Science

Infinite Powers: The Story of Calculus - The Language of the Universe

Infinite Powers: The Story of Calculus - The Language of the Universe

  • Downloads：9986
  • Type：Epub+TxT+PDF+Mobi
  • Create Date：2021-07-05 08:54:46
  • Update Date：2025-09-06
  • Status：finish
  • Author：Steven Strogatz
  • ISBN：1786492970
  • Environment：PC/Android/iPhone/iPad/Kindle
  • Download

Summary

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 Greec
e 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。

Download

Reviews

Pagan Min ，

Why the hell I was not taught maths in this manner。 （I am engineering student）If you are from science background， you will enjoy the journey。 It will give you story behind how famous equations and formulas are formed，Why some functions are special in nature。 i。e， sine， e^x。If you are not from science background still it is a good read。 Author tried to simplify concepts so it is easily relatable。 There are numerous practical examples which explains that how mathematics is deeply rooted in our day Why the hell I was not taught maths in this manner。 （I am engineering student）If you are from science background， you will enjoy the journey。 It will give you story behind how famous equations and formulas are formed，Why some functions are special in nature。 i。e， sine， e^x。If you are not from science background still it is a good read。 Author tried to simplify concepts so it is easily relatable。 There are numerous practical examples which explains that how mathematics is deeply rooted in our day to day life and technology。 。。。more

Alex Von Lehe ，

An excellent read for anyone who wants to understand why calculus works and get a glimpse into how math is developed。 Anyone， regardless of mathematical experience， can enjoy and learn from this book; all you need is some basic algebra and an open mind。 The 4 stars is because of how and how often the author talks about real world applications （as much as I like math， I do NOT want to read page after page about obscure HIV treatments）。 Regardless， this book is a necessary read。

Matthew Dai ，

I found "Infinite Powers" by Steven Strogatz to be an awe-inspiring work of popular Science。 Strogatz's book enabled me to think deeper about the concepts taught in Calculus lessons at school。 By reading the book， I was able to see how the examples given by the teachers （Brachistocrone problem） related to real-world Physics phenomena such as the refraction of light。 My initial thought about Calculus was it was developed by Newton and Leibniz。 However， reading the book made me realise that the an I found "Infinite Powers" by Steven Strogatz to be an awe-inspiring work of popular Science。 Strogatz's book enabled me to think deeper about the concepts taught in Calculus lessons at school。 By reading the book， I was able to see how the examples given by the teachers （Brachistocrone problem） related to real-world Physics phenomena such as the refraction of light。 My initial thought about Calculus was it was developed by Newton and Leibniz。 However， reading the book made me realise that the ancient Greeks， by developing infinite series， laid the groundwork for modern-day Calculus。 We see infinite Taylor Series being used to approximately model non-polynomial functions， which is extremely useful in Science and Engineering。 Reading the book also made me realise that all mathematics is linked， from Algebra to Trigonometry and Calculus。 Henceforth， knowing pre-Calculus topics well is the key to mastering Calculus。 It is an extremely worthwhile read for anyone who is currently studying mathematics or a Science course in university and anyone who may consider applying for those courses for Undergraduate studies。 。。。more

Alejandro Quiroz ，

Great algebra skills and reading this book are two key variables to understand and love calculus

Sukhman Singh ，

This marvelous book is an introduction to the beauty and power of calculus。 It gives both a historical overview of the development of calculus and describes some of its wonderful applications。 The recurring theme of this book， outlined in the beginning， is the Infinity Principle: To make sense of any continuous shape or process， imagine slicing it up into infinitely many infinitesimal parts， analyze those， and then add them up together again to understand the original whole。 Strogatz gives numer This marvelous book is an introduction to the beauty and power of calculus。 It gives both a historical overview of the development of calculus and describes some of its wonderful applications。 The recurring theme of this book， outlined in the beginning， is the Infinity Principle: To make sense of any continuous shape or process， imagine slicing it up into infinitely many infinitesimal parts， analyze those， and then add them up together again to understand the original whole。 Strogatz gives numerous examples of how the Infinity Principle was applied by mathematicians like Archimedes， who laid the foundations for calculus with his dabblings on finding the area of a circle and of parabolic segments， to Newton and Leibniz themselves。 Along the way， many other figures like Galileo and Kepler are discussed， who paved the way for calculus with their ingenious experiments and laws of planetary motion， respectively。 The reader is mesmerized by the power of calculus as Strogatz presents how it has contributed to modeling HIV concentrations in the human body， understanding aerodynamics via simulations， and probing the mathematics of music， to name a few。 By the end of the book， the reader will be much more appreciative of just how ubiquitously calculus is used， from everyday appliances like the microwave oven to GPS systems。 On a deeper note， Strogratz reflects on how calculus has enhanced our understanding of nature and of ourselves and what that means for the future and potential of us humans。 。。。more

Chris Hendriks ，

Very amusing， I should start with pen， pencil， paper and book …

Nikhil ，

This is one of the best books I have ever read about philosophy of mathematics。If you love Mathematics and admire the way it has changed our world， this is a must read for you。Steven Strogatz not only explains methods used in calculus（pretty rudimentary for those who have studied it） but also the philosophical evolution of the same。 The story of evolution of calculus from Aristotle （abstract conceptualisation） to 21st century （AI based solvers） is fascinating to say the least。

Andrew Alkema ，

This book makes me excited to teach math。 It does an excellent job of doing a recap on the basics of the math behind calculus， but is mostly a celebration of the impact and beauty of calculus。

Meddie Verlaine ，

Brilliant。 Just absolutely brilliant。

Michiel ，

Aan entertaining introduction to the history and applications of calculus。 Strogatz phrases calculus as the careful application of using infinities， from circles to microwave ovens。

Mel Brannen ，

Immensely readable and clearly written。 I’m loving this explanation of Calculus， it’s role in our modern world， it’s history and application。I took calculus 40 years ago， found it very understandable and easy to work with。 Got an A。 BUT I could not tell you until today what it is used for and it’s purpose/importance in our world。 I knew it was important but couldn’t tell you why。 You might find it as enjoyable as I did。

Antidb ，

very intuitive， so many interesting points and fields I found in this book。

Spatula ，

out of the many things this book taught me， the most prominent is that i did not do well in SL Maths Strogatz writes very well， and at points the book flies， but it was hard to wrap my head around some of the more pure maths elements of what he's talking about。 Would absolutely recommend this to anybody interested in maths， and calculus is easily one of the most interesting inventions ever， but im not a maths sorta lad so itll probably hit better to others out of the many things this book taught me， the most prominent is that i did not do well in SL Maths Strogatz writes very well， and at points the book flies， but it was hard to wrap my head around some of the more pure maths elements of what he's talking about。 Would absolutely recommend this to anybody interested in maths， and calculus is easily one of the most interesting inventions ever， but im not a maths sorta lad so itll probably hit better to others 。。。more

Sam ，

A great read about important of Calculus。 Thoroughly enjoyed it！

Donny ，

Great summary of mathematics history。

Serhiy Dzyubin ，

Однозначно варта для прочитання всім。

Restia ，

"Everything becomes simpler at infinity。"Reading two methods book together is intriguing， a conversation emerging between the two; about linear and non-linear systems; reductionism and path dependency。 "Everything becomes simpler at infinity。"Reading two methods book together is intriguing， a conversation emerging between the two; about linear and non-linear systems; reductionism and path dependency。 。。。more

Jagjit Singh ，

Un-put-down-able！ Although I had studied calculus as an undergraduate， this book was engrossing。 I wish it was a pre-req at my university but unfortunately it was not。 I had to pass Calculus as Physics was my major。 This book doesn't contain calculations but an explanation and how Calculus changed mathematics and science。 Feynman quipped to Herman Wouk， "Calculus is the language God talks。" This book goes on to show that！ In a multitude of fields。 I hope you enjoy reading this book as much as I Un-put-down-able！ Although I had studied calculus as an undergraduate， this book was engrossing。 I wish it was a pre-req at my university but unfortunately it was not。 I had to pass Calculus as Physics was my major。 This book doesn't contain calculations but an explanation and how Calculus changed mathematics and science。 Feynman quipped to Herman Wouk， "Calculus is the language God talks。" This book goes on to show that！ In a multitude of fields。 I hope you enjoy reading this book as much as I did， if not more。 。。。more

Javi ，

This book made me go back in time to when I was a teenager （or even a child） that loved learning about numbers。 It made me （once again） feel a sense of wonder and awe at the universe， math， how math are universal and how the universe is mathematic。 （Or how， at the very least， we can pretend it is to about eight decimal places of accuracy。）The book does a fantastic job following the history of calculus （even well before it was called this way） as it relates to the history of humanity itself - it This book made me go back in time to when I was a teenager （or even a child） that loved learning about numbers。 It made me （once again） feel a sense of wonder and awe at the universe， math， how math are universal and how the universe is mathematic。 （Or how， at the very least， we can pretend it is to about eight decimal places of accuracy。）The book does a fantastic job following the history of calculus （even well before it was called this way） as it relates to the history of humanity itself - it also includes many anecdotes and short bits of information about how specific mathematical discoveries and techniques have positively affected a variety of fields from aerospacial enginnering to medicine。 It's a book for the general public so it may not be as worth if you already know a lot about calculus and its history， though I'd still 100% recommend reading the introduction。 Overall 5/5 I loved the book， big thanks to Grant Sanderson （3Blue1Brown） for recommending it in a video。 。。。more

Lars ，

Interesting read about a very dry topicIt is really hard to write about math， but given this circumstance I think the author did a good job with this。 He touches on some particularly elegant/interesting proofs， but most importantly he shows patterns in how math works， mostly what he calls the "Infinity Principle"。 Interesting read about a very dry topicIt is really hard to write about math， but given this circumstance I think the author did a good job with this。 He touches on some particularly elegant/interesting proofs， but most importantly he shows patterns in how math works， mostly what he calls the "Infinity Principle"。 。。。more

Enrique ，

If you studied calculus at the university this book is an excellent refresher。It’s an introduction to the history of calculus。 So you can’t judge this book by its philosophical value because is not the main purpose， and is clear that the author is not interested in such a business。It’s not very smart to say that calculus is a language。 Is not， not even possible to say that。 The very root of the word “language” is the noun “tongue”， what you speak， the talk， the uttered words。 Calculus， and witho If you studied calculus at the university this book is an excellent refresher。It’s an introduction to the history of calculus。 So you can’t judge this book by its philosophical value because is not the main purpose， and is clear that the author is not interested in such a business。It’s not very smart to say that calculus is a language。 Is not， not even possible to say that。 The very root of the word “language” is the noun “tongue”， what you speak， the talk， the uttered words。 Calculus， and without a doubt the nonlinear part， is about things that you don’t have any word to say about that。 Chaos， complexity， fat tails， information， a lot of things that we don’t have a word， and we will not have any “language” to express all the details that we have in front of us。 Calculus wants to have a glimpse， maybe help with a graspable representation， but even the multiple dimensions are imposible to describe， we don’t have not intuitions， not images not words for that。 Calculus help us to walk in these shadows。Excellent book！ 。。。more

Alb85 ，

«L’arte» diceva Picasso， «è una bugia che ci permette di conoscere la verità»。 Si potrebbe dire lo stesso del calcolo infinitesimale come modello della natura。Oltre ad essere un ottimo matematico， Strogatz è anche un ottimo divulgatore。L’autore riesce a rendere appassionante lo studio del calcolo infinitesimale， che lui chiama “il segreto dell’universo”。 Il calcolo infinitesimale si compone di essenzialmente di due processi: -tCalcolo differenziale。 Il processo di scomposizione che richiede semp «L’arte» diceva Picasso， «è una bugia che ci permette di conoscere la verità»。 Si potrebbe dire lo stesso del calcolo infinitesimale come modello della natura。Oltre ad essere un ottimo matematico， Strogatz è anche un ottimo divulgatore。L’autore riesce a rendere appassionante lo studio del calcolo infinitesimale， che lui chiama “il segreto dell’universo”。 Il calcolo infinitesimale si compone di essenzialmente di due processi: -tCalcolo differenziale。 Il processo di scomposizione che richiede sempre una sottrazione infinitamente sottile per quantificare le differenze tra le parti。 -tIl calcolo integrale。 Il processo di riassemblaggio prevede un’addizione infinita， che reintegra le parti nell’insieme iniziale。 Il libro viene diviso in tre argomenti: le curve， il moto e il cambiamento e passa attraverso le scoperte di Archimede， Galileo， Keplero， Cartesio， Fermat， ed in particolare con Newton e Leibniz。"Newton pensava al moto e al flusso， l’aspetto continuo della matematica。 Leibniz vi arrivò dalla parte opposta: pur non essendo un matematico per formazione， da giovane aveva riflettuto per qualche tempo sulla matematica discreta （numeri interi e conteggi， combinazioni e permutazioni， frazioni e somme particolari）。"Dopo aver letto anche l’ottimo La gioia dei numeri: Viaggio nella matematica da uno a infinito di Strogatz， penso leggerò anche Sincronia。 I ritmi della natura， i nostri ritmi。Spunti interessanti:-tÈ inquietante che il calcolo infinitesimale sia in grado di rispecchiare con precisione la natura， se pensiamo a quanto sono diversi questi due ambiti: il calcolo è un regno immaginario di simboli e logica， la natura è un regno reale di forze e fenomeni。 Eppure， in qualche modo， se la traduzione da realtà a simboli avviene correttamente， la logica del calcolo può sfruttare una verità del mondo reale per generarne un’altra: verità in ingresso， verità in uscita。 Si comincia da qualcosa di vero nel mondo empirico， formulato attraverso dei simboli （come fece Maxwell con le leggi di elettricità e magnetismo）， si applicano le giuste manipolazioni logiche e si ottiene un’altra verità empirica， potenzialmente nuova， un fatto dell’universo di cui nessuno era a conoscenza （come l’esistenza delle onde elettromagnetiche）。 È così che il calcolo ci permette di sbirciare nel futuro e di prevedere l’ignoto， ed è questo che lo rende uno strumento potente per la scienza e la tecnologia。-tPer descrivere e ragionare sulle quantità continue， quei matematici capirono che serviva qualcosa di più potente dei numeri interi， così svilupparono un sistema basato sulle figure e sulle loro proporzioni。 Tale sistema era legato alla misurazione di oggetti geometrici: lunghezze di segmenti， aree di quadrati， volumi di cubi; tutti valori a cui diedero il nome di grandezze， che consideravano distinte dai numeri e a essi superiori。 - --- Questo è puro stile greco: tutto è espresso in proporzioni， un’area è rapportata a un’altra area， un volume a un altro volume。-tCome ci insegna il principio dell’infinito， il rettilineo e il frastagliato possono imitare il curvo e il liscio。-ttutte le equazioni legate a termini di secondo grado in x e y （senza potenze superiori） possono dare solo quattro tipi di curve: parabole， ellissi， iperboli e cerchi。-tParole troppo simili per le potenze del dieci possono risultare fuorvianti。 Durante la campagna presidenziale del 2016 negli Stati Uniti， il senatore Bernie Sanders si è scagliato spesso contro le esorbitanti agevolazioni fiscali previste per millionaires e billionaires （“milionari e miliardari”）。 Al di là delle opinioni politiche di ciascuno di noi， Sanders dava l’impressione che in termini di benessere economico milionari e miliardari fossero equiparabili。 In realtà i miliardari sono molto， molto più ricchi dei milionari: per farvi un’idea della differenza tra un milione e un miliardo， pensate che un milione di secondi equivale a poco meno di due settimane， e un miliardo di secondi a circa trentatré anni。 Il primo è la durata di una vacanza， il secondo è una porzione significativa della vita di una persona。-tIl modo in cui percepiamo i toni， per esempio， è approssimativamente logaritmico: quando una nota musicale sale di un’ottava， da un do all’altro， l’aumento corrisponde a raddoppiamenti successivi della frequenza dell’onda sonora associata。 Eppure， anche se le onde oscillano con velocità doppia per ogni aumento di ottava， percepiamo questi raddoppiamenti （che sono cambiamenti moltiplicativi della frequenza） come salti uguali di tono， ovvero salti additivi。 È strano: la nostra mente ci confonde facendoci credere che la distanza fra 1 e 2 sia la stessa che intercorre fra 2 e 4， 4 e 8 e così via。 Per qualche motivo percepiamo la frequenza in modo logaritmico。-tRicorderete che per trovare π abbiamo dovuto calcolare il perimetro di un poligono a molti lati inscritto in un cerchio， in modo da approssimarlo man mano che il numero di lati n si avvicinava all’infinito e la lunghezza dei lati a zero。 In modo analogo， il numero e è definito come un limite， con l’unica differenza che nasce da un altro contesto， quello della crescita composta continua。-tper stimare il tempo necessario a raddoppiare una somma di denaro sottoposta a un certo tasso di rendimento annuale， basta dividere 72 per il tasso di rendimento。 Quindi， se per esempio la somma aumenta con un tasso annuo del 6 per cento， raddoppierà dopo 72/6 = 12 anni。 Questa regola deriva dalle proprietà del logaritmo naturale e della crescita esponenziale， e funziona bene con tassi di interesse piccoli。-tLe derivate descrivono i tassi di cambiamento。 Gli integrali descrivono l’accumularsi del cambiamento。 Le derivate rispondono a problemi su un cambiamento di variabile dipendente diviso per un cambiamento di variabile indipendente。 In simboli， il tasso di cambiamento prende sempre la forma Δy/Δx （un cambiamento di y diviso per un cambiamento di x）。-tLa pendenza， insomma， è una sorta di tasso universale: poiché qualsiasi funzione di una variabile può sempre essere rappresentata come una curva nel piano xy， si può ottenere il suo tasso di cambiamento calcolando la pendenza del suo grafico。-tPer una crudele ironia della sorte， sia Newton sia Leibniz， i pionieri del calcolo infinitesimale， morirono tra dolori atroci per colpa di calcoli: della vescica Newton， renali Leibniz。-tcome l’accelerazione è il tasso di cambiamento della velocità， così la velocità è il tasso di cambiamento della distanza。-tLe derivate suggerivano quindi un legame tra pendenza e velocità， e più in generale tra geometria e moto。-tRisolvere il problema all’indietro aveva implicazioni anche maggiori: da un punto di vista archimedeo， un’area è una somma infinita di strisce rettangolari infinitesime， e come tale è un integrale， una raccolta integrata di tutti i pezzi riassemblati， accumulo di un cambiamento infinitesimo。 Come le derivate sono più importanti delle pendenze， così gli integrali sono più importanti delle aree: l’area è cruciale per la geometria， gli integrali sono cruciali per tutto，-tDa un punto di vista moderno， il problema dell’area si occupa di prevedere il rapporto tra un qualcosa che varia con tasso variabile e il suo accumulo nel tempo: il flusso variabile di un conto in banca e quanto denaro accumula; il tasso di crescita della popolazione mondiale e il numero netto di persone sul pianeta; la concentrazione variabile di un farmaco chemioterapico nel sangue di un paziente e l’aumento dell’esposizione a questo farmaco nel tempo （l’esposizione totale influisce sul potere della chemioterapia， ma anche sulla sua tossicità）。 L’area è importante perché il futuro è importante。-tLa differenziazione è un’operazione locale。-tL’integrazione è un’operazione globale。 Invece di un microscopio utilizziamo un telescopio， e cerchiamo di scrutare a grande distanza， nello spazio o nel tempo （anche se in questo secondo caso avremmo bisogno di una sfera di cristallo）。-tDubito che Newton ne fosse consapevole， ma con il suo lavoro sulle serie di potenze si comportò come un artista del mash-up: affrontò il problema geometrico dell’area con il principio dell’infinito degli antichi greci， e lo alimentò con decimali indiani， algebra islamica e geometria analitica francese。-tun’equazione differenziale ordinaria descrive la variazione infinitesima di qualcosa （la posizione di un pianeta， la concentrazione di un virus） come conseguenza della variazione infinitesima di qualcos’altro （per esempio， un incremento di tempo）。-tLe equazioni differenziali parziali sono molto più ricche di quelle ordinarie: descrivono sistemi continui che si spostano e cambiano simultaneamente nello spazio e nel tempo， o in due o più dimensioni dello spazio。-tLa forza unificante dell’idea di Fourier è che si può sintetizzare il suono di qualsiasi strumento musicale con una schiera infinita di diapason: basta colpirli con la giusta intensità e al momento giusto， e incredibilmente si ottiene il suono di un violino o di un pianoforte， ma anche di una tromba o di un oboe， pur usando nient’altro che onde sinusoidali incolori。 Questo， in sostanza， era il meccanismo dei primi sintetizzatori elettronici: riproducevano il suono di qualsiasi strumento combinando un gran numero di onde sinusoidali。-tla derivata di un’onda sinusoidale è un’altra onda sinusoidale anticipata di un quarto di ciclo。 Questa è una proprietà notevole， che non vale per altri tipi di onde。-tnella legge del moto di Newton， F = ma， l’accelerazione a comporta due derivate， perché è la derivata della velocità， e la velocità è a sua volta la derivata della distanza; l’accelerazione è quindi la derivata della derivata della distanza， o， per dirla in modo più conciso， è la derivata seconda della distanza。 Le derivate seconde si incontrano dappertutto in fisica e in ingegneria。 Oltre all’equazione di Newton， sono protagoniste delle equazioni del calore e delle onde。-tÈ possibile fare previsioni perfette sui sistemi caotici fino a un tempo noto come orizzonte di prevedibilità11。 Prima di questo valore il determinismo del sistema lo rende prevedibile。-tL’aspetto positivo è che anche all’interno dei sistemi caotici esistono vestigia di ordine， per via del loro carattere deterministico。 。。。more

Manikanta Avinash ，

I heard great things about this book and it lives up to all the great reviews。 The author is really the best writer among mathematicians and the best mathematician among writers as one of the sayings on the blurb goes。 The author explains calculus in the best possible way to a beginner and even people with science background and who knows calculus can still enjoy a lot learning the history and evolution of calculus which is generally not taught to us。 I felt the author went a little over board s I heard great things about this book and it lives up to all the great reviews。 The author is really the best writer among mathematicians and the best mathematician among writers as one of the sayings on the blurb goes。 The author explains calculus in the best possible way to a beginner and even people with science background and who knows calculus can still enjoy a lot learning the history and evolution of calculus which is generally not taught to us。 I felt the author went a little over board sometimes giving credit to calculus for some of the breakthroughs but he also acknowledges it and understandable given how much he seems to love calculus。。。 This is a must read for every Maths enthusiast just to appreciate the evolution and the beauty of calculus 。。。more

Tamra Stanley ，

I really liked this book。 It is a bit long but it is interesting。 The background on how things developed and how calculus has impacted the world is shared in a more simple language。 I do have a math background， so I could be wrong but I felt it would be understood by a non-math person。

Suzanne ，

I'm not done yet！ Every time I read a few more pages I'm surprised how much I enjoy， learn， and look at things - Toy Story， squares， and rectangles in a different light。 I get the simple edge but I know there is deeper， richer space explained。 I'm not done yet！ Every time I read a few more pages I'm surprised how much I enjoy， learn， and look at things - Toy Story， squares， and rectangles in a different light。 I get the simple edge but I know there is deeper， richer space explained。 。。。more

Jorien ，

If you ever had proper calculus classes at uni， this book is a lot of things you already know。 If you never understood anything about maths， this may be a book for you。 It does a good job explanation how calculus works。 And the arch of the story is good。 However it felt like it starting rambling for the last third of the book。 All in all I think the author did a good job in explaining calculus。

Anahita ，

Deep Thought was on the right track indeed。 （this reference to The Hitchhiker's Guide To The Galaxy had me pleasantly surprised :）This book takes us on a tour through calculus— origins， development， and usage in the real world（which are just too many）。 And God was it interesting。 We study things， ideas in textbooks， never realising anything about the work and thoughts that the hundreds of people in history put in， coming up with those ideas。 I'll recommend this to everyone interested in working Deep Thought was on the right track indeed。 （this reference to The Hitchhiker's Guide To The Galaxy had me pleasantly surprised :）This book takes us on a tour through calculus— origins， development， and usage in the real world（which are just too many）。 And God was it interesting。 We study things， ideas in textbooks， never realising anything about the work and thoughts that the hundreds of people in history put in， coming up with those ideas。 I'll recommend this to everyone interested in working of Mathematics。 It will develop a lot of insight in calculus。 It sure helps a lot when in Physics or Maths class I do differentiation or integration and I know exactly what I'm doing and why。 。。。more

Ману ，

A really wonderful read for someone outside of mathematics who wants to connect the theory to the practice。 This book does both， and does it well in an “intuitive” sense as Morris Kline once wrote。 The examples are visual， logical， theoretical， and empirical。 The author’s repeated appeal to the concept of the infinitesimal is helpful to make sense of many things outside the realm of mathematics。 To me， it helps me understand why Hegel， who was mostly opposed to mathematics as a tool to understan A really wonderful read for someone outside of mathematics who wants to connect the theory to the practice。 This book does both， and does it well in an “intuitive” sense as Morris Kline once wrote。 The examples are visual， logical， theoretical， and empirical。 The author’s repeated appeal to the concept of the infinitesimal is helpful to make sense of many things outside the realm of mathematics。 To me， it helps me understand why Hegel， who was mostly opposed to mathematics as a tool to understand reality and life， found calculus a potentially suitable candidate precisely because of its inherent contradictions （using infinity to understand the finite， using continuums to understand discreteness， etc。）。 Anyway， while this application is specific， the book is an incredible introduction。 The only issue I see is that the examples are a bit politically problematic， especially the “neutral” discussion of rockets， missiles， weapons， etc。 that many readers would find disturbing。 Regardless， calculus IS used to describe these phenomena， so it’s up to the reader to decide what to do with this information。 。。。more

Ezequiel Foncubierta ，

An excellent book that I truly enjoyed。 If you are interested in math， and how calculus changed our world， this is a must read。 The author walks you through the history of calculus， with all its principal actors。 You don't need to be good at calculus to read and understand this book。 The examples used by the author are clear and concise enough to make his point。 An excellent book that I truly enjoyed。 If you are interested in math， and how calculus changed our world， this is a must read。 The author walks you through the history of calculus， with all its principal actors。 You don't need to be good at calculus to read and understand this book。 The examples used by the author are clear and concise enough to make his point。 。。。more

Dipa Raditya ，

This book was super dragging and too much but if you are keen to do some sort of scientific journalism with math vocabulary all over the places， I wish you good luck。

Reference

google book https://www.google.com/search?tbm=bks&q=Infinite Powers: The Story of Calculus - The Language of the Universe

hathitrust digital library https://babel.hathitrust.org/cgi/ls?q1=Infinite Powers: The Story of Calculus - The Language of the Universe&field1=ocr&a=srchls&ft=ft&lmt=ft

The British Library https://bll01.primo.exlibrisgroup.com/discovery/search?query=any,contains,Infinite Powers: The Story of Calculus - The Language of the Universe&tab=LibraryCatalog&search_scope=Not_BL_Suppress&vid=44BL_INST:BLL01&lang=en&offset=0