The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time

by Jason Socrates Bardi

"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 sowed 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. 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 history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

Genres: Mathematics, History, Science, Nonfiction, Biography, History Of Science, Physics

304 pages, Paperback

First published January 1, 2006

Reviews

[Valerie · Rating 5 out of 5]

I found this book fascinating and funny. But I couldn't really explain the dry humor. But 2 grown men hiding Calculus from each other and accusing each other of stealing it...priceless. As far as my students are concerned, they both could have kept it to themselves.

[Jason Miller · Rating 4 out of 5]

I picked this book up impulsively, rationalizing the purchase using my profession (mathematics educator) and a curiosity about the conflict described in the book. When I teach courses related to the Calculus, I often remark on the 'discovery' of the Calculus and the conflict between Newton and Leibniz. What little I know about the conflict came from some histories of mathematics by Boyer which treated the conflict comparatively lightly. This book wades deep enough into the nitty-gritty of the parallel discoveries of the Calculus to satisfy my 'academic' interest in the event, but it is written in an enjoyable narrative style. I feel like I understand the two main characters (including their flaws) well enough to frame the conflict more honestly for my future students.

[Scott · Rating 2 out of 5]

The content of this book, insofar as it actually talked about the invention of calculus, cultivated, for me, a profound respect for the genius of both Newton and Leibniz, respectively.

Still, this is a very sloppy book which would've benefited from some simple editing. I checked it out from the local library and was relieved to find that the person who checked it out before me actually went through with a blue pen and corrected the majority of Bardi's grammatical errors (the Bibliographical Essay, especially, was riddled with them... such that it was distracting).

The book also seemed to lack focus and drifted among a vast array of topics which seemed irrelevant to the essential conflict which Bardi purported to be writing about--the dispute between Leibniz and Newton over the invention rights of calculus. The result was a book which seemed to drag on and on, repeating much of the same information from earlier chapters.

Perhaps obscure anecdotes from history aren't always meant to yield commentaries of almost two-hundred and fifty pages in length...

[Yelena · Rating 4 out of 5]

I knew a little about Newton's miserable childhood before reading this book but had no idea that both Leibniz and Newton were essentially self-taught mathematicians (and neither were stellar students). Although both men had some unsavory tendencies toward egotism, I have to admire both their commitment to their craft as well as the breadths of their curiosity. Newton would stick needles in his eye and stare directly at the sun to explore the effects of light on the eye. Leibniz would sit for days working out problems and correspond with Jesuit priests to learn about the latest happenings in China. Leibniz is also known as "the father of geology" and was one of the first scientists to propose that marine fossils were not sea monsters, but rather extinct species.
This fracas between two geniuses about who "invented" calculus encapsulates for me how late 1600s and early 1700s Europe operated: a mixture of the divine and the mundane, of plagues and printing presses, of intellectual ferment and childish infighting. It gives me hope that in our current era of anti-intellectualism (I am looking at you, anti-vaxxers), something positive can emerge.
P.S. Newton and Lebniz would not have become nearly as well-known and the discoveries of Bernoulli, Fermat, and Faraday would not have occurred as a result were it not for two wildly brilliant princesses: Caroline, princess of Wales, and Sophia Charlotte, who would become queen of Prussia. Sophie is said to have exhausted even Leibniz's intellect by her fierce questions. She was, incidentally, the grandmother of Frederick the Great. I would like to read books on both of these women!

[Leo · Rating 2 out of 5]

This book is written exceptionally poorly. I would not recommend it to anyone interested in learning about the intellectual achievements of either of these mathematicians. It is an over-researched list of unimportant details about their lives and historical context, with no sustained attempt to characterize their way of thinking or seeing the world. Unable to determine what facts would actually help the reader understand these men, JSB just went ahead and included everything. And the whole book is a "lead up" to the "vicious calculus wars," which last all of two chapters before both men die. There is neither petty drama nor intellectual intrigue - nothing but a laundry list of publications where they vagued each other. Disappointing.

[Quin · Rating 3 out of 5]

My teacher: "You have to read the calculus wars."
Me: "Nerds fighting? ...I'll just go watch the Big Bang Theory..."

Jokes aside, the Calculus Wars is actually quite interesting, however the chronology is a bit jumpy and can become hard to follow. On a different note, the book tries very hard to deceive you into believing it is soley about the Calculus Wars, when it is really more of a biographical intersection of the lives of Sir Issac Newton and Gottfried Wilhelm Leibniz. As a reader, if I had already read biographies on both of the men, I don't think I'd waste my time reading this.

[Upom · Rating 1 out of 5]

This was a fairly poor book. The writing style was just droning, and the central event the book builds up to, "the calculus wars", turned out to be just a bunch of back and forth bickering. Furthermore, the book doesn't really talk much about mathematics. Definitely feel there are better books out there concerning the development of calculus.

[Shilpi · Rating 5 out of 5]

Loved this book!

[CraftyCat · Rating 3 out of 5]

Despite being very interested in the subject matter because of my strange love for calculus, I was rather disappointed in this book. It started in the beginning when it became very apparent that the author struggles with prose. The way in which he repeats several sentences and points very early on struck me as reminiscent of one too many high school essays that repeat the central premise four times in their initial paragraph because the subject matter is lacking and must be stretched to meet an unforgiving word count. Some of the reviews I glossed over took issue with this prose as being too “chatty,” but I don’t think that was the real issue at all. The chatty bits seemed to flow better and had less, shall we say, ugly sentence structures than the ones that really seemed to be hammered out with much difficulty.

But probably the biggest disappointment was that the book doesn’t really have much math in it. I thought this observation made me a bit odd, but apparently I’m not the only one who took issue with this point. It does stand to reason that the people who would be most interested in a history of calculus would be mathematicians, physicists, engineers, or students of any of these or related subjects, so I’m not really sure why the text needed to be completely geared towards the layperson. A large part of the reason for why I read these histories is because I’m interested in the evolution of the ideas in them. Science and Math both evolve as subjects, and I find it fascinating to learn about the way the world was viewed by the greatest intellectuals of centuries past. We often assume that they thought much like we do, but that is not really the case.

Still, I feel that the history here is something I am glad to have learned. It did seem that in a few cases the author could have done a bit more research--I recall one paragraph specifically referred to a document written by Leibniz as having apparently well-written, and my first thought was, “you didn’t read it yourself?!?!?” It shouldn’t be that hard to find old texts these days, and if it is I expect it would be noted in the text somewhere as to why.

If you are truly, truly interested in the subject matter here, you may enjoy this book, but ultimately I think the title was misleading (it was, in fact, a very slow and not very confrontational war--more like academic politics, really), and there are better books about calculus out there.

[Eric Abell · Rating 4 out of 5]

Having taught Calculus for seven years now, I continue to be interested in the history and people involved in its development. In my opinion, Calculus is a subject that can be approached in many different ways. From experience, my first impression would be that Calculus provides methods for solving interesting problems. Compute this derivative, or find this integral became the language I used when talking about Calculus.

As I taught the subject, I started to uncover a much deeper understanding. Taking a course in Real Analysis provided the jumpstart into these investigations. My previous language of Calculus as computation began to change into Calculus as the Language of Change. How is the change in one quantity related to change in another quantity? How are derivatives and integrals related? The subject became less about memorized derivatives and integrals and more about understanding what was really happening.

I guess what I'm getting at is this: If you're interested in learning and understanding Calculus, you should not only practice the methods from your textbook but you should also learn about the history of the subject.

Pair this book with Infinitesimal by Alexander and you will be well on your way.

[Pablo · Rating 4 out of 5]

Sobre o livro em si, é em grande medida uma fofoca das antiga, o que achei divertido. Porém, penso sim que há alguns aspectos que valem nota, e vou falar um pouco sobre um deles: o desperdício de tempo e energia ao qual não só os dois se submeteram no embate pela autoria do cálculo como também em suas trajetórias de vida -- embora Newton tenha escolhido mas livremente do que Leibniz.

Estou falando aqui do tempo de Newton à frete da casa da moeda e, mais tarde, pesquisando teolgia e alquimia; e dos empreendimentos de Leibniz na corte de Hanower, principalmente as ambiciosas pesquisa e escrita nunca concluídas da longa história enfadonha de uma família nobre.

Ficou em mim a marca de pelos uma reflexão interessante: será que estamos Newton mestre da casa moeda? Ou Leibniz pesquisando sobre a família Brunswick? Cito aqui o que marca o início do último capítulo deste livro:

"A morte não se preocupa nem com a execução de nossos projetos, nem com o progresso da ciência." (Leibniz).

Por fim, tiro disso tudo a ideia de que a vida é muito curta e nosso tempo é valioso demais para legarmos projetos significantes inacabados porque demos atenção a outros impertinentes. Isso foi o que me tocou no final das contas.

[Chris · Rating 4 out of 5]

Probably would do 3.5 if I could, so I guess I will round up. The book seems well-researched and at times is incredibly interesting. Other times it wanders into long passages about royal lineage and 17th century European politics that, I guess, give context, but it probably could have been more concise. There also is a lot of "Newton wrote a letter this person" and "Leibniz complained to that person." It made the whole story seem like a bunch of whiny people just spreading gossip and pouting to their friends. I guess maybe that is a true characterization of what actually happened. This book was also riddled with grammar and typographical errors like no book I have ever read, and the author's style often borders on distractingly informal. Despite its flaws, I am glad I read it. I already knew a lot of this story, but as a teacher of math it is good to have a deeper understanding of these men, their time, and the circumstances that created this intellectual beef from 300+ years ago

[Dillard · Rating 4 out of 5]

It's kinda peculiar to read this book while I'm having a course um calculus in university, although this course will last like 2 years or so, lol. It was definitely good to see some background on Newton and Leibniz, I think this book did not really teach me anything about calculus that I find to be relevant, but it was good to compare the historical background with my formal studies in mathematics. Leibniz did die in misery, maybe even in regret, but prevailed in history and his notation for Calculus and another discoveries in philosophy survived the test of time. For Newton, although clearly played dirty with Leibniz in the end of his lives, did some important discoveries in physics and mathematics. It was a good historical read.

[Jcaddell · Rating 4 out of 5]

Who knew two mathematicians could have so much beef with each other? This book does a great job of establishing the context with which Newton and Leibniz fought for the ownership of the title of inventor of calculus. It identifies the major events of both Newton's and Leibniz's lives relative to globally as well as locally significant events to give the reader a sense of when this war was happening and why it is so overlooked. It tells a lot about Leibniz because of his very active public presence as opposed to Newton, who stayed cooped up in his lab for most of his life, instilling the conclusion with a bit of a sour sting.

[Dubi Kanengisser · Rating 2 out of 5]

This is a book about calculus that explains virtually nothing about calculus itself or why it's so important. It also isn't a very good historical account, full of what feels more like gossip and conjecture, meandering writing, and mired in grammatical errors that shouldn't have made it past copy editing.
I don't know if there are any better books or there on the subject, but even if there aren't, that's not a good enough reason to read this one. I personally barely managed to trudge through it.

[Qhenn Manns · Rating 3 out of 5]

The general theme was interesting, and I am glad I read it and finished for the story. But ... it was very poorly edited (I even thought it might have been self-published) and, at times, the writing was sophomoric. “... was the Greta Garbo of Europe”. I have no idea what Bardi meant by that. He coined the phrase “The Affair of the Eyebrow”, of which he was unjustly proud, meaning simply someone did something that raised an eyebrow. I doubt there is a better teller of this conflict, but Bardi missed a chance to be a great one.

[Tony Gualtieri · Rating 5 out of 5]

I'm not sure why there is so much criticism of the prose and editing of this book. It's an excellent intellectual history of the era, and while there's no mathematics, it covers the controversy in a reasonable manner for a popular book. I enjoyed the digressions, which are part of the charm of a work like this. Those who want to solely focus on the back and forth between Newton and Leibniz might consider reading the much briefer Wikipedia article. It's all there: Leibniz–Newton calculus controversy

[Pedro Guedes · Rating 5 out of 5]

Durante final do século XVII e início do século XVIII tivemos o embate entre dois Titãs do pensamento humano. Newton e sua forma singular de enxergar o mundo de uma forma tão pragmática e o grande Leibniz um gênio em diversas partes do conhecimento. Uma pena, fico imaginando o poderia ter nascido de uma cooperação dessas grandes mentes que a humanidade jamais produzirá igual.

É um livro super interessante, recomendo muito a leitura !

[Kostas Kiousis · Rating 5 out of 5]

Great book about two masterminds that couldn't tame their egos and acted more like children in the kindergarten about who won the game and gets to be first.
It's sad to find that Newton bellitled himself through childish behavior and malintentend accusations.
Leibniz I didn't know, and though he too fell prey to his ego, I ended up admiring him and wanting to learn more about his vast work.
A beautiful read that keeps your interest undeminished to the end.
The closing line is superb!

[Kristoffer Landes · Rating 3 out of 5]

While the content of The Calculus Wars is indeed quite interesting, the reader's experience is marred by prolific typographical errors that detract from what had the potential to be an informative and thought-provoking read.

[Gazifah Naqshbandi · Rating 5 out of 5]

Although the focus of this book is the rivalry between Newton and Leibniz. But what is a lesson for all young scientists is that even Newton published his main work quite late in his career. He had a propensity for hiding his work and not publishing his ideas until forced by friends or enemies.

[Alfred Timperley · Rating 3 out of 5]

Colored the time, the conflict, and the characters invoked. But the conflict itself is not all that interesting. More interesting is learning how science was done back then and seeing how it has progressed to present day, where a squabble like this would be almost impossible

[Rodanthi Perdikaki · Rating 5 out of 5]

A Must read! Jason Bardi tells a fascinating story of the clash of 2 of the greatest minds of all time.

[Letícia Pagoto · Rating 2 out of 5]

esse é interessante

[Salil Sharma · Rating 4 out of 5]

Due to the lack of sharing of knowledge, these 2 giants were involved in nasty fighting.
Great read though.

[Alberto Tebaldi · Rating 4 out of 5]

a fascinating story on how irrationality can haunt even the best minds, and how society itself encourages it.

[Andre Abukawa · Rating 4 out of 5]

Muito interessante o embate entre 2 gigantes da matemática: Newton e Leibniz. Recomendo.

[Zach LaFond-Hudson · Rating 2 out of 5]

This needed a better editor.

[Evanston Public Library]

My two middle-school kids are learning algebra and geometry, which I discovered I mostly remember. But they’re heading toward calculus, which I discovered I had mostly forgotten. So I started re-educating myself. While getting re-educated I learned the remarkable story behind calculus.

But first: What is calculus? In simple terms, it’s the mathematics of changing values. In less simple terms, it’s the set of tools for calculating “momentary” values like acceleration, deceleration, or slopes of curves (that’s differential calculus), and the related set of tools for calculating “cumulative” values like area, volume, or work (that’s integral calculus).

In metaphorical terms, it’s the song of the universe. I think of algebra as the words, and geometry as the music. Combine them and you get the song: the song of motion, engineering, physics, medicine, statistics, business, computers, even sports—any field in which problems can be mathematically modeled, and in which optimal solutions are desired.

So it matters who invented calculus. Was it the Englishman, Sir Isaac Newton (1642-1727)? Or the German, Gottfried Leibniz (1646-1716)? Probably the best answer is that it was both.

Newton came up with the basics first (building on predecessors’ work, of course—that’s another story). But Leibniz published first, independently, and did more to advance understanding. Neither saw it this way: each felt threatened by the other, perhaps even plagiarized by the other, and they battled bitterly. Their battle held back mathematical progress for decades, separating the English-speaking scientific world from the scientific world of continental Europe.

Ackroyd’s book highlights Newton’s personality, connecting it to his amazing insights not only into calculus, but also into gravitation and optics. It is a delight to read. Each sentence is a springboard for the next, and you gain keen insight into the character of the man voted by many the “scientist of the millennium.” Bardi writes more amateurishly, but explains the calculus battle in rich detail, exploring both Newton’s and Leibniz’s characters and linking them to the complex politics of their era. But if you don’t have the time (or the interest) to spend on a whole book, zero in on chapter three of Hellman—just twenty pages, almost as well-written as Ackroyd. (Jeff B., Reader's Services)

[Stephanie A. Higa · Rating 2 out of 5]

Quick read but boring. This book has too much history and not enough math. If I wanted to learn about scandals that "would make a soap opera-loving housewife blush," I'd watch The Bold and the Beautiful, mmkay. The style, while generally harmless, occasionally goes from professional/historical to personal narrative (i.e. the author injects himself into the story), and the figurative language is also anachronistic, with odd comparisons between Newton and a startup CEO and eBay and...I don't remember.

Some of the content is enlightening. Leibniz displayed a lot of integrity when facing Newton's arsenal of devotees. He did invent calculus independently, and he was, in his own right, a genius. He just wasn't Isaac Newton, and it would be unfortunate for anyone, especially someone who's a genius on his own right, to have to battle it out with this superhuman. Leibniz died after he was basically bullied out of his claim to differential fame. Newton lived to 80, over thirty years longer than Leibniz, after establishing himself as the preeminent inventor of calculus, even though calculus was trivial to him in light of all his other amazing achievements. You'd think he would have given Leibniz some sort of consolation prize for devoting the greater part of his life to calculus and for developing the framework and notation that would enable legions of nongeniuses to get it, generation after generation, but no. Newton couldn't wrap his superhuman mind around the idea that someone else could have come to the same conclusions as he did without his help. Well, I guess it does seem fishy.

Neither of these men married. Newton was gay in a very, very latent way; Leibniz proposed to a woman, but she took too long to respond, and he lost interest. They were brains without bodies. The most evolved type of human? Or freaks of nature? Probably both.