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Editorial Review Product Description
Now regarded as the bane of many college students’ existence, calculus was one of the most important mathematical innovations of the seventeenth century. But a dispute over its discovery sewed the seeds of discontent between two of the greatest scientific giants of all time — Sir Isaac Newton and Gottfried Wilhelm Leibniz. Today Newton and Leibniz are generally considered the twin independent inventors of calculus, and they are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret. This long and bitter dispute has been swept under the carpet by historians — perhaps because it reveals Newton and Leibniz in their worst light — but The Calculus Wars tells the full story in narrative form for the first time. This vibrant and gripping scientific potboiler ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad and, in the end, completely human. ... Read more Customer Reviews (16) 
not good....
This book is poorly written. In fact, considering that its subject is most likely to be chosen by discriminating readers, it is so bad that I am surprised it made it into print. Among many other faults noted by other reviewers, most jarring to me is the way the author continually yanks the reader from the 17th century into the present by making reference to something that he'd recently seen or done. That may be the fault of the author, or of his editor, or both; regardless, it gives the book a wildly alternating tone and perspective. Both the author and the editor should feel embarrassed at having produced this shoddy work.
Please avoid this pomposity, at all costs!
If you've read the reviews that preceded this, you probably have an idea of how disastrously this book has been edited. I will add only that which hasn't been mentioned in other reviews, which is my two cents.
I must say that I only finished this book to give the author the benefit of doubt, after fuming over the many typos, disgustingly careless grammar, factual errors and irreverent first-person comments. I'm sorry to say it wasn't worth the effort.
Before sounding like a gripe, let me tell you what this book is good for. If you like reading your history as a smattering of tidbits within the confines a specific social context, in this case the lives of two prominent scientists at the turn of the 18th century, this is worth skimming over. At best, it is a slightly precocious commentary, and at worst it has the pretentions of being an analysis, with random, irrelevant and condescending first-person accounts thrown in. Worse still, in the epilogue, we are made to feel that Bardi is really modest as he claims to be embarassed by a friend's comments regarding his expertise on the subject.
There are questions that arise out of the subject matter, however, and relevant ones. The overarching one is whether the introvert inventor or the original but flambuoyant expositor gets the credit for an issue as thorny as the invention of Calculus? If this was the question Bardi set out to answer in his book, he should have realized that a chronological biographical sketch with some seemingly relevant characters thrown in would be insufficient.
There is no level of detail regarding the mathematics here. This is disdainful, and only shows how much regard even a science writer has for the subject, or was he perhaps muffled by his very competent publishers? I tend to lean away from the latter explanation because even the verbal treatment of the mathematics is shamefully cursory. A case in point is the description of the brachistochrone problem, infamous in the calculus of variations. How is one to understand the gravity (sic) of the problem if one doesn't quite follow what has led up to it? Merely mentioning that it was a Leibniz challenge is like conjuring a rabbit out of a hat.
It is one thing to avoid equations, lest the audience feel they are talked down to, but another thing altogether to use mathematical symbols for the purely decorative, as the equations in the illustratitive section have done. They have no explanations, no context whatsover, provide no insight to those who are unfamiliar with Calculus, and tautological to those who are. Instead of pulling out pages from text and rendering them unreadable in fine print even the briefest description of Newton's explanation of rainbows would have sufficed. Equations could have been in the body of the text, and where relevant, at the very least.
A discussion about Calculus necessiates a discussion about the tools and the formalism, and even if Bardi wished to avoid excessive technicality, he could have done what most good science journalists do, which is to collate and quote opinions from folks who are well-versed in the mathematical subtleties.
There are a few instances when Bardi stoops from his pedestal to do just this, and those are the few slivers of salvation this book offers. At one point (page 130), he quotes a balanced review of the Pricipia, and mentions how it lauds Newton's geometry but not his physics, since Newton is to have famously declared that 'I do not invent hypothesis' [for gravity]. At another (page 207), Bardi quotes Johann Bernuolli's defense of Liebniz when he mentions that Newton didn't quite demonstrate his method of fluxions in the Principia when he had ample chance to do so, but dogmatically stuck to the geometrical style of his predecessors.
The first case was interesting because it echoes something of Edwin Hubble's attitude regarding his data for receding galaxies. He apparently refused to interpret what his data implied, even if it favoured something like the Big Bang. From a philosophical standpoint such extreme empericism must have indeed looked bizzare and rattled Leibniz in his time, as it did contemporary astronomers.
The other instance, involving Bernuolli's commentary, is somewhat more illuminating of Newton's character. It is an irony that Newton avoided his method of fluxions (perhaps embittered by Hooke's criticism) in the Principia so it would be widely understood, and Leibniz introduced the formalism of Calculus so that it would be widely used to solve a broad class of problems. While Newton's approach was to introduce his concepts of motion and gravitation using existing geometrical tools, looking backward, Leibniz's was to introduce a generic technique of solving infinitesimal problems, complete with a set of tools and it associated new symbols, moving forward. As testimony to the latters vision, we still use his symbols today. In this sense, contrary to the review of the Principia from long ago, Newton was really original in his physical insight about gravitation while Leibniz had the vision to understand that the scope of Calculus was much wider, and not just restricted to gravitation.
The redemption factors are not able to salvage the book, alas. It remains balanced but shallow, and goes to show that however well a book may be researched, an interesting narrative is one where the assimilation is almost invisible, and in a way that inspires meaningful questions. To this end, even an exhaustive bibliography still remains a means, not an end.
Just okay, borrow from library
The author presents a less technical account of the development of the calculus and the acrimony between Newton and Leibniz later in their lives.Other reviewers here have noted many of the deficiencies of this book editorially; I completed the entire book, and have the following additional criticisms.The "warring" part of the book is only about the last 20%.While the author has done his research, in his presentation I detect only a superficial scholarship that suggests a post-modern, blasé approach to describing the topic. (A reader might get a slightly more engaging account of Newton and Leibniz in Neal Stephenson's "Quicksilver", but there again you have to slog through hundreds and hundreds of pages of post-modern writing).
Beyond the vast amount of editorial mistakes, in one instance the author also seems to have confused the Balkan peninsula, the Iberian peninsula, diplomacy, politics and wars in these areas, etc. with his mention of "France would indeed eventually invade Egypt under Napoleon, who grasped the value of the peninsula..."Finally, there are serious instances where the author's personal opinion has no place in the text.
Overall, it is an okay effort, but more serious readers might best go elsewhere.
Heavy on Biography, Light on the Origins of Calculus
Students of mathematics at the calculus level and beyond are usually made vaguely aware that, despite some minor historical contention, Isaac Newton is credited for the discovery of calculus. Fewer in number are those who learn the name Gottfried Wilhelm Liebniz as Newton's rival claimant for that honor, and still fewer are those who are informed that Newton's methods of fluxions and fluents were almost immediately abandoned in favor of Liebniz's differentials and his superior mathematical notation (essentially that still in use today).
Author Jason Bardi aims to correct that knowledge shortfall in THE CALCULUS WARS: NEWTON, LIEBNIZ, AND THE GREATEST MATHEMATICAL CLASH OF ALL TIME. The use of the word "wars" and the hyperbolic phrasing "greatest clash of all time" set the expectations stage for an epic battle of intellectual giants as potentially juicy as 20-year-old Evariste Galois's fatally romantic duel with pistols. The historical facts are rather less sensational, however, consisting largely of letters and journal articles (most submitted anonymously at the time) hurling nationalistic accusations, often petty or unfounded, from one side of the English Channel to the other. As a result, Mr. Bardi struggles to deliver the implicit drama: there is no critical face-off between the principals, no momentous debate (even the British Royal Society largely shrugs it off thanks to Newton's presidency of that august body), no climactic moment when the truth is laid bare.
Perhaps more disconcerting, the vast majority of Bardi's book is not about calculus at all, not about the battle over its discovery, its historical underpinnings, or its subsequent development along the lines of Liebniz's work. We never see a comparative representation of the Newtonian and Liebnizian models, their notational differences, or their intellectual geneses from the mathematical work of their predecessors (Archimedes' famous method of exhaustion, for example, receives just one passing mention). Instead, the author falls back on the more conventional approach of chronological biography, trailing the two men's parallel lives from 1642 to 1728. It could certainly be argued that their respective biographies give important background to their personalities and professional status when the "calculus wars" finally broke out in 1699 (175 pages into Bardi's 250-page book). However, Bardi writes extensively on Liebniz's silver mining schemes, invention of a leather folding chair and a new type of windmill, promotion of binary numbers, theories of planetary motion and theology, political machinations, court genealogical work, and studies of China, to name a few. Similarly with Newton, it is his optics, theories of universal gravitation, stewardship of the British Mint, dabblings in alchemy, psychological mood swings, even his sexual orientation.
In the end, Bardi sides with Liebniz as the more aggrieved party, clearly innocent of the charges of plagiarism. Newton is clearly the loser in this "war," both for hoarding his great discovery to the detriment of fellow scientists and mathematicians and for treating his Continental contemporaries with such disdain. Sadly, the entire affair did nothing to polish the honor of either man.
Bardi's storytelling prose is fluid and well suited to his task, with one significant exception. In a tale of dueling mathematical, scientific, and intellectual giants, one inserts oneself at the greatest of risks. Perhaps a Stephen Hawking could merit an occasional authorial "I" in this story, but decidedly not a Jason Bardi (despite his ostentatiously displayed middle name, Socrates, that ironically only emphasizes the disparity). Author Bardi is given to repeated, utterly trivial, and mostly parenthetical insertions of his own opinions that are presumptuous, irrelevant, and distracting: "When I was in London, I noticed..." , "...an event I like to call..." , "I get this picture when I think about it..." ,"...as I recall from my encounter..." , "For my part, I can't help but wish..." , "a docent told me..." , "I examined..." , "...I have read..." , "I examined... [again]" , culminating with the irrepressible "I'm not surprised, really" and the exquisite "For me, what's really interesting... " Every one of these first person insertions should have been removed by a more exacting editorial pencil.
I approached this book hoping to discover a comparative treatment of the origins and development of Newton's and Liebniz's twin lines of calculus development, to learn how two intellectual giants of the 18th Century each separately made a conceptual mathematical leap nearly on a par with Einstein's leap to relativity. The similarities and differences in their developmental threads would surely be part and parcel of the historical argument over rights of discovery and accusations of plagiarism. Regrettably, I found instead seemingly endless pages of biographical minutiae about everything else in these two great men's lives.
Proofreading Errors Are Too Distracting
When I received the book, I began reading the section "Bibliographical Essay" and encountered ten proofreading errors in nine pages.I found this too distracting to continue, and I lost trust in whatever scholarship was used in the preparation of this book.There is no excuse for such carelessness.If I were the publisher, I would be embarrassed.
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