The Maths That Made Us: how numbers created civilisation

by Michael Brooks

Quadratic equations, Pythagoras’ theorem, imaginary numbers, and pi — you may remember studying these at school, but did anyone ever explain why? Never fear — bestselling science writer, and your new favourite maths teacher, Michael Brooks, is here to help. In The Maths That Made Us , Brooks reminds us of the wonders of how they enabled explorers to travel far across the seas and astronomers to map the heavens; how they won wars and halted the HIV epidemic; how they are responsible for the design of your home and almost everything in it, down to the smartphone in your pocket. His clear explanations of the maths that built our world, along with stories about where it came from and how it shaped human history, will engage and delight. From ancient Egyptian priests to the Apollo astronauts, and Babylonian tax collectors to juggling robots, join Brooks and his extraordinarily eccentric cast of characters in discovering how maths made us who we are today.

Genres: Nonfiction, Science, History, Mathematics, Audiobook, Popular Science, Stem

362 pages, Kindle Edition

First published January 1, 2021

About the author

Librarian Note: There is more than one author in the Goodreads database with this name.

Michael Edward Brooks is an English science writer, noted for explaining complex scientific research and findings to the general population. Brooks holds a PhD in Quantum Physics from the University of Sussex. He was previously an editor for New Scientist magazine, and currently works as a consultant for that magazine. His writing has appeared in The Guardian, The Independent, The Observer, The Times Higher Education Supplement. His first novel, Entanglement, was published in 2007. His first non-fiction book, an exploration of scientific anomalies entitled 13 Things That Don't Make Sense, was published in 2009. Brooks' next book, The Big Questions: Physics, was released in February 2010. It contains twenty 3,000-word essays addressing the most fundamental and frequently asked questions about science.

Reviews

[Paul · Rating 4 out of 5]

Our brains are not wired specifically for counting. Until we are taught otherwise, the untrained maths brain will only notice up to three things, before considering any above that is just more. Instead, we have a deeply ingrained culture that tells us that maths is important and that it matters. But we all have our limits, for some, it is the GCSE, but others go on to much higher levels.

Brooks begins with arithmetic, the simplest form of maths. As a species, we have been counting for around 20,000 years and even now we can see differences in cultures in the way that people use their fingers to count. He touches on fractions and negative numbers before we arrive at geometry. For some this may bring back the horror’s of a Pi you can’t eat, but it is more straightforward than algebra where we are reminded of that moment in maths when they add the complexity of letters to maths. Who remembers the quadratic formula?
For me though, the point when my brain juddered a little was calculus. I still understand it in principle, but it has been sooooo very long since I did it and rusty is an understatement… His chapter on logarithms seems easy by comparison and for some reason, imaginary numbers for me were relatively straightforward to master. As the saying goes, there are lies, dam lies and statistics and those that have a mastery of these slippery numbers can often hold the upper edge on those that can’t.

As maths books go, this is a pretty good one. Brooks tells us about the history behind each particular subject and some of the key people who have been instrumental in making our modern world a mathematical one. It is very readable, and only occasionally veers into the realm of the formula. Should that bring back nightmares from school then that can be skipped if necessary. If the thought of maths doesn’t terrify you too much, then this is a good place to start.

[Grace · Rating 4 out of 5]

Super interesting read! It does get pretty math-y in a lot of places, so I can see how it might lose people, but I thought it was pretty cool and a great sort of primer to introduce me to several concepts I want to explore in more depth!

[Adam · Rating 4 out of 5]

What a fabulously entertaining and enjoyable read! Mathematics has such a rich human history that I don’t think many people know much about. I certainly didn’t, even after having reasonable exposure to maths throughout my education.

I recognised many of the names, but Michael Brooks provided an entirely different view of them, plus introduced me to many more names I was completely ignorant of. He does a wonderful job of telling their stories in an informative and very engaging way.

If you’re thinking of reading this, but are hesitant because you don’t like maths or maybe think it is boring, or too hard - I encourage you to take the leap and read it anyway. You may well be pleasantly surprised!

[Anita]

Dnf at 118/291

[Emilija · Rating 3 out of 5]

2023 52 Book Challenge - 19) Typographic Cover

I found the historical parts of this book really interesting, and I didn't want to put it down. I specifically liked the chapters on statistics and information theory and the parts that discussed scientists.

I did find the mathematics quite difficult to follow, to the point that I had to ask somebody else to explain it to me, and the explanations in this book assume that you have some understanding of what you're reading mathematically. For instance, when formulas are being rearranged, it would have been easier to understand if the author had explained the rearranging step by step rather than just the beginning and the end because I literally had no idea what was going on every time a formula was discussed, which kinda takes away from the impact of the book.

[Mehtap exotiquetv · Rating 4 out of 5]

Mathematik. Das hört der ein oder andere nicht gern. Während wir bei Zahlen an die traumatisierenden Mathestunden denken, erklärt uns Brooks wieso die Bahnbrechenden Matheberechnungen unsere Zivilisation und das Miteinander verändert haben. Nur mit Hilfe von Mathe konnten Gebäude wie Hagia Sofia gebaut werden. Nur mit Mathe haben wir ein Verständnis für das Universum bekommen. Nur mit Hilfe von Mathe konnten wir Krankheiten reduzieren.
Wie stark verankert es in der Mitte unserer Gesellschaft verankert ist und wie toll eigentlich Mathematik ist, in diesen Bann kann uns nur Brooks führen.

[Kristin Hirsch · Rating 5 out of 5]

4.5 stars rounded up - a little tough to follow the derivations on audio. I LOVED hearing all the pettiness that was 16th century mathematicians though

[Riley White · Rating 5 out of 5]

This was a good book and I enjoyed reading it.

While my review could end there, I would like to voice the complaints that I had about the book, despite them ultimately being relatively minor. The Art of More belongs to a category of books which I like to call "books for people who erroneously believe that they do not like mathematics," and it feels as though the author has gone out of his way to ensure that the reader does not believe for a single second that they will be made to solve a math problem. The result is a book that seems to get tantalizingly close on several occasions to revealing how a type of mathematics was actually done, only to fall back on giving an uninteresting list of applications; this tactic seems to be a particular favorite of the author, and whenever he used it I couldn't help but feel as though I were being told when I would have preferred to be shown. As someone who reads a lot of math history, I also felt that there were certain subtleties which were not quite captured correctly in one or two places.

Another interesting aspect of the book was the fact that the author seemed particularly insistent that people should not try to ascribe mystical or spiritual properties to mathematics. This was especially apparent in the conclusion, where the author seems to claim that mathematics is a purely mundane thing which is entirely a product of the human mind, and that we should not be surprised by or see beauty in things such as prime numbers. This is of course a matter of opinion, but I feel that many mathematicians, myself included, would disagree with this description for a variety of reasons. As the author is a physicist, I wonder if this is simply due to the differences between pure and applied mathematicians. He also claims that there has always been a kind of mathematical elitism, where a small proportion of people make it difficult for others to learn mathematics. While this has certainly been true to some extent for most of human history, I have some trouble believing that modern mathematicians in particular continue to do this. Perhaps others have had different experiences than I have, but I feel that mathematics currently is extremely accessible, and the community very welcoming. I'm sure most mathematicians today would be very happy to see every person engaging with mathematics, so I am not sure exactly what the author has in mind when he suggests that we "demystify mathematics."

Complaints aside, the parts of the book which focus on historical figures and stories, which is most of it, are enjoyable, and I learned a few new things. I do hope that the book has the intended effect on people who have an inaccurate view of what mathematics really is.

[Scribe Publications]

Ambitious.
Tom Gatti, New Statesman

At school, many of us wondered about the point of geometry, calculus and algebra. Brooks shows how the childhood question ‘What’s the point of this?’ can be reframed: esoteric concepts such as imaginary numbers, cryptography and the semi-mystical digits of pi are revealed to be the essential building blocks of the 21st century.
Liz Else and Simon Ings, New Scientist

How brilliant of Michael Brooks to be able to reignite my almost-forgotten childhood love of mathematics. Written with beauty, style, and care for the history as well as for the science. A tour de force.
Angela Saini, author of Superior: the return of race science

Michael Brooks has written the formula that reduces to near zero any sense that maths could be a dull subject to study. The Art of More brings to life in accessible, lively terms how maths helps us navigate pandemics, space travel, and encrypted apps — all while celebrating the complicated and fascinating characters, from Euclid to Florence Nightingale, who have pushed our knowledge forward. Why isn’t school maths taught like this?
David Rowan, founding editor-in-chief of WIRED UK and author of Non-Bullshit Innovation

In this thrilling, colourful, and deeply researched book, Michael Brooks tells the epic story of how mathematics has driven human progress, spanning millennia to trace the numerical innovations — from geometry and algebra to the mind-bending landscapes of imaginary numbers and extra dimensions — that have woven our history and shape our lives today. Along the way, he explores the passions and intrigues of the people behind the numbers, transforming mathematics from dry equations into a gripping drama. This is maths as you’ve never experienced it: inspiring, fun, and utterly human.
Jo Marchant, author of The Human Cosmos

Michael Brooks has a rare gift for making science come to life, and in this book he is at his best, fusing mathematics with storytelling as he takes us on an exhilarating sweep through human history. The Art of More shows just how deeply numbers have propelled the advance of civilisation. And it does so with enormous narrative brio and good cheer. This is a serious — but seriously readable — history which I enjoyed from the first page to the last.
Dan Jones, New York Times bestselling historian

A friendly, readable account of the huge influence that mathematics has had on human civilisation. If you’ve ever wondered what the maths you did at school was for, and what it has done for us, you’ll find the answer here. Michael Brooks’s enthusiasm for the beauty and utility of the subject shines from every page.
Ian Stewart, author of What’s the Use?

From Fermat’s last theorem to quantum computers, pi to probability, slides rules to golden ratios, The Art of More is no mere bluffer’s guide, but a rich introduction to the elegance and importance of mathematics. Michael Brooks shows what a global and multicultural task it has been, ever since prehistory, to figure out how we can benefit from quantification and calculation. He shows that maths is not just, as Eugene Wigner said, unreasonably effective for understanding the world, but also unfathomably wonderful in its own right.
Philip Ball, science writer and author of Beyond Weird

Suddenly it all makes sense. This brilliant book shows maths as something concrete, real, and crucial to our lives, rather than some dry, abstract code designed to make school kids’ lives miserable.
Charlie Higson, actor, comedian, and author of the Enemy series

Michael Brooks has written both a lively history of civilisation, and a delightful introduction to the power of mathematics. Either would be an achievement, but to do both simultaneously is a wonder.
Tim Harford, author of How To Make the World Add Up

If you love maths, you’ll enjoy this book. But if you’re a little scared of maths (as I am), you’ll adore The Art of More. Michael Brooks knows how to tell the hidden stories behind numbers, formulas, and logarithms.
Andrea Wulf, author of The Invention of Nature

Mathematics is quite unique in that even much earlier results do not change with the passing of time. This book is not only a passionate love letter to mathematics, it offers an important lesson in the appreciation of mathematics, and of its crucial role in humanity’s history.
Mario Livio, astrophysicist, and author of Galileo and The Science Deniers

An enviably good history of how ideas in mathematics have shaped (and been shaped by) the progress of civilisation.
Tim Harford, author of How To Make the World Add Up

What is the driving force behind the development of human civilisation? In this unique and surprising book, Michael Brooks makes the case that it is the growth and progress of mathematics — and he does it in a way that will be interesting to the mathematical and math-phobic alike! As entertaining as it is informative, The Art of More takes us on a journey through the ages, demonstrating how mathematics played a crucial role in the evolution of how we live. Not since Jared Diamond’s Guns, Germs, and Steel has there been such an insightful and compelling analysis of how we got here.
Leonard Mlodinow, New York Times bestselling author of The Drunkard’s Walk

Moving from ancient Egyptian priests to a hobbyist who solved a mapmaking puzzle that confounded NASA and the US Geological Survey, science writer Brooks aims to persuade readers that mathematics was one of the great innovations that made civilisation happen.
Barbara Hoffert, Library Journal

[Victor Porras · Rating 2 out of 5]

There are some interesting tidbits, but I thought most of it was too basic. Perhaps it would be good book for a bright 10 year old. I also thought the nonlinear jumping around within chapters was a bit annoying. The writing was breathless and overexcited.

[Sharof Hamroh · Rating 5 out of 5]

Certainly the best book I have ever read. Everyone must be familiar (preferably to be in love) with mathematics. This book can tell you why

[Chris Aylott · Rating 3 out of 5]

There are some neat tidbits of history here, but I had trouble connecting with the math. I could follow what Brooks was saying, and I learned some new things, but I didn't have many moments where I felt like I understood the math he was talking about better.

One moment that did work for me was in the imaginary numbers chapter -- the graph that shows how you can essentially travel around a number line to reach the square root of negative one and then negative one itself. That's the kind of explanation I needed more of to really grasp the concepts in this book.

[Michelle · Rating 3 out of 5]

Actual rating: 3.5 stars

The only thing that kept this from being a 4 for me were some of the more detailed explanations of certain math equations. That's not a critique of the work or the author -- I think they were well-placed and well-written -- they just affected my personal enjoyment of the book because I'm useless at math (even though I'm extremely fascinated by it).

[Bryan Higgs · Rating 5 out of 5]

Michael Brooks has written other interesting books. I read his 13 Things That Don't Make Sense: The Most Baffling Scientific Mysteries of Our Time, and gave it five stars.

This one similarly deserves five stars because the author has pulled together so much history and so many interesting characters and contributors to the various kinds of math he describes.

He is trying to show, he hopes, to people who don't appreciate math, or have turned off math from their lives, how mathematics has been a major contributor to our civilization. And we (even those of us who like math and have been exposed to it) tend not to realize that, and to what extent it's true.

As one who has a Ph.D. in Particle Physics, and who has read extensively in the area of "intelligent laymen's" science and math books, I was aware of some of his stories and characters and math areas. But he introduces so much that I was unaware of, and he does it by writing in a very understandable and engaging way.

He admits right from the start that he wants to engage those who are math-phobic, or math-ignorant, or simply not interested in math (my terms, not his). As a result, he doesn't have math formulae in the text, and he says to the reader that if those formulae don't make sense, just to ignore them and move on.

I wish that math were taught from this perspective in high school and in college. Unfortunately, too many times, math courses convince students that math is boring, that it is black and white (far from reality!), that there is only one way to solve a problem (the teacher's preferred way, and then solve hundreds of almost identical problems to the point of insanity). This is so far from the real math that I know, as to be really sad, and a terrible commentary on how we teach math in our society. The fact that math breakthroughs have repeatedly been made by people approaching a problem from a different perspective should indicate that the very essence of math is to try to look at solving problems from different perspectives, and choose the method that makes the most sense. Math teachers who say 'do it my way only' are doing a terrible disservice to math teaching and to their students. Yes, I know that there are practical limitations to what we can do in the teaching of math, but I think it is vital that we convey something of the excitement that is inherent in math, but is so often lost in math courses.

I would love to say that this book should be part of, say, a high school math curriculum (or even at the college level). Ideally, it should, but I think the density of the content (so many characters, so many areas of math, etc., etc.) precludes that. Perhaps the author (or someone) should come up with a version that might be more accessible to a teen audience that no doubt has limited historical or scientific knowledge?

Way back in 1959. C. P. Snow gave a lecture on The Two Cultures and The Scientific Revolution that argued that the breakdown of communication between the "two cultures" of modern society – the sciences and the humanities – was a major hindrance to solving the world's problems. He wrote:

"A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: 'Have you read a work of Shakespeare's?'

I now believe that if I had asked an even simpler question – such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, 'Can you read?' – not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their Neolithic ancestors would have had."

He was right then, and he's right now. Unfortunately, not only do we not seem to be making progress in that area, it seems that we are actually losing ground. No school (high school or college) would consider dropping the coverage of Shakespeare from its curriculum, but many do not cover Physics at all for most of their students. The same could be said of math courses, other than relatively simple ones. That is a sad state of affairs, especially given how much our society is dependent on math, science, and technology -- far more than a century ago.

I highly recommend this book. It provides a fascinating insight into the influence of mathematics, in all its forms, on the progress of civilization.

[Froggarana · Rating 5 out of 5]

great book, good stories, and GASP ! it has equations !

[Eilonwy · Rating 5 out of 5]

I wish we all got taught more math history as part of math classes, because this was fascinating, if a little disconcerting (it turns out that geometry, my least favorite math classes ever, is the basis for lots of branches of other math. And yet algebra, trigonometry, and calculus made sense to me when I was studying them, while geometry and all those proofs will forever remain utterly pointless to me, so go figure).

I for one would have felt a whole lot better knowing how little of math history is eureka insights, and how much was actually people spending decades trying to work out a single problem -- it would have made me feel much better about struggling to grasp those problems myself when they were presented in class.

[Osedaxx · Rating 4 out of 5]

I loved the historical/"philosophical" parts of this book -- the thing that's missing from what you generally learn about math. But I also found the depth of the actual explanations a bit unbalanced: lots of time spent on basic stuff everyone (presumably) learned at school, while more abstract or difficult topics like information theory were more glossed over. But of course everyone will be differently prepared; and this book's purpose is to provide a new appreciation of math.

[Tyler Critchfield · Rating 4 out of 5]

Combining math and history? Can't get much more nerdy than that - right up my alley :) Brooks does a decent job at not shying away from the math while not boring with it either. Though I wouldn't have minded more math details - this was definitely geared toward those who don't think of it or use it much. 

[Nicole Simovski · Rating 5 out of 5]

A fantastic book on the history of math discoveries from whole numbers to calculus to information theory. Each chapter recounts the major discoveries of the major branches of maths and its impact on human society. Great read.

[Ron · Rating 4 out of 5]

I mostly listened to this book. It goes through the major areas of mathematics (eg, geometry, algebra, calculus, statistics) and shows how things were figured out and what was accomplished because of it. I can't imagine somebody who doesn't have a math background really enjoying this book.

[Alan Teesdale · Rating 4 out of 5]

A genuinely good read for those interested in mathematics and even for those who are not. Mathematics analyzed through a unique historical lens, highly recommend.

[Andrea Itta · Rating 5 out of 5]

The branches of Maths through a historical lens.

[Fred Hughes · Rating 4 out of 5]

A great book about mathematics and how much of what we enjoy in our modern life came from the application of mathematics principles.

A nice middle ground dive into the subject with over powering the reader with esoterica

[Mishehu · Rating 5 out of 5]

Book covers a lot of familiar ground, some less familiar. It’s written in a breezy tone and is both informative and entertaining. Well worth the read for enthusiasts of pop math/math history.

[Katrina · Rating 3 out of 5]

This probably would have been higher had a read on paper but I really tuned out the derivations. The history was interesting and I still can't get over that there used to be legit math duels.
Audio

[Adrian · Rating 4 out of 5]

The book is a mathematical journey spanning millennia, touching on various civilizations with different cultures and religions. He appreciated their contribution to mathematics, hence he shouldn’t have used the Christian reference to eras, but the secular one (i.e. BCE and CE).

[Chris DuPre · Rating 4 out of 5]

A great argument for the importance of mathematics in civilization and history. Some of the points are a little confused from a modern perspective(the most jarring is for instance the claim that calculus is an outgrowth of algebra), but overall the book does a great job of showing the importance of math across a wide variety of fields to those who are not already deeply engaged in its intricacies. Of course, the call for democratization and appreciation of mathematics to all is a profoundly important movement and has my full support and a goal I hope to work on everyday.

[Annie · Rating 5 out of 5]

Originally posted on my blog: Nonstop Reader.

The Art of More is a layman accessible examination of how mathematics has shaped civilisation well explained by Dr. Michael Brooks. Due out 9th Sept 2021 from Scribe, it's 336 pages and will be available in hardcover format.

This is a fascinating look at mathematical concepts and how they have fostered exploration and discovery and why mathematics is fundamental to, well, everything. The author is wonderfully adept at explaining complex ideas and auxiliary concepts in simple and understandable ways and even for maths-shy readers, there are fascinating and valuable takeaways to be found here.

The chapters are arranged in essay style units written around a field of mathematics: arithmetic, geometry, algebra, calculus, logarithms, imaginary numbers, statistics, information theory, and a summary at the end giving a good broad overview tying everything together, and poking a bit of a pin into Le Corbusier's pomposity and the ascription of mystical significance to mathematical concepts like pi, e, and Planck's constant (and jolly well deserved, says this bionerd). If we can de-mystify, we can maybe make them more accessible, more useful, and more fun to everyone.

Five stars. This would be a good choice for public or school library acquisition, and for readers of popular science. For readers who still have a dog-eared copy of Gödel Escher Bach on their bookshelves, there's a lot to love in The Art of More, and I found Dr. Brooks' style much more accessible and less impenetrable than Dr. Hofstadter's.

Disclosure: I received an ARC at no cost from the author/publisher for review purposes.

[Maurizio Codogno · Rating 3 out of 5]

Brooks è troppo innamorato della sua tesi

La storia della matematica è anche una storia della civiltà. Fin qui penso che anche i platonisti di più stretta osservanza siano d'accordo. Brooks parte da questo punto di vista e prova a leggere lo sviluppo della matematica come uno sviluppo della civiltà. Ecco che i numeri per esempio sono legati a doppio filo all'economia: se sai gestirli non rischi di andare in bancarotta. E non è un caso che Chaucer fosse il sovraintendente delle dogane britanniche, dunque. Ma tutti gli esempi del libro sono strettamente legati alla vita reale: per esempio quando si parla di algebra Brooks mostra come FedEx e UPS abbiano scelto le posizioni dei loro hub (Memphis e Louisville) per minimizzare le distanze percorse dai suoi vettori, mentre i numeri immaginari arrivano come risultato della ricerca di un suono particolare per le chitarre elettriche. Come avrete intuito, l'idea non è affatto malvagia e potrebbe avvicinare alla matematica chi pensa di odiarla: però il libro mi ha dato tanto l'impressione di una salva di fuochi artificiali ("potevamo stupirvi con i nostri effetti speciali, ma questa è matematica") il che almeno per me risulta un po' troppo alienante.

Pollice verso alla traduzione di Benedetta Antonielli D'Oulx, visti gli svarioni dal punto di vista scientifico che si trovano nel testo.

[Maddie Rayner · Rating 3 out of 5]

Another science communication book that is covered in quotations about how 'It all makes sense now!' I liked the human history of maths explored in this book, and I also really appreciated the repeated acknowledgement that maths is something humans learn, not an innate ability. But large swaths were still very confusing to me, and it hasn't all suddenly clicked lol.