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The Calculus Wars

Calculus is a word that brings trepidation to many students , and they may wonder who is responsible for this branch of mathematics. In The Calculus wars Jason Bardi shows how two great thinkers claimed to have invented it. At first Newton and Leibniz were willing to grant that they invented the subject independently, and that each provided a useful part. But somehow, in their later lives, it turned nasty and each accused the other of plagiarism. Bardi is a skilled writer, putting together a interesting story from the historical data and I would recommend the book to anyone with an interest in the history of mathematics or more generally in how the modern approach to science came about.

Personally I would have liked to have seen more of the actual mathematics involved in the book. I can understand the avoidance of equations in a work written in a popular style, but my feeling is that the readership of this book is likely to be those who do not mind a bit of mathematics. Not only would this give more of a central thread to the book, it would also allow the readers to form their own judgement on the competing claims - did Leibniz do the hard work of making calculus into a useful subject, or was it all there in Newton's original work?

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Hardcover 288 pages
ISBN: 1560257067
Salesrank: 545653
Weight:1.01 lbs

Published: 2006 Basic Books

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Hardcover 288 pages
ISBN: 184344030X
Salesrank: 496424
Weight:1.1 lbs

Published: 2006 High Stakes Publishing

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Hardcover 288 pages
ISBN: 1560257067
Salesrank: 217711
Weight:1.01 lbs

Published: 2006 Thunder's Mouth Press

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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.

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.

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.

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.

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.

Tangentially integrated **
Isaac Newton invented calculus in 1665 and 1666, but chose not to publish due to criticism (by Hooke) of his published work on light. Leibniz invented calculus independently ten years later and published his findings. Things seemed fine between the two men until, primarily through the actions of good-hearted meddlers, controversy was stirred up, words like "plagiarism" were used and bad feelings were had all around. Of the situation, one might wonder, "Who cares?" Well, smart guy, skilled researcher and appropriately named Jason Socrates Bardi did and does and so chose to compose an entire book on the subject. Unfortunately what he produced is unlikely to enlighten the reader much beyond the basic facts, which are set forth early on and detailed later, nor is it likely to entertain due to its repetitive nature (in facts and words), and the awkward tangents taken, whereby he switches from objective writer to, in the very next sentence, commentator, generally without even the use of parentheses. Some form of the word "society" comes up 11 times on page 189 and ten on page 191, "many" occurs five times in one paragraph on page 146, and "escape" is used thrice in one sentence (page 135), "He escaped again, his second escape apparently helped by the fact that he was allowed to escape." Transitions from storyteller mode to commentator mode occur regularly (Pp 120, 156, 167), for example, after explaining that Newton described in a notebook his use of a needle to perform experiments on his own eyes, the author writes, "I saw a copy of this notebook...[p 29]," and gets further off track in telling of an encounter with a mother and son viewing same. Upon describing a process for manufacturing phosphorus, he comments, "I get this picture when I think about it:...[p 105]" Additionally, he chooses to bestow a seemingly official name, used as a chapter title, on an eyebrow-raising occurrence (The Affair of the Eyebrow). And inexplicably writes, "As it was, court intrigues in Hanover at the time were enough to make a soap-opera-loving housewife blush [p 163-164]." Neither man achieves a clear victory in the wars, and although the topic is book worthy, the repetition and clumsy transitions take away from what would otherwise be interesting reading. Better books on math and science: American Prometheus by Kai Bird and Martin J. Sherwin, Obsessive Genius by Barbara Goldsmith, A Beautiful Mind by Sylvia Nasar, and The Double Helix by James D. Watson.

Tangentially integrated **

Isaac Newton invented calculus in 1665 and 1666, but chose not to publish due to criticism (by Hooke) of his published work on light. Leibniz invented calculus independently ten years later and published his findings. Things seemed fine between the two men until, primarily through the actions of good-hearted meddlers, controversy was stirred up, words like "plagiarism" were used and bad feelings were had all around. Of the situation, one might wonder, "Who cares?" Well, smart guy, skilled researcher and appropriately named Jason Socrates Bardi did and does and so chose to compose an entire book on the subject. Unfortunately what he produced is unlikely to enlighten the reader much beyond the basic facts, which are set forth early on and detailed later, nor is it likely to entertain due to its repetitive nature (in facts and words), and the awkward tangents taken, whereby he switches from objective writer to, in the very next sentence, commentator, generally without even the use of parentheses. Some form of the word "society" comes up 11 times on page 189 and ten on page 191, "many" occurs five times in one paragraph on page 146, and "escape" is used thrice in one sentence (page 135), "He escaped again, his second escape apparently helped by the fact that he was allowed to escape." Transitions from storyteller mode to commentator mode occur regularly (Pp 120, 156, 167), for example, after explaining that Newton described in a notebook his use of a needle to perform experiments on his own eyes, the author writes, "I saw a copy of this notebook...[p 29]," and gets further off track in telling of an encounter with a mother and son viewing same. Upon describing a process for manufacturing phosphorus, he comments, "I get this picture when I think about it:...[p 105]" Additionally, he chooses to bestow a seemingly official name, used as a chapter title, on an eyebrow-raising occurrence (The Affair of the Eyebrow). And inexplicably writes, "As it was, court intrigues in Hanover at the time were enough to make a soap-opera-loving housewife blush [p 163-164]." Neither man achieves a clear victory in the wars, and although the topic is book worthy, the repetition and clumsy transitions take away from what would otherwise be interesting reading. Better books on math and science: American Prometheus by Kai Bird and Martin J. Sherwin, Obsessive Genius by Barbara Goldsmith, A Beautiful Mind by Sylvia Nasar, and The Double Helix by James D. Watson.

Great insights *****
I really enjoyed this book and found it offered a great many wonderful tidbits to fill in my understanding of the issues. My most recent previous reading on Leibniz was the wonderful book "The Courtier and the Heretic," which covers Leibniz' interrelationship with Spinoza and the two books fit nicely together. It is clear from Bardi's book that there are many more wonderful possibilities out there many of which have been available for years - a book relating Huygens and Leibniz for example. Perhaps this is one of the most wonderful aspects of a book like this. It points to many sources to explore if one is interested in following up. This book clearly details how the situation got so mixed up and why it will forever remain an embarrassment to those who value the advance of reason and wish human frailties would not create so many bumps on the path. I did not check these reviews before picking up the book and (not plagiarizing them but independently noting them myself!) found the sheer number of editorial mistakes annoying. One wants to send it back to have it corrected out of habit. These are the sorts of mistakes Word doesn't let happen. I bet I could not even reproduce many of them here without Word automatically correcting them. But I agree this seems to be the editors fault not Bardi's since even if they were Bardi's the editor should have easily caught them. But I myself have seen multiple errors magically appear in a published text that were not there in the original. Perhaps the paperback is corrected? I did not see any mention of this on Bardi's web page either. But I have a major point to question concerning Bardi's view that Leibniz's vortex argument has been disposed of by Newton's gravity. Would not Einstein's view of the curvature of space achieve essentially the same explanation of Leibniz'? in short, though the short history following the controversy seemed to make Newton's position on gravity the winner (not as an explanation of movements) hasn't more recent history at least shown both theories useful for different purposes and therefore both correct in context? Perhaps my understanding of this issue is wrong? After all, in the short introduction to the Principia in "On the Shoulders of Giants" edited with commentary by Stephen Hawking he seems to suggest the same thing. What gives? What happened to Relativity?

Great insights *****

I really enjoyed this book and found it offered a great many wonderful tidbits to fill in my understanding of the issues. My most recent previous reading on Leibniz was the wonderful book "The Courtier and the Heretic," which covers Leibniz' interrelationship with Spinoza and the two books fit nicely together. It is clear from Bardi's book that there are many more wonderful possibilities out there many of which have been available for years - a book relating Huygens and Leibniz for example. Perhaps this is one of the most wonderful aspects of a book like this. It points to many sources to explore if one is interested in following up. This book clearly details how the situation got so mixed up and why it will forever remain an embarrassment to those who value the advance of reason and wish human frailties would not create so many bumps on the path.

I did not check these reviews before picking up the book and (not plagiarizing them but independently noting them myself!) found the sheer number of editorial mistakes annoying. One wants to send it back to have it corrected out of habit. These are the sorts of mistakes Word doesn't let happen. I bet I could not even reproduce many of them here without Word automatically correcting them. But I agree this seems to be the editors fault not Bardi's since even if they were Bardi's the editor should have easily caught them. But I myself have seen multiple errors magically appear in a published text that were not there in the original. Perhaps the paperback is corrected? I did not see any mention of this on Bardi's web page either.

But I have a major point to question concerning Bardi's view that Leibniz's vortex argument has been disposed of by Newton's gravity. Would not Einstein's view of the curvature of space achieve essentially the same explanation of Leibniz'? in short, though the short history following the controversy seemed to make Newton's position on gravity the winner (not as an explanation of movements) hasn't more recent history at least shown both theories useful for different purposes and therefore both correct in context?

Perhaps my understanding of this issue is wrong? After all, in the short introduction to the Principia in "On the Shoulders of Giants" edited with commentary by Stephen Hawking he seems to suggest the same thing. What gives? What happened to Relativity?

This is a good read! ****
I thorougly enjoyed this book. I was not aware of the history of Newton and Leibnitz, and so this was a new subject for me. I really feel that in history classes we should read books like this, because it really opens up mathematics. I am going for phD later this year, and so I am starting to review my mathematics textbooks, such as discrete mathematics and calculus. Reading about the extraordinary men that created calculus and battled over it, made calculus seem to me like a living thing, and actually I am looking forward to reviewing my calculus textbook! On the other hand, if you aren't a science geek, this book is still a good read, because it also gives us psychological insights into two brilliant men and the time period in which they lived.

This is a good read! ****

I thorougly enjoyed this book. I was not aware of the history of Newton and Leibnitz, and so this was a new subject for me. I really feel that in history classes we should read books like this, because it really opens up mathematics. I am going for phD later this year, and so I am starting to review my mathematics textbooks, such as discrete mathematics and calculus. Reading about the extraordinary men that created calculus and battled over it, made calculus seem to me like a living thing, and actually I am looking forward to reviewing my calculus
textbook! On the other hand, if you aren't a science geek, this book is still a good read, because it also gives us psychological insights into two brilliant men and the time period in which they lived.

Needs an editor **
Bardi writes in a wildly variable style which is infuriating to the discerning reader. There are occasional typographical errors, frequent grammatical solecisms (split infinitives aren't always wrong, but they are here!), the use of ?! and frequent unnecessary references to the author himself eg p29 "I saw a copy of this notebook on display..." followed by an account of the reactions of a woman and her son. He refers to France anachronistically as a "superpower", and refers to "the Brits" in what is an unforgivable colloquiallism and another anachronism, as Britain did not exist at the time writing as anything other than a geographical entity. There is also lots of flabby repetition. No doubt a good book is to be made of this subject, (probably by Lisa Jardine) but this certainly isn't it.

Needs an editor **

Bardi writes in a wildly variable style which is infuriating to the discerning reader. There are occasional typographical errors, frequent grammatical solecisms (split infinitives aren't always wrong, but they are here!), the use of ?! and frequent unnecessary references to the author himself eg p29 "I saw a copy of this notebook on display..." followed by an account of the reactions of a woman and her son. He refers to France anachronistically as a "superpower", and refers to "the Brits" in what is an unforgivable colloquiallism and another anachronism, as Britain did not exist at the time writing as anything other than a geographical entity. There is also lots of flabby repetition. No doubt a good book is to be made of this subject, (probably by Lisa Jardine) but this certainly isn't it.

What's It All About? *
It's difficult to work out who would benefit from this book or even who would want to read it. If you know nothing at all about the calculus - a branch of mathematics which seems almost magical - you will wonder what all the fuss is about as there is hardly any real information on the importance of this subject; if you do have a knowledge of the subject, then you will be very dissappointed as the mathematical contents is virtually nil - an appendix, at least, would have been useful. There are many interesting historical anecdotes, although they are often not related to the central subject, but many bad errors; for example James ll is described as Charles ll's son and Henry Vlll is said to have been buried in Westminster Abbey. There is a dreadfully bad picture of what is said to be the front of this building and which is actually the west transept anyway.

What's It All About? *

It's difficult to work out who would benefit from this book or even who would want to read it. If you know nothing at all about the calculus - a branch of mathematics which seems almost magical - you will wonder what all the fuss is about as there is hardly any real information on the importance of this subject; if you do have a knowledge of the subject, then you will be very dissappointed as the mathematical contents is virtually nil - an appendix, at least, would have been useful. There are many interesting historical anecdotes, although they are often not related to the central subject, but many bad errors; for example James ll is described as Charles ll's son and Henry Vlll is said to have been buried in Westminster Abbey. There is a dreadfully bad picture of what is said to be the front of this building and which is actually the west transept anyway.

interesting but woefully edited ***
In places very interesting re the clash of these two giants and I learnt a lot more details about their dispute. However, my enjoyment of the book was spoiled by the unbelievable number of typos and IMO the very poor grammatical quality of the writing. The book is crying out for editing by a competent proof-reader and literate editor.

interesting but woefully edited ***

In places very interesting re the clash of these two giants and I learnt a lot more details about their dispute. However, my enjoyment of the book was spoiled by the unbelievable number of typos and IMO the very poor grammatical quality of the writing. The book is crying out for editing by a competent proof-reader and literate editor.