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

Steven Strogatz has created a masterpiece. Infinite Powers is not merely a book about Newtonian calculus; it casts its net much wider. Strogatz begins with the proto-calculus ideas that preceded Newton and builds the narrative from there in an almost thriller-like fashion. The book also blends several domains of the natural sciences in which calculus is applied; and, of course, no discussion of calculus would be complete without physics. In my view, it is even better than Strogatz’s other book, The Joy of x. It offers a rich presentation of the logical and reductionist ideas that led to the development of the beautiful and powerful toolkit we now call calculus. I cannot resist giving this mathematical non-fiction book five stars; and why should I hesitate? It is truly a masterpiece.

I read this book cover to cover over four days and found it absolutely captivating. The author does a remarkable job tracing the rise of calculus from its earliest historical roots all the way to its modern applications. He covers the actual development of calculus with numerous examples — from older methods of finding centers of gravity and curve intersections, to the derivative methods we recognize today. He then moves into Ordinary and Partial Differential Equations and explains their real-world applications clearly and accessibly. What makes this book special is how it shows calculus not as an isolated subject, but as a living framework that branches into many other fields — each with different names, but sharing a fundamental unity. The applications span aerospace, chemistry, and biology, giving you a genuine sense of just how far-reaching this "language of the universe" truly is. The author's enthusiasm is infectious and makes a subject that is so often taught poorly in schools feel like the grand intellectual adventure it really is. If you want a rich overview of calculus — its history, its beauty, and its power — this book delivers exactly that.

This book successfully explains the history and growth of calculus over the last 2000 years and helps us understand why we needed it in the first place. Then it moves on to explain what calculus is through infinity principle and the fundamental theorem. But, towards the later part of the book, I started to feel lost because of too many examples from different fields of science. This was because the author was trying to prove that everything that exists today or has been invented is because of calculus, which may have been true, but connecting the dots from such diverse fields as biology, mathematics, computers, and medicine becomes really difficult and kind of tiring. This should have been avoided.

I started loving math after reading this. Great book

A good book to read.

Good content. Must read for people scared of maths. Provides good information on evolution of maths

mind-blowing ... simply awaken

Well written !!

De este libro me gustó la forma en que destaca la importancia de considerar como un sector rectilíneo a una parte muy pequeña de una curva. Ese razonamiento detonó una gran cantidad de descubrimientos analíticos.

と、中学生の時クラスの誰かが言っていたのを聞いて、そんなわけないだろうと思ったものの、教育過程から大分離れて今日に至るまで、具体的に何の役に立つのかは、ついぞ聞いたことがない。実際に仕事で使う場合も四則計算と若干の確率くらいである。ヘンビブンとは、結局、何に使うのだろう。 ストロガッツ教授の答えは、「The application of calculus to modern science is largely an exercise in the formulation, solution, and interpretation of partial differential equations（現代の科学において微積分を使う場合、大概はヘンビブンの解釈etcである）」とのことである。電気と磁気の関係をまとめたマックスウェルの方程式もヘンビブンだし、熱でも流体でも力学はヘンビブンだし、ファイナンスで使うBlack-Scholesモデルも、神経細胞内の活動電位を扱うHodgkin-Huxleyモデルもヘンビブンである。 引用したような文章が正に本書を素晴らしいと思う理由なのだが、平易にまとめていながらも、本質をうまく表現している。このようなまとめ方をできるのはその道のエキスパートのみであり、ストロガッツ教授はその道のエキスパートそのものである。 数学の魅力というものが抽象的に理論を展開できることであるのは間違いないが、一方で、微積分が、物理・天文学・生物・医薬・エンジニアリングと具体的な技術の進歩とともに発展してきことも事実である。その点、古代ギリシアの曲線の探求、小学校で習う「円」から、熱の伝搬に関するフーリエの法則を通り現代まで、数学としての理論的な展開の歴史と、具体的な実社会での応用を、理論と応用を、ソファで寝ころびながらスラスラと読める形に仕上げるのは偉業と思う。時代に埋もれないクラシックそのもの。 ★★★★★

The best book that conceptually traces the history of calculus and how it was created, why it was created and how it affects all aspects of change in life. I can't thank Steven Strogatz enough. This is a Eurocentric history and present insight into the spirit of calculus. I have been searching for a book like this for decades. At school, I could easily compute calculus equations but whilst I felt there was a beautiful pattern to them, I never understood how they were applied in real life. I used to fantasise and wish and pine to understand how calculus came to exist, how it is mirrored in nature and now I see it everywhere like a truthful poem that never loses its awesome beauty and insights. I see calculus now as part of my being, part of all of us. The best and most illuminating book on calculus I have ever come across.

Un libro excelente, riguroso y ameno. No hay que ser un experto en matemáticas aplicadas como el autor para disfrutar y aprender con su lectura. Por mi profesión ( soy físico ) ya conocía el trabajo científico del autor, pero me ha sorprendido su faceta de comunicador de temas tan "sencillo", "lógicos" y a la vez complejos.

Mir hat das Buch gefallen. Den mathematischen Inhalt kannte ich schon aus der Schule. (Ich war in einer Klasse mit erweitertem Mathematik-Unterricht, das half später auch beim Studium sehr.) So erkannte ich vieles wieder. Das wirklich Interessante für mich sind die historischen Zusammenhänge. Das Buch ist flüssig geschrieben und gut verständlich. Sehr zu empfehlen, wenn man sich für die Geschichte der Mathematik interessiert, in ihren Grundlagen. Im Prinzip ist es der Teil, den ich immer schon am Anfang eines neuen Schuljahres im Mathe-Buch gelesen habe, aber wesentlich ausführlicher.