Customer Reviews: A Tour of the Calculus
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on October 5, 2005
I seem to be rather in the minority when I say that I actually liked Berlinski's verbose style; frankly, I don't really see what was so difficult to understand about it. On the other hand, I approached this book from the position of wanting something fun to read, and that's what I got, with the welcome addition of what I thought was lovely writing - if I had been searching for something that would give me an in-depth look at calculus, I would have looked elsewhere. Basically, I thought the book was really well-written and exciting (I had just begun calculus when I read it, so I found it really interesting to look at all the stuff we hadn't yet done.), and I highly reccomend it for a piece of fun reading and a decent overview.
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I hoped for an insightful view into calculus. Indeed, there are many deep and interesting aspects of calculus which are generally obscured in a typical calculus textbook (or in a calculus class). This is not such a book.
Most disappointing was the constant distraction of mathematical errors, small and large, throughout the book. For example, there are typos, errors in notation, and misleading or confusing notation. For these problems, I understood the author's intention at these points (being a calculus teacher myself), but to a reader less familiar with calculus, these problems will hinder understanding. When a reader can't understand the mathematical details, much of the meaning is lost.
A few errors were utterly irreparable, such as the proof of the Intermediate Value Theorem. In that case, a correct proof would diverge greatly from that of the author. This specific error is unfortunate because it is for this theorem that the author develops the real numbers (which takes chapters), and upon this theorem that all later theorems are based.
Finally, I found the author's style annoying, especially the fictional accounts of specific actions taken by historical mathematicians (crossing a river, contemplating calculus while sitting in an overstuffed chair, etc.). The author must enjoy hearing himself wax poetic on any subject which enters his head, but I don't.
The book's back cover likens this book to Douglas Hofstadter's classic _Godel, Escher, Bach_, but the comparison is laughable. Hofstadter's book has a direct and clear style of writing, whereas _A Tour of the Calculus_ is unfocused and its numerous errors makes it is mathematically a sham.
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on May 30, 2009
By reading some of these reviews, one thing is obvious: anyone who first lists their qualifications as a mathematician or calculus teacher is basically going to nay-say the heck out of the book. And in a way, I'd say this is semi-appropriate: the book is definitely not a math book; I think the grievances arise basically because it's sold as one. Sure, the word "tour" is in the title, but that does little to suggest that this book would be more appropriately marketed as....well....a memoir? Maybe?

Don't get me wrong though: the book isn't absolutely terrible. Some commenters have derided the author for using words that are too big, widely unknown, etc. But that's one of the things I enjoyed about the book: a few years back when I read it I underlined every word I didn't know or was fuzzy about and used this book as a way to build my vocabulary. I wouldn't describe myself as a cheery optimist, but I definitely turned the heightened language of the book to my advantage...instead of just whining about it on Amazon.

As for learning calculus: if you are a new student to calculus, this book won't really help. I bought this book years ago as a supplement to my calculus course and quickly found I was just wasting my time reading it. If you are a non-mathematician and just want a little glimpse into calculus, then this might be a good book. I would laugh at anyone who said they learned calculus from the book though.

In other news (finally, my qualifications...bla, bla, bla): since I've bought the book, I've taken all the calc and differential equations courses, abstract and linear algebra courses, analysis courses, graduated with a degree in physics and have completed one year of graduate school physics. With this in mind: Upon re-reading sections of the book recently, I would say that this is a pretty fun SUMMER READ for super nerds who already know it all, but just want to leisurely read about some elementary calculus by an author who writes in a conversational tone.
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on October 17, 2001
I am not a mathematician. I took calculus in college but never really understood it. I have, however, always wanted to understand it.
This book got glowing reviews so I bought it without leafing through it. My mistake. Compared to Berlinsky's book, the average college calculus textbook is a model of clarity.
Berlinsky is infatuated with words. He's never heard of a simple declarative sentence. One metaphor per sentence isn't enough. Indeed, if there is a literary conceit he doesn't indulge in to excess, I can't think of it.
His editor should have required him to read Strunk and White's Elements of Style daily for a year.
In short, as far as I am concerned, the other negative reviews I have read here are not only right on the money but not harsh enough.
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on August 7, 2001
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!
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on April 24, 2000
I have taught calculus for the past 20 years and I consider it one of the ( if not the) greatest achievements and the most beautiful constructs(or findings?) of the human mind.In the hands of MR.Berlinski it turns into a gargoyle,even worse it turns into a heap of shapless being (if any). I rated the book with one star because I had no other option. My honest opinion is that it desreves a star NOT.
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on April 9, 2014
The author is off his rocker but seriously the guy helped me make sense of Calculus I. Not only did I learn how to take derivatives and limits and find areas but this book explained why I was doing. If you're looking to know more about the subject than just how to do calc problems, this is a pretty good book to start with.
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on February 11, 2008
I found it fascinating that there are (at the time of writing) about as many 5's as 1's among the reviews of this book. As you can probably tell by the title, I am not a fan.

I confess that I did not read the whole book: I could not. As I went on, I found myself getting angry at this book, for reasons that I hope will be a little clearer by the end of the review. At that point I gave up on reading the whole book and dipped in here and there.

Here's what I think:

I found the prose purple, precious and pretentious (just like this sentence!-), but that is hardly the book's worst fault. Neither is the interjection of the author's opinions on things unrelated and irrelevant (the comment on the Duke University English Department springs to mind: a one-sentence insult is as inventive as the almost proverbial "your mama" - I find the Sokal Affair a much more effective and amusing skewering).

The worst fault of the book, imo, is that there was no light shed on the subject (nacreous or otherwise), no effulgence... (BTW, if you like these words, you *might* like the book but no guarantees). On the contrary, confusion and inaccuracy abound: the Dedekind cuts chapter is full of them for example - I had to go back to a real exposition (Ferrar's appendix in his 1938 book on "Convergence" fwiw) to regain my sanity. Somebody else pointed out the sine/cosine graph flub. The graph in the chapter on Rolle's theorem shows a function that does not satisfy the conditions of the theorem as stated two pages earlier. I found most of the explanations similarly confused and confusing: I cannot imagine how anybody can learn much from this book, be it beginner, expert or anywhere in between.

Somebody else mentioned that he enjoyed the "historical anecdotes". I 'm not sure that there are any that are not figments of Mr. Berlinski's imagination. Every time that he started a description that I assumed was factual, it ended by being clearly an invention of the author - and there was no way to tell where facts ended and invention began.

The author mentions the comment of his high school English teacher who said (I paraphrase from memory here, so the figure may be wrong, but the meaning should be clear): "Mr. Berlinski, once more you took ten pages to say nothing." The comment to some degree applies to the book. I can only assume that the poor editors who tried to cut it down to something reasonable gave up exhausted at the futility of the task.

So for me, the book fails as exposition or history of the subject. It also fails as entertainment. Is there anything left?

For an example of a book that I think is genuinely informative, honest, useful *and* entertaining, I suggest John Derbyshire's "Prime Obsession." Although you can get a whiff of Derbyshire's (rather quirky) political conservatism in the book, nevertheless the book is always about its subject (the Riemann hypothesis) and never becomes an object for the author's own aggrandizement. Mr. Berlinski's book in contrast is very much about Mr. Berlinski.
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on January 17, 2001
As I recline gently in my reproduction eighteenth-century leather-backed desk chair, my hulking athletic frame weary from the day's toils, I breathe a sigh, and casually reflect upon my Berlinski reading experience. Each evening for the previous fortnight I had curled up in front of the warm, flickering fire, book in hand, brandy at side, and marveled at how many adjectives could be strung together merely through the prolific use of commas. Oh calculus, noblest of mathematical fields, will my weary intellect ever fully comprehend your vast depths and many intricacies? As I remorselessly toss this volume onto the hungry flames I feel a flood of relief overcome my body, heightening my spirits with the knowledge that I would not have to read this drivel again.
If you enjoyed plodding through this wordy (and poorly written) review just to find out that I thought this book was not worth the paper it was printed on, then by all means buy this book. It's for you.
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VINE VOICEon March 3, 2001
Why anyone who didn't like math would read a book about calculus, I don't know, but let me preface this review by saying that if you don't like math, then you probably won't like this book. On the other hand, if you like math, then there is a lot to like in this book. And if you are currently in a calculus class--even if it's a required class--this book can help you make some sense out of what you're learning and put it in an historical context. This book is certainly a better development of the most basic concepts than you'll find in many of those 1000+ page Calculus textbooks. (Of course, it's just a conceptual development. You'll find little in the way of technique and problem-solving.)
I think the main reason I enjoyed reading this book is because I enjoy math and it's clear that Berlinski does too. It's always fun to read a book by someone who clearly enjoys what he is writing about. And he's structured the book well, giving the conceptual developments of the subject as they were ispired by the attempts to solve particular historical problems. He's also given us a taste of the personalities (Newton, Leibnitz, Cauchy, Riemann, etc.) who moved the subject forward, a look at what appears to be insights from his own experience as a teacher of calculus and mathematician, and relagated the formal math to appendices. This is a nicely done book.
My only complaint is that in his historical and classroom interludes, he gets almost a little flippant. Maybe a little too "fictional." It's certainly fun and engaging to read these sections but I began to wonder what was real and what wasn't. When he's talking about his students and colleagues who may or may not be real people this is fine but when he's reimagining important historical figures I began to wonder about accuracy. As a lover of mathematical history, I found this disturbing.
This is a small complaint, however. This is very worthwhile reading for someone who wants to understand why calculus was developed in the first place.
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