A Little History of Mathematics

by Snezana Lawrence

A lively, accessible history of mathematics throughout the ages and across the globe
 
Mathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from?
 
In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines. Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy Noether and Maryam Mirzakhani.

Genres: Mathematics, History, Nonfiction, Science

304 pages, Hardcover

First published May 13, 2025

Reviews

[Fernando Pestana da Costa · Rating 4 out of 5]

This is a very enjoyable history of Mathematics in forty chapters. Written for the curious layman with no maths background, this can be read with profit even by those who know some maths, and even by the professional mathematician. The engravings by Kat Flint at the start of each chapter are also delightful.

[Autumn Zhong · Rating 5 out of 5]

A whirlwind trip through the universe of mathematics. I’m constantly amazed by the abstraction and complexity of the questions under investigation, though I myself have no idea how to make progress on them. I do wish the book had parts dedicated to quick birds eye view explanations of how the proofs of the theorems worked, instead of just saying “through a lot of hard work/a set of fresh eyes/etc” it was figured out. Still greatly fascinating though

[Nick Rome · Rating 4 out of 5]

Really enjoyed this fun and fast paced history of maths. The book starts with the earliest recorded examples of human mathematical activity and travels all the way to cutting edge modern research. Each chapter is very short, usually around 5-6 pages making it very readable.
As a result, I think this would be a perfect introduction to a lot of mathematical ideas and stories for people outside the subject who are interested. I am a mathematician myself so a lot of the stories were familiar to me but Lawrence still found many cool nuggets that I had never heard before (like that Mersenne was a monk whose correspondence course eventually became the Academie des Sciences, or when Erdös ran afoul of the FBI). So I think there's something in here for everyone interested in maths!

One of the major strengths of the book is that it highlights stories often missing from classical histories. In the early chapters Lawrence takes us to Mesopotamia and Greece but spends just as much time in India, China, Japan and the Middle East. I really enjoyed this, there are 100s of different books where Pythagoras and his crowd make an appearance but I haven't seen as much about ancient Asian mathematics and found these sections fascinating. I particularly liked the concept of the Simpeki Sampo, mathematical puzzles hung above temples. Another aspect of this is that there is a clear emphasis on stories of female mathematicians which is a great thing. It's hard to overstate the impact that Emmy Noether had on the development of algebra, for instance, and she gets her right dues in this telling of the history. I had shamefully never heard of Alicia Boole Stott (but had heard before of the men around her like George Boole and Harold Coxeter), I am happy this book was able to correct that. Finally, Lawrence introduces readers to recent female mathematicians who have made huge impacts such as Maryam Mirzakhani and Maryna Viazovska.

This leads me to another big success of the book which is that there is a great deal of effort made to discuss *modern* mathematics. Something like a 1/3 of the book is dedicated to topics coming from the 20th and 21st centuries. I feel this is rare for this kind of book and admirably ambitious. The pace of research, the level of branching and specialisation and the level of abstraction in mathematics all ramp up in this period. I was very excited to read about the Bourbaki group, for instance, and to see people like Grothendieck, Terry Tao and Claude Shannon make appearances.

Of course, the operative word in the title is "little". The author is not setting out to write an encyclopedia and so as a result no one subject is going to get more than a few pages and there has to be a lot of interesting topics left on the cutting room floor. In the choices made you can see the author's own preferences, which seem to be for geometry, number theory, discrete mathematics. This suited me in a way, because these are exactly the subjects I care most about! However, the flip side is that I felt I missed out on learning new things about maths topics which I know the history of less well. For instance, I would have loved to have seen something about developments in the study of PDEs, or the birth of financial mathematics (things like Ito calculus and the Black-Scholes equation), or the formalisation of probability and the work of Kolmogorov (in fact, in general a chapter on the work of Soviet mathematicians behind the iron curtain would have been fascinating, much of this is lost now), or about fluid dynamics.
However I don't mean for this to come off as a slight at all, I think if you asked 100 mathematicians which topics should be included in such a book, you would get 100 radically distinct lists.

As well as not being able to capture every subject, the short nature of the explanations can sometimes be a little problematic. One issue is that I feel like some matters of importance sometimes feel like they aren't being given the weight they deserve. I personally felt this the most with Alexander Grothendieck. He is mentioned but very briefly as the father of category theory. This is somewhat true but his influence spreads all over almost all of pure mathematics, he more or less reinvented algebraic geometry in his own image and this lead to radical impact in number theory and other areas. Another potential issue with the brevity is that sometimes explanations of complex ideas are made so simple that they cross the line into being false or a little misleading. The instance that comes to my mind is in the discussion of the Riemann zeta function. The author refers to "a Riemann zeta function" when there is only one and says that is defined as the sum of the series n^{-s} which is true but only when the real part of s>1. For any other complex s, this definition doesn't make sense and it's in this other region that all of the interesting stuff (i.e. the mysterious zeros) happens. However, these instances are very few and far between, and don't diminish the experience at all as there is always some new interesting topic right around the corner.

Finally, I think this book would make an amazing jumping off point for someone interested in mathematics. However, the biggest missed opportunity is not providing the reader with endnotes or further reading suggestions. This is a real shame, I could imagine a reader being interested in some piece of maths and then having to navigate Google to try and find a good resource to learn more. To that end, I thought it might be nice to try and gather some here (caveat: I don't have a suggestion in mind for every chapter and some of the books I haven't read myself, these I'll mark with an asterisk).

- Chapter 2 Unearthing Wisdom: Words and Pictures - New Light on Plimpton 322 by Eleanor Robson (this is a research paper but a very readable one!)
- Chapter 4 Secrets of the Pythagoreans: Pythagoras by Kitty Ferguson
- Chapter 8 The Origin of Nothing: Zero, Biography of a Dangerous Idea by Charles Seife*
- Chapter 13 The Cubic Affair: Veritasium YouTube video "How Imaginary Numbers were Invented"*
- Chapter 14 Cracking Algebra's Code: The Code Book by Simon Singh
- Chapter 24 The Romantic Mathematicians: The Equation That Couldn't Be Solved by Mario Livio (highly recommend!)
- Chapter 25 A Logical Wonderland: Lewis Carroll in Numberland by Robin Wilson
- Chapter 26 The Quiet Birth of Chaos: Chaos by James Gleick
- Chapter 27 Sizes of Infinities: Everything and More by David Foster Wallace (Yes, that DFW)
- Chapter 30 In Pursuit of Perfection: Logicomix by Apostolos Doxiadis and Christos Papadimitriou or Incompleteness, the Proof and Paradox of Kurt Gödel by Rebecca Goldstein*
- Chapter 31 Ramsey and Friends: The Man Who Loved Only Numbers by Paul Hoffman*
- Chapter 34 The Games People Play: The Maniac by Benjamín Labatut (quasi-fictional but fantastic!)
- Chapter 36 The Unfinished Business: Fermat's Last Theorem by Simon Singh
- For the final few chapters the best bet is probably a Quanta article but one could also look at the Fields Medal Laudations for Tao, Mirzakhani and Viazovska.

Anyway if you enjoyed this book and are still in the mood for maths, maybe your next read is on this list somewhere.

[Stef Gijssels · Rating 4 out of 5]

In one of the first chapters of this book, the story is told about Greeks in the 5th Century BC who consulted the oracle of Delphi to appease the god Apollo after the plague rampaged across the country. The oracle said that "in order to assuage the god, they should double the size of Apollo's altar, an ornate then-foot-high cube. That didn't sound very difficult to do. Double the cube? How hard could it be? (...). This problem, known as the Delian problem, 'rested on how to find the cube root of 2, and was eventually proven - not until the 19th Century - to be an impossible task using only Euclydian tools of geometry available in the fifth century". (p. 31).

This little example illustrates the book well. It's a historical overview of new challenges and solutions in mathematics from the earliest ages to today. Math was definitely not my thing in school, and I only realised that integrals could be used to calculate volumes when on the exam we had to calculate the volume of a flat tyre. I never knew what it was actually used for. In retrospect, a lot of math could have been made more attractive by using some of the challenges in this book. It requires some basic knowledge of math, but not exceptionally so.

The example also demonstrates the weird thing that is relatively unique to mathematics: on a very abstract form, there are many riddles that have no other apparent function or relationship with reality other than keep very smart minds busy for centuries, yet other times, the link with reality becomes obviously clear, and most of our current technology would not be possible without it.

Lawrence takes us step by step through the creative processes of mathematical geniuses who solved ancient and new problems with sometimes completely creative approaches, opening new vistas for other scientists to go even a step further. This includes the amazingly long time it took to have a symbol for zero or for the equation, things which are so obvious today.

Maybe in stark contrast to other sciences, discoveries in math have usually been the result of the stubborn passion of individuals to find solutions for mind-boggling problems. I have used the approach of Kepler in some of my presentations: to make people understand that the earth is revolving around the moon, he forced his audiences to imagine they were looking at the earth from the moon, which gave a totally different perspective on how the planets rotated. This sudden change in perspective clarified everything.

From the early use of numbers to calculating in 24 dimensions, her story is accessible as it is fascinating. Her explanations and examples are sufficiently well explained for non-mathematicians to also enjoy the book, even if many will have trouble understanding how you can work in 4 or 5 dimensions, let alone in 24, but yes, today's math is capable of that. (More on my Blog "The Axe and the Frozen Sea" https://literatuur2.blogspot.com)

[Roberto Salgado · Rating 4 out of 5]

This is my third book from the "Little Histories" collection and my first book completely about history of math. Last year I read El lenguaje de las matemáticas. Historias de sus símbolos on the history of math symbols (also available in English now), and I had been looking forward to reading a book on math history. I found out that this one was released last year, and decided to give it a go.

The book is quite readable and meant for a wide audience, the author tries to introduce briefly some of the ideas without getting too technical or assuming too much background, although the later chapters involve some advanced abstract math that would be too hard to simplify and summarize, but still, the historical aspects are readable to almost anyone.

I appreciated the inclusion of less-known (at least to me) developments in other parts of the world like ancient China or Japan, as well as the inclusion of some female mathematicians like Emmy Noether and Maryam Mirzakhani, besides the usual big names in the history of math. Of course, given that it's just a "little history" book, there are topics and people who didn't get covered - or just got mentioned- but I still found the selection of people and topics good and the book well organized in short chapters, with pretty illustrations may I say.

I would totally recommend it to anyone interested in math history, with or without a background in related fields like engineering or math itself. I found a couple of typos and errors that hopefully will be solved in a future edition, but overall, is a very well-made book.

[Cornelius Harold · Rating 4 out of 5]

A Little History of Mathematics offers a clear and engaging overview of how mathematical ideas have developed across civilizations and centuries. Ian Stewart traces the evolution of mathematics from early counting systems and geometry to calculus, probability, and modern abstract thought. By connecting mathematical discoveries to historical contexts and individual thinkers, the book shows how mathematics grows through curiosity, problem-solving, and cultural exchange rather than sudden genius alone.

The strength of the book lies in its ability to make complex ideas understandable without oversimplifying them. Stewart explains concepts conceptually rather than technically, which makes the book accessible to readers without formal mathematical training while still remaining intellectually satisfying. At times the pace feels brisk, and some topics invite deeper exploration, but the book succeeds in presenting mathematics as a living discipline shaped by human imagination and persistence. It leaves the reader with a renewed appreciation for how deeply mathematics is woven into the way we understand the world.

For non-mathematics enthusiasts, this book would not give you headaches nor the derivation of Schrödinger’s equation, so don’t worry about the book being too complex to comprehend.

[Chris Jaffe · Rating 3 out of 5]

It's a decent overview. I had trouble understanding a lot of it in the second half of the book. It just plain over my head. I did pick up on some stuff in the first half. There's a nice point in the last chapter: mathematics is basically the study of patterns. Huh - never thought of it like that.

Some nuggets: There are three impossible problems of Greek antiquity: 1) how do you double the volume of a cube, 2) how do you trisect an angle, and 3) how do you square a circle (create a square with the same volume as the circle). Abelard translated Euclid, reestablishing him in western Europe. Fibonacci helped popularize Arab numerals in Europe. The Fibonacci sequence led to the golden ratio (a nice spiral). Even in late Medieval Europe, practical and metaphysical math were separating. There was graphing of coordinates before Descartes. A French mathemtician named Frncois Viete helped popularize modern algebra notation in the late 1500s. A Welsh mathematician named Robert Recorde gave us the equals sign in the mid-1500s. Logrithms were invented in 1614 (and I still have yet to really understand their purpose). Blaise Pascaul gave us the first real calcuating machine, around 1643-ish. This helped with the construction of boats, buildings, as well as helping with ballistics. Descartes combined geometric shapes and algebratic equations to create analytical geometry. Pascal invented probabilty theory with his triangle. There is also the invention of calculus. We get game theory much later on. Fractals help everythign from medicine to video games.

[Victoria Roberts · Rating 5 out of 5]

A brisk walk through the history of mathematics. It discusses what people knew at that time and how they were applying these concepts. It covers everything from the beginning of numbers, Euclidean geometry, algebra, calculus, and then goes into more advanced math like set theory, non-Euclidean geometry, and aperiodic tiling.
It's explains the concepts and their applications that are simple enough for beginners in math.

[Rachel Bare · Rating 5 out of 5]

Absolutely fantastic. Writing a math book without using actual mathematical proofs has to be so hard and this was pretty well done. Even the beginning chapters where really fundamental math was discussed were still presented in interesting ways. I wish there was more about the contexts of some developments and how it impacted its time more broadly. Otherwise, it was great.

[Justin Evans · Rating 4 out of 5]

Very pleasant, even for someone like me who only knows maths from other popularizing books. My main complaint is the lack of a 'Further Reading' section, which, to Lawrence's credit, I desperately needed for a number of chapters, which were very interesting but, by design, very short.

[Aina · Rating 3 out of 5]

cute

[Abram · Rating 1 out of 5]

https://abramreviewsbooks.substack.co...

[James Robinson · Rating 3 out of 5]

first non-fiction read in a good while, i thought it was paced well and had a good mix of actual maths and history. Learnt alot from it. 7/10

[gracefullyreading · Rating 5 out of 5]

learned and felt connected a lot! not a math genius but the subject never fails to mesmerize me😍 and being able to learn more about its history is even more mind blowing! my professor was right, it’s truly the queen of sciences. btw, i missed listening to my professor’s little talk about the history of math during class because i’m no longer in her class, so reading this kinda heals my longing