Unlocking the Secrets of Calculus: A Review of Strogatz's Work
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Chapter 1: The Essence of Calculus
Calculus stands as one of humanity's most significant innovations. It forms the backbone of many contemporary technologies, including radio, television, radar, GPS systems, mobile phones, and MRI scans. Its influence extends into fields such as meteorology, economics, social sciences, epidemiology, biology, and medicine. Consequently, a basic understanding of calculus is essential for every educated individual.
In Steven Strogatz’s eloquently crafted book, Infinite Powers: The Story of Calculus — The Language of the Universe (Atlantic Books, 2019: Amazon US / Amazon UK), readers are introduced to the foundational concepts of calculus. The narrative takes us through its modest beginnings and chronicles its evolution over the centuries, tackling challenges from calculating the area of a circle to ensuring a spacecraft successfully lands on the moon.
Calculus is a deeply human pursuit, and through it, we explore the lives of its pioneers, starting with the groundbreaking ideas of Zeno and Archimedes. We trace the development of calculus over more than three millennia, highlighting the vital contributions made by numerous dedicated individuals, which have enabled the exploration of modern abstract concepts like chaos theory and artificial intelligence.
Section 1.1: The Genius of Breaking Down Problems
This engaging book reveals that the unique brilliance of calculus lies in its ability to deconstruct complex and often daunting problems into infinitely small, manageable components. These pieces can then be analyzed and recombined to form a coherent whole that is much less intimidating. Beyond mere fragmentation, this approach has transformed calculus into a formidable instrument that has driven technological progress and addressed real-world challenges—many of which go unnoticed in traditional math curricula.
For instance, I found the insightful discussion on calculus's pivotal role in the global adoption of the triple drug cocktail for tackling the perplexing mutation rate of HIV particularly intriguing. Furthermore, it shed light on the intricate balance during the asymptotic phase of HIV infection, where the production of new virus particles and their eradication by the immune system reach a delicate equilibrium (pp. 218–225).
My thoughts on “Infinite Powers” by Strogatz - YouTube
In this video, various perspectives on Steven Strogatz's work are discussed, highlighting the significance of calculus and its historical context.
Section 1.2: Theoretical Insights
On a theoretical plane, Strogatz’s exploration of the challenges inherent in synthesis compared to analysis was particularly enlightening (pp. 102–103). This contrasts the relative ease of mastering differential equations with the more intellectually demanding integral equations.
Chapter 2: The Infinity Principle
In this narrative, infinity serves as both a starting point and a conclusion, providing a fitting and aesthetically pleasing framework for the discussion.
For those who wish to appreciate the historical and philosophical underpinnings of calculus without delving into the mathematics, this book stands out as one of the most accessible works on the subject in recent years. Its remarkable achievement has earned it a spot among the six finalists for the esteemed Royal Society Insight Investment Science Book Prize for 2019.
For serious calculus students, Infinite Powers offers the historical and conceptual context frequently absent from current math education, fostering a deeper and more intuitive understanding of the material.
Steven Strogatz: The Infinite Power of Calculus - YouTube
This talk elaborates on Strogatz's insights into calculus, emphasizing its impact on various scientific disciplines and everyday life.
NOTE: I receive small commissions for purchases made through Amazon links in this article, in exchange for my honest and unbiased review.
NOTE: A copy of this book was provided by the publisher for my honest and unbiased evaluation.
Originally published at Forbes on September 30, 2019.