There's a few books which have created true inspiration and passion for physics and maths. This book *Mathematics and the Physical World*, by the late Morris Kline, is one of them.

I chanced upon this book in the depths of the ANU library, searching for a few mathematics textbooks. With an unassuming title, cracked spine and yellowed pages, it caught my eye for no apparent reason. I opened a random page on a whim, and was struck by a surprising, and somewhat poetic description of polynomials, in a chapter titled "Wedding of Curve and Equation". Having a glance through other chapters, with names such as "Deeper Waters of Arithmetic", "From Calculus to Cosmic Planning" and "More Light on Light", I was immediately intrigued and borrowed it out immediately. For the first time in recent memory, I truly had excited anticipation for starting to read this book.

Kline starts from the utter, pure basics that even the laziest of laymen can grasp. From there, he takes a rather well paced walk through the history of mathematics and physics co-evolving with each other in a discussion of ideas, people and sprinklings of mathematics here and there. Despite having "known" most of the mathematics and physics covered in the book, I was enthralled by the sheer simplicity and grace with which Kline presents both basic and advanced mathematical principle; with intuition and subtle humour. One chapter in particular, on the mathematics of light and optics, Kline showed how with two basic principles (light travels in a straight line, and angle of incidence = angle of reflection) one can deduce rather profound results with immediate practical outcomes.

Perhaps the most striking aspect of the book is how it threads the natural evolution of mathematical and physical ideas together throughout each chapter, forming a very coherent narrative. You might hear book, movie and video game reviews describe them sometimes as "weaving" several narratives or plot threads together, but none I can think of get close to how masterfully *Mathematics and the Physical World* achieves this literary form.

Despite there being no "main protagonists", the characters are ones many will be familiar with (at least by name). Aristotle, Euler, Newton, Lagrange, Gauss, Galileo - just to name a few. By giving an insight into the lives of these academic giants, Kline injects a much needed human element to the whole exploration. At the same time, in reading *Mathematics and the Physical World*, the scholastic, "Ivory Tower" quality of these two subjects is done away with as the reader realizes just how much grit and effort was required to accomplish these feats of pure reason.

As an avid hobbyist writer myself, I was rather pleased with the nuanced literary devices Kline utilizes. I should note, these are quite rarely well executed in academic works, or even popular science (usually written by scientists). Not only does Kline present a coherent, meandering account of both history and mathematical ideas, but with well-placed humour and analogies, Kline makes what would usually be a soulless and insomnia-curing endeavour into a fascinating journey through the very nature of physical reality. Kline has a very nuanced understanding of the average reader's cognitive stamina too, which is exemplified in just how well paced the mathematics, descriptions and historical bits are all partitioned. Each chapter in itself, whilst not fictitious by any means, has an overarching goal which Kline outlines from the very start, making the journey much more clear and directed, than the hazy stumbling to-and-fro that many non-fiction readers may be tired of.

Those retaining scars from the their high-school experiences in maths will be glad to know that this aspect of the book is handled aptly, and in such a way that it is accessible to anyone with little to no mathematics background. Let me put it this way, if you can read, and know how to count to ten, you can manage this book. It is true however, that the mathematical sections, whilst small, are tempting to skip over when reading. For me personally that was more of an artefact of my previous (recent) education, so I already knew the answer and most of the argument. Imperial units don't help either! This being said, a newcomer will surely find all of this approachable, if they are willing to be patient and not employ any speed-reading techniques - this is not such a book to be glazed over.

The last few chapters in particular (on non-euclidean geometries) offer profound philosophical revelations that even the most adept students of mathematics will likely enjoy discovering. Kline alludes to the simple, but deep question of "why does mathematics describe the physical world" from the outset - and does both literary and philosophical justice in answering by the end. I will almost certainly have to write a whole separate essay about the ideas presented by the last few chapters of this book, simply because they are the rare few nuggets of knowledge of which it is an ethical disservice for a modern human to not hear about.

I'd highly recommend this book to any reader from high-school age onwards. High school 'education' is not a prerequisite.

I'll be putting this one on my personal "Required reading" list though.

#Summary

*Mathematics and the Physical World*, by the late mathematician and brilliant science-communicator, Morris Kline, highlights the real historical stories behind the most important subjects in mathematics, and how they co-evolved with physics through the ages of Aristotle, Newton and Gauss. With a deliciously satisfying literary style, and masterful presentation of complex ideas, Kline successfully binds together not only ideas but deep philosophical questions - and answers, in a quaint and appropriately sized book that everyone with an inkling of curiosity should read.

** Style: 8.5/10 **

** Substance: 9/10 **

-A

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