, with that wonderful freshly baked aroma; step forward the chef Berlinski, he has something behind his back and the others eye him suspiciously. But, Berlinski is quick, and before they can prevent it he smothers the perfect cake in all manner of creams, icing and decorative candy beads; the cake that was so lovingly crafted is an inedible mess, offensive to the nose and painful to the eye. The mathematical cooks, from antiquity to modern times, shake their heads in disgust and walk out of the kitchen. This is a review of a short history of mathematics which selects some of the great mathematicians through history and discusses some of their most important works; however it is so smothered by Berlinski's, awful, flowery style that it becomes irritating to read. If you think my parody above was bad wait until you read this book.

Good overview but painfully over-written **

The chef Berlinski stands before the amassed ingredients. One by one he beckons to his accomplices: Pythagoras walks forward, newly laundered toga draped gracefully, and adds Number to the mixing bowl; next Euclid, calculating his best angle of approach, drops freshly squeezed axioms into the mix and pens a proof of the eventual shape of the cake; Descartes sprinkles analytic geometry; Newton and Liebniz, staring suspiciously at each other reluctantly drip calculus into the bowl, nearly tipping its contents in their eagerness to squeeze out the first drop. Cardano, with an Italian flare, takes the dish into a new dimension with his spicy, complex addition. By now Galois is not at all happy with the look of things and starts trying to group the ingredients appropriately. Gauss wonders if the cake will still preserve its shape in a non-Euclidean space and Cantor considers the possibility that the flour grains are not countable. Finally Gödel speculates that the cake will never be complete no matter how long they continue, so stopping now is as good a time as any.

The cake is baked and emerges from the oven as a fine example, perfectly formed, with that wonderful freshly baked aroma; step forward the chef Berlinski, he has something behind his back and the others eye him suspiciously. But, Berlinski is quick, and before they can prevent it he smothers the perfect cake in all manner of creams, icing and decorative candy beads; the cake that was so lovingly crafted is an inedible mess, offensive to the nose and painful to the eye. The mathematical cooks, from antiquity to modern times, shake their heads in disgust and walk out of the kitchen.

This is a review of a short history of mathematics which selects some of the great mathematicians through history and discusses some of their most important works; however it is so smothered by Berlinski's, awful, flowery style that it becomes irritating to read. If you think my parody above was bad wait until you read this book.