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: 707331
Weight:0.7 lbs

Published: 2005 Modern Library

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Amazon.co.uk info

Paperback 192 pages
ISBN: 0297848518
Salesrank: 629766
Weight:0.71 lbs

Published: 2006 Weidenfeld & Nicolson

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Amazon.ca info

Hardcover 224 pages
ISBN: 067964234X
Salesrank: 551783
Weight:0.7 lbs

Published: 2005 Modern Library

Marketplace:New from CDN$ 15.77:Used from CDN$ 0.83

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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.

Too clever by half **
Math teachers and math writers face a daunting problem. Some subjects are just difficult and some students and some readers just lack the intellectual wherewithal to understand. This problem is made worse when teachers and writers like Berlinski not only undertake a difficult task but add to their burdens and those of their students by taking on one final task, convincing the reader or student just how very smart the teacher or author is. Too often in Infinite Ascent the author goes off on metaphorical tangents which seem little more than ego driven side trips to impress the reader with the brilliance of the author. That he is well read and literate, I have no doubt. I just wish he would put more effort into a better explanation of metamathematics. I still don't get it.

Too clever by half **

Math teachers and math writers face a daunting problem. Some subjects are just difficult and some students and some readers just lack the intellectual wherewithal to understand.

This problem is made worse when teachers and writers like Berlinski not only undertake a difficult task but add to their burdens and those of their students by taking on one final task, convincing the reader or student just how very smart the teacher or author is.

Too often in Infinite Ascent the author goes off on metaphorical tangents which seem little more than ego driven side trips to impress the reader with the brilliance of the author. That he is well read and literate, I have no doubt. I just wish he would put more effort into a better explanation of metamathematics. I still don't get it.

Thanks, Mr. Berlinski , for your tingles! ****
"The sum total of what a man knows is vanishingly small. What seems in the end more important is that one should pursue knowledge." Bertrand Russell Discussed mostly are mathematical things which will always be beyond me. But, to my credit, I keep trying to understand them. To David Berlinski's credit he keeps trying to explain them. (Yes, he can be obtuse--but can anyone make some of this stuff clear? . .Yes, he can be flippant. . .Yes, he can be arrogant. . .) (He can be refreshing and funny, too!) But instead of finding fault with any of the presentation, I would rather praise him for bringing me some insight and for bringing me somewhat closer to understanding. He ends this book with a reference to the tingle that mathematicians sometimes sense. That, perhaps, is how Berlinski should be judged; and there are times this book tingles.

Thanks, Mr. Berlinski , for your tingles! ****

"The sum total of what a man knows is vanishingly small. What seems in the end more important is that one should pursue knowledge." Bertrand Russell

Discussed mostly are mathematical things which will always be beyond me. But, to my credit, I keep trying to understand them. To David Berlinski's credit he keeps trying to explain them. (Yes, he can be obtuse--but can anyone make some of this stuff clear? . .Yes, he can be flippant. . .Yes, he can be arrogant. . .) (He can be refreshing and funny, too!) But instead of finding fault with any of the presentation, I would rather praise him for bringing me some insight and for bringing me somewhat closer to understanding. He ends this book with a reference to the tingle that mathematicians sometimes sense. That, perhaps, is how Berlinski should be judged; and there are times this book tingles.

Does not eschew obfuscation *
What an annoying book! There are some authors with the knack of taking a difficult subject and making it understandable: Richard Dawkins comes to mind, or the late Isaac Asimov. Mr. Berlinksi has the opposite talent, of taking a subject that could be clearly explained and making it mystifying! I have some background in math (college courses in advanced calculus, probability, and number theory, most of it now long forgotten) and hoped to get some insight into other fields. Alas, no such luck. His discussion of Euler's famous equation (e to the i pi..., which I used to understand) was so astonishingly obscure that I now despair of ever figuring it out again. The book is full of quirky turns of phrase and startling allusions, which may give the casual reader the impression that he is learning something, but I can't see any conceivable audience. Those with little or no math knowledge will be utterly mystified. And to judge from the other reviews here, those who do know their math will find the book full of errors. I just found it confusing.

Does not eschew obfuscation *

What an annoying book! There are some authors with the knack of taking a difficult subject and making it understandable: Richard Dawkins comes to mind, or the late Isaac Asimov. Mr. Berlinksi has the opposite talent, of taking a subject that could be clearly explained and making it mystifying! I have some background in math (college courses in advanced calculus, probability, and number theory, most of it now long forgotten) and hoped to get some insight into other fields. Alas, no such luck. His discussion of Euler's famous equation (e to the i pi..., which I used to understand) was so astonishingly obscure that I now despair of ever figuring it out again. The book is full of quirky turns of phrase and startling allusions, which may give the casual reader the impression that he is learning something, but I can't see any conceivable audience. Those with little or no math knowledge will be utterly mystified. And to judge from the other reviews here, those who do know their math will find the book full of errors. I just found it confusing.

A quirky commentary rather than a history ***
The first thing to say is that this book isn't a "short history of mathematics," as the subtitle indicates. Rather, it's a commentary on a handful of key developments in mathematics, namely numbers, proof, analytic geometry, calculus, complex numbers, groups, non-Euclidean (and Euclidean) geometry, sets, and Godel's theorems. David Berlinski is surely brilliant and erudite (and he clearly wants us to realize that), but he's also a quirky fellow who has never really "fit in" with polite academic society, perhaps not even society in general. Stylistically, this book reflects its author, with Berlinski constantly making all sorts of tangential remarks. Overall, I did find his remarks to invigorate the book and entertain, but they don't add much insight. Moreover, some of his remarks are just plain weird and have no place in the book, especially his perverse sexual remarks (and it's telling that he couldn't resist putting them in the book). As far as presenting information about mathematics, this book is rather weak. If you don't already know the mathematics, you won't be able to learn it effectively from this book, since Berlinski compromises clarity for cleverness. And if you do already know the mathematics, you'll still have to do some work to fill in the frequent gaps in Berlinski's presentation. I was also a bit disappointed that Berlinski didn't suggest any further reading; as a non-mathematician with a serious interest in mathematics, surely he could have told like-minded readers about some of the books he's personally found helpful? Overall, I think this book merits 4 stars for entertainment value but only 2 stars for content delivery, so a net 3 stars. With a more honest title like "Comments on Some Milestones of Mathematics," I could have rated this book 4 stars. Since it's a quick read, I can still recommend this book to the mathematically initiated who are looking for entertainment. But I can't recommend it to readers with limited mathematics background, nor to readers looking for a genuine history of mathematics. Personally, I enjoyed this book, but learned almost nothing.

A quirky commentary rather than a history ***

The first thing to say is that this book isn't a "short history of mathematics," as the subtitle indicates. Rather, it's a commentary on a handful of key developments in mathematics, namely numbers, proof, analytic geometry, calculus, complex numbers, groups, non-Euclidean (and Euclidean) geometry, sets, and Godel's theorems.

David Berlinski is surely brilliant and erudite (and he clearly wants us to realize that), but he's also a quirky fellow who has never really "fit in" with polite academic society, perhaps not even society in general. Stylistically, this book reflects its author, with Berlinski constantly making all sorts of tangential remarks. Overall, I did find his remarks to invigorate the book and entertain, but they don't add much insight. Moreover, some of his remarks are just plain weird and have no place in the book, especially his perverse sexual remarks (and it's telling that he couldn't resist putting them in the book).

As far as presenting information about mathematics, this book is rather weak. If you don't already know the mathematics, you won't be able to learn it effectively from this book, since Berlinski compromises clarity for cleverness. And if you do already know the mathematics, you'll still have to do some work to fill in the frequent gaps in Berlinski's presentation. I was also a bit disappointed that Berlinski didn't suggest any further reading; as a non-mathematician with a serious interest in mathematics, surely he could have told like-minded readers about some of the books he's personally found helpful?

Overall, I think this book merits 4 stars for entertainment value but only 2 stars for content delivery, so a net 3 stars. With a more honest title like "Comments on Some Milestones of Mathematics," I could have rated this book 4 stars.

Since it's a quick read, I can still recommend this book to the mathematically initiated who are looking for entertainment. But I can't recommend it to readers with limited mathematics background, nor to readers looking for a genuine history of mathematics. Personally, I enjoyed this book, but learned almost nothing.

Basically Garbage *
This book irritated me so much that I'm going to just rant and abandon any hope of writing a 'helpful' review. I picked the book up on a remainder table for $1, and I clearly paid too much. Berlinski doesn't appear to know any more than a smattering of mathematical history (or math for that matter), but he dearly loves to hear himself talk as if he does. His flowery, grandiloquent delivery style accomplishes nothing remotely useful. An example from Chapter two: "Not until the twentieth century would mathematics and logic, having for so long exchanged their moist breath (sic), fuse ecstatically into the single subject of mathematical logic." Come on - "moist breath"?, "fuse ecstatically"? Nothing is being accomplished here except for the author going on a linguistic ego trip. Other reviewers have commented on the sloppy fact-checking and needlessly obscure presentation of the mathematics, and I agree with every one of those comments. Don't waste your time or money on this clunker.

Basically Garbage *

This book irritated me so much that I'm going to just rant and abandon any hope of writing a 'helpful' review. I picked the book up on a remainder table for $1, and I clearly paid too much. Berlinski doesn't appear to know any more than a smattering of mathematical history (or math for that matter), but he dearly loves to hear himself talk as if he does. His flowery, grandiloquent delivery style accomplishes nothing remotely useful. An example from Chapter two: "Not until the twentieth century would mathematics and logic, having for so long exchanged their moist breath (sic), fuse ecstatically into the single subject of mathematical logic." Come on - "moist breath"?, "fuse ecstatically"? Nothing is being accomplished here except for the author going on a linguistic ego trip. Other reviewers have commented on the sloppy fact-checking and needlessly obscure presentation of the mathematics, and I agree with every one of those comments. Don't waste your time or money on this clunker.

A good read for the curious generalist or any scientist *****
Just what the title says, and fun to read. I learned much about things I knew a little about once upon a time. Certainly a personal point of view especially with respect to choice of issues, but written with style and confidence: fast summer read for almost everyone interested in the subject.

A good read for the curious generalist or any scientist *****

Just what the title says, and fun to read. I learned much about things I knew a little about once upon a time. Certainly a personal point of view especially with respect to choice of issues, but written with style and confidence: fast summer read for almost everyone interested in the subject.

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.

My kind of book *****
Any reader could wait years for a book that fulfils his/her expectations in his/her favorite subject. Mine is history of science, and particularly, history of math. I'm engineer, and since college I'd read classic representative books in topics of history of math from E.T Bell, W. Rouse Ball, J. Rey Pastor and Leo Infeld, to quote few. This is one shares the merit of some of the previous authors not only in the sense that allows you to embrace the great mathematicians as human persons but also to appreciate their extraordinary legacy to human knowledge. The narrative style is clear and colorful, but I agree this book is easier to read for the math inclined. Do not expect an encyclopedia: the author focus on key characters and sketches minor contributors. Nevertheless, the treatment of subjects like Galois group's theory or Godel's incompleteness is brief yet thoroughly. That is why after reading Berlinsky's book I feel more confident mastering the milestones of math history. The general yet comprehensive vision offered by his book definitely helped me.

My kind of book *****

Any reader could wait years for a book that fulfils his/her expectations in his/her favorite subject.
Mine is history of science, and particularly, history of math. I'm engineer, and since college I'd read classic representative books in topics of history of math from E.T Bell, W. Rouse Ball, J. Rey Pastor and Leo Infeld, to quote few. This is one shares the merit of some of the previous authors not only in the sense that allows you to embrace the great mathematicians as human persons but also to appreciate their extraordinary legacy to human knowledge. The narrative style is clear and colorful, but I agree this book is easier to read for the math inclined. Do not expect an encyclopedia: the author focus on key characters and sketches minor contributors. Nevertheless, the treatment of subjects like Galois group's theory or Godel's incompleteness is brief yet thoroughly. That is why after reading Berlinsky's book I feel more confident mastering the milestones of math history. The general yet comprehensive vision offered by his book definitely helped me.