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Infinite Powers: How Calculus Reveals the Secrets of the Universe Paperback – April 14, 2020

4.7 out of 5 stars 2,355 ratings

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From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better. 
 
Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.

As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew. 

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A New York Times Bestseller Featured on NPR's Science Friday Shortlisted for the 2019 Royal Society Science Book Prize Named one of 10 Best Books to Read this Spring by Amazon's Chris Schluep “Marvelous . . . an array of witty and astonishing stories . . . to illuminate how calculus has helped bring into being our contemporary world and so many of the instruments whose role we now blithely assume.” —The Washington Post “Fortunately, we live in an era when a top mathematician can write a book about calculus that is accessible to the mathematically challenged...it is the historical detail in the book that not only allows me to follow the math by taking me through how it was discovered, but also sticks in my mind. [Strogatz] makes me want to get out a textbook and start studying calculus.” —Five Books “Wonderful . . . bringing the insights of calculusamong the most important of all developments in the history of mathematicsto everyone.” —Brian Greene, on Twitter “I've never read a clearer explanation of calculus or the significant powers we gained by harnessing infinity. Michael and I highly recommend it!” —Vsauce, on Twitter “Fascinating anecdotes abound in Infinite Powers . . . Strogatz uses the right amount of technical detail to convey complex concepts with clarity . . . evocatively conveys how calculus illuminates the patterns of the Universe, large and small.” Nature “A brilliant, appealing explanation of how calculus works and why it makes our lives so much better.” —Amazon's Chris Schluep, for the Saturday Evening Post “Strogatz does a great job of explaining a difficult subject . . . he lays out the case that calculus is fundamental to the way we live today . . . a solid choice for readers who want to know what calculus is all about, and for teachers who wish to improve their presentation.”  Library Journal “An energetic effort that successfully communicates the author’s love of mathematics.” Kirkus Reviews “Far-ranging survey . . . clear and accessible . . . Strogatz successfully illuminates a notoriously complex topic and this work should enhance appreciation for the history behind its innovations." Publishers Weekly “A tale of how mathematics has changed all of our lives… Strogatz is a terrific storyteller and patient teacher…. By bringing infinity down to earth… and coupling those stories with some periodic excursions back out to the stars, Infinite Powers does a marvelous job of bringing calculus to life.” —Dan Rockmore, LitHub “Are you one of those people who always said you’d someday learn calculus? Well, someday is here, thanks to Steven Strogatz’s wide-ranging, humane, thoroughly readable take on one of the greatest ideas our species has ever produced.” —Jordan Ellenberg, author of How Not to Be Wrong   “This is a glorious book. Steven Strogatz manages to unmask the true hidden wonder and delightful simplicity of calculus. Infinite Powers is a master class in accessible math writing and a perfect read for anyone who feels like they never quite understood what all the fuss was about. It had me leaping for joy.”  —

About the Author

STEVEN STROGATZ is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday. He is the author of Sync and The Joy of x. He lives in Ithaca, New York.
 

Product details

  • Publisher ‏ : ‎ Mariner Books; Reprint edition (April 14, 2020)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 400 pages
  • ISBN-10 ‏ : ‎ 0358299284
  • ISBN-13 ‏ : ‎ 978-0358299288
  • Item Weight ‏ : ‎ 2.31 pounds
  • Dimensions ‏ : ‎ 5.25 x 1.25 x 8 inches
  • Customer Reviews:
    4.7 out of 5 stars 2,355 ratings

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Steven H. Strogatz
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STEVEN STROGATZ is the Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday. He lives in Ithaca, New York.

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4.7 out of 5 stars
2,355 global ratings

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Customers say

Customers find the book an utterly fascinating read with excellent information, particularly appreciating its nice overview of how calculus has been applied. Moreover, the book provides a detailed history of the subject and outstanding explanations of simple concepts, making it a must-read for those interested in the topic. Additionally, the storytelling receives positive feedback, with one customer noting its engaging narrative structure.

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131 customers mention "Readability"123 positive8 negative

Customers find the book highly readable, describing it as an utterly fascinating and insightful read that goes beyond being educational, providing excellent information.

"...how humanity discovered this strange language, how they learned to speak it fluently and finally harnessing its forecasting powers, how they used it..." Read more

"...an enjoyable book, beyond the fact that I am simply stimulated by really enthusiastic people and Professor Strogatz is one of the most enthusiastic..." Read more

"...There are some interesting basics of the relationship of logarithms to exponents...." Read more

"This may well be the best, most captivating book I have ever read...." Read more

115 customers mention "Calculus"108 positive7 negative

Customers appreciate the book's approach to calculus, particularly its nice overview of applications and detailed history, with outstanding explanations of simple concepts and key contributors to its evolution.

"...First, he shows that calculus is one of humankind's most inspiring collective achievements, roots going back to Archimedes, even Zeno, to the..." Read more

"A great dive into the history and application of Calculus. You do not need to be a mathematician in order to understand the material covered...." Read more

"...Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols...." Read more

"...Here you’ll discover a decent definition of e, an intuitive explanation of general relativity, the common cause of death of Leibniz and Newton, a..." Read more

6 customers mention "Idea of infinite powers"6 positive0 negative

Customers find the book's exploration of infinitesimals intriguing and consider it a must-read.

"...One of the first things introduced is the “infinity principle,” where things are broken down into infinite simpler parts, analyzed, and then added..." Read more

"...Really enjoyed the first three chapters on the history and idea of infinitesimals...." Read more

"...Infinite Powers is a must read if you like history or math. The book is even better if you like history and math." Read more

"...I found the idea of infinitesimals intriguing...." Read more

6 customers mention "Story telling"6 positive0 negative

Customers appreciate the storytelling in the book, with one review highlighting its engaging narrative and another noting its well-structured plot.

"...Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols...." Read more

"...more than a series of mini-portraits of mathematicians, it’s almost got a plot...." Read more

"...to explain everything with the help of pictures, metaphors, and anecdotes...." Read more

"...discipline that the world depends on, he also makes that story deeply interesting on both a human as well as an abstract level in a remarkably..." Read more

Calculus--The big ideas behind it and how to think about it.
5 out of 5 stars
Calculus--The big ideas behind it and how to think about it.
This book is a great primer for calculus. Most classes teach calculus algebraically, all symbols, no meaning. Infinite powers guides the reader through the development of algebra and its relation to geometry, and provides the why and how of how we got to calculus. With this methodology (and some light proofs) Strogatz is able to guide the reader into asking questions, and seeing the limitations of the math developed by calculus' founding fathers. This is followed by a solid introduction to calculus itself in the time of Newton and Leibniz. Before you know it, you too will have a chill run down your spine as you slowly look up from the book and realize that you understand the meaning of a derivative, not just how to find one.
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Top reviews from the United States

  • Reviewed in the United States on July 11, 2024
    Prof. R. Feynman, after an interview with a novelist who was doing research for a book about WW. II, as they were departing, asked him if he knew calculus. No, was the reply, he didn't. ''You had better learn it'' said Feynman. ''It's the language God talks''.
    Mr. Strogatz starts the Introduction part of his wonderful book by telling this anecdote. He continues, ''For reasons no body understands, the universe is deeply mathematical. May be God made it that way. Or maybe it's the only way a universe with us in it could be, because non-mathematical universes can't harbor life intelligent enough to ask the question. In any case, it's a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations.''
    ''Such equations describe the difference between something right now and the same thing an instant later. The details differ depending on what part of nature we are talking about, but the structure of the laws is always the same... There seems to be something like a code to the universe, an operating system... Calculus taps into this order and express it.''
    ''Isaac Newton was the first to glimpse this secret of the universe... If anything deserves to be called the secret of the universe, calculus is it.''
    Mr. Strogatz tells the story behind how humanity discovered this strange language, how they learned to speak it fluently and finally harnessing its forecasting powers, how they used it to remake the world.
    He has written this book 'in an attempt to make the greatest ideas and stories of calculus accessible to everyone'. I can say that he has greatly achieved this.
    First, he shows that calculus is one of humankind's most inspiring collective achievements, roots going back to Archimedes, even Zeno, to the concept of infinity. He tells the development of ideas in a comfortable, casual way, demanding only average mathematical knowledge. He gives examples of applications from our time, which is familiar to most of us. He has furnished his story with very informative drawings.
    What is very important is that, he tries to navigate the reader within the story of development of calculus in the historical, natural order of the development, which makes it much easier for the reader to grasp the ideas. He has added some wise, sense of humor here and there which makes the reading easy and fun. The rich bibliography at the end is very useful. I was able to meet another wonderful book 'The Calculus Gallery' of William Dunham from within that bibliography.
    I loved the book. No wonder it was a bestseller. I highly recommend this book to everyone who is or was scared of calculus and who wants to approach to understanding 'the language of God.'
    12 people found this helpful
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  • Reviewed in the United States on March 31, 2025
    A great dive into the history and application of Calculus. You do not need to be a mathematician in order to understand the material covered. I highly recommend this book if you are interested in the history of Calculus.
  • Reviewed in the United States on October 20, 2019
    This is not intended to be a textbook on calculus. And, like a lot of calculus itself, it is and it isn’t - quite. It is, however, a book about the history of calculus, which is fascinating, and the degree to which the universe seems to have been coded in a way that calculus seems to have an uncanny ability to explain is, well, somewhat inexplicable.

    But as the author notes in the beginning, “For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be, because nonmathematical universes can’t harbor life intelligent enough to ask the question.” How often do you hear a Professor of Applied Mathematics, at an Ivy League school no less, say something even remotely so self-reflective?

    Steven Strogatz is a great communicator who is both a great mathematician and who, it is easy to tell, gets goose bumps every time he thinks about the wonders of calculus. I am not a professional mathematician but have always found mathematics to be both fascinating and, well, not easy, but very relatable. It’s predictable, and that’s comforting once you can see the pattern.

    If you don’t feel quite that way you may – spoiler alert – find this book to be a bit more like a textbook than advertised. There are plenty of equations and symbols and the like. That is, after all, the alphabet of calculus. But here’s the thing. Unless you are also a math professor, you can ignore all of that. Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols. If you do you will miss nothing and you will find the professor’s enthusiasm to be quite contagious.

    The beauty of the book is that it is written from a perspective of humility. Both in terms of the enormity of calculus (Most people will relate to the subject matter simply as science.), and in terms of how far we have yet to go in terms of truly understanding the universe and the reality that defines it. We’ve only explained the tip of the iceberg.

    Math is a human convention. It’s not hydrogen or oxygen. It’s not even dark matter, which we “know” makes up most of the universe but which no one has ever isolated, although the Chinese are close. It is very accurate at deciphering reality if getting close to the “real” explanation is close enough. But close is only close. It isn’t reality itself. Reality is, after all, by definition, real.

    That is, ultimately, the problem with the promise of AI. Because AI is ultimately dependent on calculus and other disciplines of mathematics, it will get very smart, but it will never be human. What it will do, however, if we let it, is dumb down what it means to be smart to a standard perfectly suited to its abilities but ignorant of its shortcomings.

    That’s why, despite the promises of the silicon gods, we are very unlikely to see fully autonomous vehicles for decades to come. The only way that could happen is if we take all human drivers off the road overnight (The AI isn’t the problem; it’s us. We are unpredictable.), switch every vehicle to an autonomous vehicle all at the same time, and rebuild our infrastructure to accommodate the vulnerabilities of the various disciplines of mathematics on which the technology is based. And that’s obviously not going to happen. Nor do we want it to.

    Pi, as but one example, despite what you were taught in school, is not a number; it’s a range. It’s a small range, to be sure, but it’s a range nonetheless. In other words, it is precise enough for most things, but it is NOT the fabric of the universe.

    Science is a methodology for understanding reality; it is not, in the most literal sense, reality itself. Reality is not “waiting” to be discovered. It is. And just as an artist can draw a landscape, science can draw reality. Neither, however, IS reality.

    The history of calculus is truly fascinating. And that, to me, as a reader, makes it entertaining. Newton and Galileo and all the rest were truly amazing people. It boggles the mind to think of what they concluded when they did.

    Perhaps the book’s greatest contribution, however, is that it will put Silicon Valley in perspective. You may think your smart phone has changed your life in ways that nothing else possibly could. You’re wrong. I am a great admirer of Steve Jobs but James Clerk Maxwell (a Scot in the 1860s) changed your life in ways that Steve did not come close to.

    And that is why this book is so timely. Calculus is changing our world, and not entirely in good ways. If ever we needed perspective we need it now. Math is elegant. It was designed that way. (Remember that it is not of the universe, like rain or sunshine.) And it does have an uncanny reliability that helps us to understand the world around us.

    Take GPS. We all use it. We all rely on it. But did you know that GPS is all about time, not navigation. Those GPS satellites don’t “see” you; they time you. It only works because scientists came to understand the mathematics of what we call time at a very precise level. That’s not reality, of course, because time is a concept (time, even as we understand it, varies with altitude), but it is close enough to give us GPS. And isn’t that an amazing thing.

    I think so. And that’s why I found this to be such an enjoyable book, beyond the fact that I am simply stimulated by really enthusiastic people and Professor Strogatz is one of the most enthusiastic people I have had the privilege to read in a really long time.

    If, on the other hand, you prefer a good murder mystery, or something with a little romance, at least, you won’t find it in this book. But that’s just my opinion. A little like pi, if you will. Pretty accurate, but not reality itself.

    Decide for yourself. You won’t be wasting your time.
    66 people found this helpful
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Top reviews from other countries

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  • PumpkinPieLatte
    5.0 out of 5 stars Love the book
    Reviewed in Canada on February 22, 2025
    Love the topic. Request to the author, for future work:
    - more math
    - better print
  • ADELMAR DE M TORRES
    5.0 out of 5 stars Importance of knowing the value of infinite's conception
    Reviewed in Brazil on July 25, 2020
    It is a delicious narrative about the origin of calculus and its importance in our daily life. It is a great book for those not familiar with mathematics.
  • Roger
    5.0 out of 5 stars Entender la parte fina del cálculo Diferencial Integral
    Reviewed in Mexico on January 2, 2020
    Me gusta mucho el enfoque del libro donde se tratan los aspectos del cálculo a partir del concepto matemático del infinito, de una manera amena y hasta divertida. Creo que para personas que desean consolidar sus conocimientos en el tema puede ser muy útil, también a los docentes de nivel medio y superior les puede ayudar a dar enfoques más interesantes a sus clases. No soy hablante nativo del inglés, por lo que tuve que recurrir continuamente al diccionario, me parece que al autor le gusta utilizar un inglés elegante con términos no muy frecuentes. Eso puede ser un plus lingüístico, aunque puede hacer perder la continuidad en la lectura. Vale la pena de todas maneras. Muy recomendable
    One person found this helpful
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  • ALAIN DUENKY
    5.0 out of 5 stars Just great, fun like a novel, insightful like a math book
    Reviewed in Germany on April 13, 2025
    Just great, fun like a novel, insightful like a math book.
  • Amazon Customer
    5.0 out of 5 stars A gem
    Reviewed in the United Kingdom on June 10, 2019
    This book is much more than just a history of a branch of mathematics. It's a framework for thinking about calculus. I was mind blown at how Strogatz explains calculus; like I had been blind all those years and now I saw. His 'breaking down and reassembling' analogy may not be the best explanation to the more mathematically inclined, but to me it made perfect sense, at last. This book provided me with a mind model to think about calculus. A gem.

    "To shed light on any continuous shape, object, motion, process, or phenomenon - no matter how wild and complicated it may appear - reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole."
    2 people found this helpful
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