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Ponderables: 100 Discoveries that Changed History, Who Did What When
Mathematics - An Illustrated History of Numbers
Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was even born, but the story begins long before that, with tally marks on rock and bone surviving from the Stone Age.
Here is the essential guide to mathematics, an authoritative reference book and timeline that explores the work of history's greatest mathematicians. From the teasing genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, to the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes, here are 100 landmark moments in this intensely rigorous discipline, seen through the eyes of the people who lived them.
Glimpse the abstract landscape of infinite numbers and multi-dimensional shapes as you learn about the most famous math men of all. Pythagoras had a love of numbers so strong it led to a violent death. Then there is Fibonacci, whose guide for bookkeepers changed the way we add and Descartes, who took inspiration from a fly to convert numbers into shapes and back again, changing math forever.
Over many centuries, great minds puzzled over the evidence and, step-by-step, edged ever closer to the truth. Behind every one of these breakthrough moments there's a story about a confounding puzzle that became a discovery and changed the way we see the world. Here are one hundred of the most significant and we call these Ponderables. In Mathematics: An Illustrated History of Numbers, you'll get a peak into the Imponderables, too, the mysteries yet to be solved that will one day lead great thinkers forward to an even greater understanding of the universe.
Includes a removable fold-out concertina neatly housed in the back of the book. This fold-out provides a 12-page Timeline History of Mathematics that embeds the story in historical context and shows Who Did What When at a glance. The reverse side features some of the greatest mathematical enigmas and interesting facts about the world of numbers.
Here is the essential guide to mathematics, an authoritative reference book and timeline that explores the work of history's greatest mathematicians. From the teasing genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, to the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes, here are 100 landmark moments in this intensely rigorous discipline, seen through the eyes of the people who lived them.
Glimpse the abstract landscape of infinite numbers and multi-dimensional shapes as you learn about the most famous math men of all. Pythagoras had a love of numbers so strong it led to a violent death. Then there is Fibonacci, whose guide for bookkeepers changed the way we add and Descartes, who took inspiration from a fly to convert numbers into shapes and back again, changing math forever.
Over many centuries, great minds puzzled over the evidence and, step-by-step, edged ever closer to the truth. Behind every one of these breakthrough moments there's a story about a confounding puzzle that became a discovery and changed the way we see the world. Here are one hundred of the most significant and we call these Ponderables. In Mathematics: An Illustrated History of Numbers, you'll get a peak into the Imponderables, too, the mysteries yet to be solved that will one day lead great thinkers forward to an even greater understanding of the universe.
Includes a removable fold-out concertina neatly housed in the back of the book. This fold-out provides a 12-page Timeline History of Mathematics that embeds the story in historical context and shows Who Did What When at a glance. The reverse side features some of the greatest mathematical enigmas and interesting facts about the world of numbers.
144 pages, Hardcover
First published October 1, 2012
32 people are currently reading
387 people want to read
About the author
Tom Jackson
632 books56 followers"I'm a non-fiction author and project editor (plus I do a bit of journalism). I'm available for project development, writing, project management and I also work as a packager. Click on the links above to see examples of my work.
But first some background: Over the last 20 years, I've written books, magazine and newspaper articles, for online and for television. I get to write about a wide range of subjects, everything from axolotls to zoroastrianism. However, my specialties are natural history, technology and all things scientific. I've worked on projects with Brian May, Patrick Moore, Marcus de Sautoy and Carol Vorderman and for major international publishers, such as Dorling Kindersley, National Geographic, Scholastic, Hachette, Facts on File and BBC Magazines.
I spend my days finding fun ways of communicating all kinds of facts, new and old, to every age group and reading ability. I live in Bristol, England, with my wife and three children. I studied zoology at Bristol University and have had spells working at the zoos in Jersey and Surrey. I used to be something of a conservationist, which included planting trees in Somerset, surveying Vietnamese jungle and rescuing buffaloes from drought-ridden Zimbabwe. Writing jobs have also taken me to the Galápagos Islands, the Amazon rainforest, the coral reefs of Indonesia and the Sahara Desert. Nowadays, I can be found mainly in the attic."
~http://tomjackson.weebly.com/
But first some background: Over the last 20 years, I've written books, magazine and newspaper articles, for online and for television. I get to write about a wide range of subjects, everything from axolotls to zoroastrianism. However, my specialties are natural history, technology and all things scientific. I've worked on projects with Brian May, Patrick Moore, Marcus de Sautoy and Carol Vorderman and for major international publishers, such as Dorling Kindersley, National Geographic, Scholastic, Hachette, Facts on File and BBC Magazines.
I spend my days finding fun ways of communicating all kinds of facts, new and old, to every age group and reading ability. I live in Bristol, England, with my wife and three children. I studied zoology at Bristol University and have had spells working at the zoos in Jersey and Surrey. I used to be something of a conservationist, which included planting trees in Somerset, surveying Vietnamese jungle and rescuing buffaloes from drought-ridden Zimbabwe. Writing jobs have also taken me to the Galápagos Islands, the Amazon rainforest, the coral reefs of Indonesia and the Sahara Desert. Nowadays, I can be found mainly in the attic."
~http://tomjackson.weebly.com/
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Displaying 1 - 30 of 33 reviews
January 18, 2018
Thanks to this book, I finally understand the difference between an irrational number and a transcendental number :) While I enjoyed this overview of math concepts and significant mathematicians throughout the ages, I must admit that many instances of poor editing (comma splices, run-on sentences, oddly-constructed sentences) did distract at times from the content. Also, I found several new-to-me topics which were covered with such brevity that I was left without any sort of a clear picture of their significance. Still, overall an enjoyable read.
July 28, 2022
This book gave me exactly what I wanted: a broad overview of the basic concepts of mathematics.
I was good at math and liked it when I was a child, but math and I parted ways when I took trigonometry in my sophomore year of high school. The class was first thing in the morning, when I was barely awake, and as soon as we got into imaginary numbers, I completely lost the plot. My counselor generously offered to switch me to remedial math class, which was the last math class I ever took.
I studied humanities in college and became a high school English teacher. In the years since I gave up on math, I've found myself time and again wishing I was better acquainted with the "universal language of numbers." I'm a musician and deeply appreciate the mathematical beauty reflected in music theory. I also love reading books about quantum mechanics and wish I had a better grasp of math so I could appreciate the quantum equations in their native language.
Whenever English students asks me if I can help them with their math homework, I have to tell them that if I "help," it'll just make their grade worse.
In order to address all of these issues, I recently started doing a math lesson a day on Khan Academy, and when I saw this book I bought it, hoping it would give me the big picture idea of the concepts that make up mathematics.
The book did just that. It was easy to read. I read a page a day, along with my Khan Academy lesson, and I know I feel like I have a much better sense of where I'm headed in my journey toward mathematical competence.
I was good at math and liked it when I was a child, but math and I parted ways when I took trigonometry in my sophomore year of high school. The class was first thing in the morning, when I was barely awake, and as soon as we got into imaginary numbers, I completely lost the plot. My counselor generously offered to switch me to remedial math class, which was the last math class I ever took.
I studied humanities in college and became a high school English teacher. In the years since I gave up on math, I've found myself time and again wishing I was better acquainted with the "universal language of numbers." I'm a musician and deeply appreciate the mathematical beauty reflected in music theory. I also love reading books about quantum mechanics and wish I had a better grasp of math so I could appreciate the quantum equations in their native language.
Whenever English students asks me if I can help them with their math homework, I have to tell them that if I "help," it'll just make their grade worse.
In order to address all of these issues, I recently started doing a math lesson a day on Khan Academy, and when I saw this book I bought it, hoping it would give me the big picture idea of the concepts that make up mathematics.
The book did just that. It was easy to read. I read a page a day, along with my Khan Academy lesson, and I know I feel like I have a much better sense of where I'm headed in my journey toward mathematical competence.
July 28, 2022
An overall enjoyable read, I liked it. This is a decent introductory text which makes mathematics accessible for those taking their first steps into the world of math. At times, however, I found that the brevity of this text could be detrimental to the text's underlying objective, i.e. explaining the developmental timeline of mathematics to a popular audience. Some concepts in the modern mathematics section warranted greater elucidation than was provided for the intended target audience, which may explain a common critique here on Goodreads that this book seems to struggle with identifying exactly who it's for.
Finally, I consider the "history" component of this book to be somewhat lacking. The history of mathematics is rich, dramatic, and often spectacularly petty. I wish this would've been highlighted (rather than squeezed into the margins) by presenting the contributions to mathematics in a way which placed more emphasis on the climate and parties of the research community across time. Give me the Newton-Leibniz drama in all its glory. The Cantor denouncement by Kronecker and Poincaré. Anything relating to Galois. Mathematical invention is the product of these relationships between thinkers over time, and it's impossible to gain a complete picture of what mathematics has become without first seeing where/who these ideas came from.
Finally, I consider the "history" component of this book to be somewhat lacking. The history of mathematics is rich, dramatic, and often spectacularly petty. I wish this would've been highlighted (rather than squeezed into the margins) by presenting the contributions to mathematics in a way which placed more emphasis on the climate and parties of the research community across time. Give me the Newton-Leibniz drama in all its glory. The Cantor denouncement by Kronecker and Poincaré. Anything relating to Galois. Mathematical invention is the product of these relationships between thinkers over time, and it's impossible to gain a complete picture of what mathematics has become without first seeing where/who these ideas came from.
August 13, 2023
A concise and accessible journey through a hundred of the key concepts in the field of mathematics. Topics covered range from early counting methods right the way through to Einstein's General Relativity and beyond. The usual suspects (ie, the Greek philosophers, Newton, Descartes, Pythagoras) are present as expected, but some of the lesser known mathematicians and scholars are represented in this book.
As to be expected, other scientific disciplines are touched upon mainly to highlight the importance the mathematical concepts have had on each. For example astronomy, quantum mechanics, chemistry, but even topics such as genetics and epidemiology are touched upon.
While I suspect those with more than merely a casual interest in mathematics may find this book lacking in substance and brief, it provides a perfect whistle-stop tour of the history of the subject for most readers.
As to be expected, other scientific disciplines are touched upon mainly to highlight the importance the mathematical concepts have had on each. For example astronomy, quantum mechanics, chemistry, but even topics such as genetics and epidemiology are touched upon.
While I suspect those with more than merely a casual interest in mathematics may find this book lacking in substance and brief, it provides a perfect whistle-stop tour of the history of the subject for most readers.
December 14, 2024
Where are the women?
July 24, 2018
Mathematics: an Illustrated History of Numbers is what it says it is. I somewhat realize that I say that a lot, but generally if you can judge a book by its cover that is considered a good thing; though only when it comes to books. So the book seems to be part of a series called Ponderables. I don’t think I have read any of the other books in the series, but I suppose it is worth pointing out. Since the book is Illustrated there are images and pictures that represent the ideas listed in the book.
The book is organized chronologically. It starts with the ideas of Learning to Count, Positional Notation, the Abacus, and so on. Each idea is treated to a paragraph or some other bit of coverage that demonstrates its importance. Some ideas get more coverage or a longer entry. Take the idea of the Pythagorean Theorem. Since it did not exactly originate from Pythagoras, one may wonder how it became named after him. According to the book, he was probably the first one to demonstrate a proof of it. Meanwhile, other entries might only be around half a page in length. This does not necessarily show that this entry is of less importance. Take the entry on the Rhind Papyrus. It is half a page in length, shows a picture of it, and talks about what it contains.
Further on in the book it eventually gets to The Renaissance and beyond. This book is pretty simplistic, but that doesn’t make it bad. It explains some things in a way that seems to skip over some information, but it is difficult to really go through it that much.
The book is organized chronologically. It starts with the ideas of Learning to Count, Positional Notation, the Abacus, and so on. Each idea is treated to a paragraph or some other bit of coverage that demonstrates its importance. Some ideas get more coverage or a longer entry. Take the idea of the Pythagorean Theorem. Since it did not exactly originate from Pythagoras, one may wonder how it became named after him. According to the book, he was probably the first one to demonstrate a proof of it. Meanwhile, other entries might only be around half a page in length. This does not necessarily show that this entry is of less importance. Take the entry on the Rhind Papyrus. It is half a page in length, shows a picture of it, and talks about what it contains.
Further on in the book it eventually gets to The Renaissance and beyond. This book is pretty simplistic, but that doesn’t make it bad. It explains some things in a way that seems to skip over some information, but it is difficult to really go through it that much.
July 10, 2022
This book can’t decide on it’s target audience. Basic concepts are described multiple time (which is fine), but then complex concepts are discussed without much introduction, and in several cases, theorems etc are referenced with no description at all. Maybe I should add that I’m a physicist and was lost in some of this.
Disturbingly, the book makes it seem like all of math comes from European men (with the exception of a couple of references to early Middle Eastern and Indian math/mathematicians). Three women are mentioned briefly in the whole book, despite coverage of programming and code breaking, which were both female-dominated at one time - not mentioned even in passing. Even Emmy Noether doesn’t warrant a mention.
Here’s a list of some important/ accomplished female mathematicians. Links at the bottom of the page lead to African, African American, and Islamic mathematicians.
https://mathshistory.st-andrews.ac.uk...
Disturbingly, the book makes it seem like all of math comes from European men (with the exception of a couple of references to early Middle Eastern and Indian math/mathematicians). Three women are mentioned briefly in the whole book, despite coverage of programming and code breaking, which were both female-dominated at one time - not mentioned even in passing. Even Emmy Noether doesn’t warrant a mention.
Here’s a list of some important/ accomplished female mathematicians. Links at the bottom of the page lead to African, African American, and Islamic mathematicians.
https://mathshistory.st-andrews.ac.uk...
December 12, 2022
Great coffee table book on mathematics! I learned quite a few fun facts along the way, and expanded my understanding of the different fields of mathematics along the way. It's a fun and easy read I'd recommend.
August 28, 2025
This book is a coffee table book listing top 100 math concepts, terms, milestones, events, and topics with about 1-2 pages each. It tracks history of math from the earliest - from basics of counting and Euler/Archimedes to the most recent decade. Topics are collections of math concepts, math proofs, key numbers, application of math to physics, and legendary mathematicians. For a person familiar with high-school math, half of it will be familiar, but there are some pithy interesting anecdotes to maintain interest. However the book is better suited to kindle interest for a smart middle-schooler or junior-schooler (age 8-14) who has at least passing interest to pick up this book. Often though, the content is short so that beauty and complexity may not impress the reader. An easy read in few sitting and couple of hours, full of colourful pictures, the book is a solid three-star rated.
July 10, 2023
An excellent first third of the book, history of the thought and philosophy of mathematics with accessible content. I have a bachelor science in Economics with a year of calc, year of stat, semester of finite. The math gradually pulled away from my ability to master the concepts as the book progressed. It is obvious the author loves math, as I do, the book is well illustrated, funny, witty and insightful. The math in the latter part was just cognitive overload for me.
As a middle school social studies teacher I will be using many excerpts from the book as examples of societal contributions to culture, adding to my cross curricular content.
As a middle school social studies teacher I will be using many excerpts from the book as examples of societal contributions to culture, adding to my cross curricular content.
April 9, 2025
Still reading through this series of Ponderables because if I remember just one thing, I'll be smarter for it and this one is no different than the others. It's about math. And reading several of them in a row I realized that there is overlap but it is approached differently in each one because it's about a different overarching topic.
Mathematics covers topics like game theory and proof by computer in addition to pi and e.
I was curious, as is everyone it seems, about our Russian friend Perelman who solved the French mathematician, Poincare,'s 1904 conundrum. Perelman solved it 98 years later but refused awards, commendations, or money for proving it.
Mathematics covers topics like game theory and proof by computer in addition to pi and e.
I was curious, as is everyone it seems, about our Russian friend Perelman who solved the French mathematician, Poincare,'s 1904 conundrum. Perelman solved it 98 years later but refused awards, commendations, or money for proving it.
May 23, 2025
meh...if the internet did not exist, maybe this book is more valuable. it just very short one to four paragraphs on bear 100 important discoveries in science but they are often presented clumsily and don't really generate that much interest for me. If you want to know something like the history of algebra, quantum mechanics, or a quick timeline of math history, you are better off doing an intenet search for it.
August 24, 2019
It took me forever to finish the book but reading this was a delight. Though some of the topics were a little advanced for me, I got to learn a lot from this book. Basically, it's not for everyone, you need to have a mathematical background to understand it all.
November 15, 2022
A very nice coffee table book for the layman. Some topics don't have much detail, and frankly it would be asking too much for the intended audience. A really nice way to see how modern math grew out of people counting livestock on clay tablets thousands of years ago.
November 13, 2025
I studied mathematics, and it was interesting to realize just how much of this book I was actually taught in my undergrad and graduate programs. From stories of Galois being killed in a duel to how some theorems came into existence, this really covered a lot of mathematical history.
March 8, 2019
169 - 2019
September 4, 2019
Very entertaining summary of greatest mathematical concepts.
December 23, 2019
A great overview of the most important discoveries in mathematics!
August 15, 2021
Very entertaining for what it's for. Nicely presented and well told.
December 13, 2024
More of a coffee table book, this accurate volume present a collection of 100 big ideas in mathematics, roughly in chronological order.
January 6, 2019
“The Universe offers an unending stream of new mathematical puzzles to explore, and mathematicians have never stopped looking for patterns both in numbers and in the real world.
Counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math.
The Pythagorean Theorem was used to plot out fields for planting crops before the Ancient Greek Pythagoras was even born. ‘Mathematics, an Illustrated History of Numbers tells the fascinating story behind mathematical discoveries.
* Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell.
* The largest number the ancient Greeks envisioned was a myriad ‘myriad’ which is 100 million, but the 1920s a nine-year-old coined the word Googleplex, 10googol, a number so large it can never be written down.
* The great German mathematician Georg Cantor showed that there is an infinite number of infinities.
* One of the central tools of statistics was developed in 1898 when Ladislaus Bortkiewicz, a Russian mathematician, computed the odds on a Prussian cavalryman being killed when kicked by a horse.”
In general this book is nice and easy to read without complicated equations. I’d read it to my daughter, a nine years old, and she enjoyed the explanations and she looked at each illustrations with enthusiastic! At the end, on the back cover of the book you will find a ‘Time History Of Math’ bookelet with a contend of “Culture, World Events, Science & Invention, Mathematics, from 4000 BCE—1000 BCE
Enjoy it if you read it!
Counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math.
The Pythagorean Theorem was used to plot out fields for planting crops before the Ancient Greek Pythagoras was even born. ‘Mathematics, an Illustrated History of Numbers tells the fascinating story behind mathematical discoveries.
* Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell.
* The largest number the ancient Greeks envisioned was a myriad ‘myriad’ which is 100 million, but the 1920s a nine-year-old coined the word Googleplex, 10googol, a number so large it can never be written down.
* The great German mathematician Georg Cantor showed that there is an infinite number of infinities.
* One of the central tools of statistics was developed in 1898 when Ladislaus Bortkiewicz, a Russian mathematician, computed the odds on a Prussian cavalryman being killed when kicked by a horse.”
In general this book is nice and easy to read without complicated equations. I’d read it to my daughter, a nine years old, and she enjoyed the explanations and she looked at each illustrations with enthusiastic! At the end, on the back cover of the book you will find a ‘Time History Of Math’ bookelet with a contend of “Culture, World Events, Science & Invention, Mathematics, from 4000 BCE—1000 BCE
Enjoy it if you read it!
January 13, 2013
review via Cracking the Cover
I’ve always loved books that tell the history behind things, that explain elements in smaller snippets yet still go into detail. So I was excited when I received a copy of “Mathematics: An Illustrated History of Numbers.”
The coffee-table book is more than 100 pages and features various illustrations, pictures, charts and graphics. Following an introduction, it’s divided into four sections based on time/advances: prehistory to the middle ages; the renaissance and the age of enlightenment; ne numbers, new theories; and modern mathematics. A section on “great mathematicians” is also included.
An added bonus is a 12-page removable timeline that features key moments in culture, world events, science and invention, and mathematics dating from 4000 B.C. to today. On the other side of the timeline: all sorts of mathematical enigmas (games, paradoxes, primes, problems, etc.) and a chart of mathematical symbols.
“Mathematics: An Illustrated History of Numbers” isn’t the type of book you read cover to cover — unless you’re a true math geek, of course — rather, it’s best paged through, stopping at your areas of personal interest. Though some of the topics may at first appear over your head, the authors have made them accessible. The writing is well done and there’s not too much jargon to wade through.
Bottom line: Not only is this book interesting, it’s fun, too.
I’ve always loved books that tell the history behind things, that explain elements in smaller snippets yet still go into detail. So I was excited when I received a copy of “Mathematics: An Illustrated History of Numbers.”
The coffee-table book is more than 100 pages and features various illustrations, pictures, charts and graphics. Following an introduction, it’s divided into four sections based on time/advances: prehistory to the middle ages; the renaissance and the age of enlightenment; ne numbers, new theories; and modern mathematics. A section on “great mathematicians” is also included.
An added bonus is a 12-page removable timeline that features key moments in culture, world events, science and invention, and mathematics dating from 4000 B.C. to today. On the other side of the timeline: all sorts of mathematical enigmas (games, paradoxes, primes, problems, etc.) and a chart of mathematical symbols.
“Mathematics: An Illustrated History of Numbers” isn’t the type of book you read cover to cover — unless you’re a true math geek, of course — rather, it’s best paged through, stopping at your areas of personal interest. Though some of the topics may at first appear over your head, the authors have made them accessible. The writing is well done and there’s not too much jargon to wade through.
Bottom line: Not only is this book interesting, it’s fun, too.
January 18, 2014
A coffee table book about mathematics? Why not? I spent a couple of very agreeable evenings paging through this lavishly illustrated book about 100 important ideas in mathematics. Some of the entries could be understood by anyone with a high school math education, some were more about ideas (chaos theory, game theory) and some I gave up reading after two lines (topology, Poincare). The format of 100 items worked for me; I drifted from one to another, reading this, reading that. The illustrations were gorgeous and chosen with care. Not just portraits of mathematicians, or graphs, or pictures of cones and Moebius strips and things like that, but wonderful reproductions of pages from old mathematics books, maps, globes, representation of the cosmos. A book that can be enjoyed by non-mathematicians. As a matter of fact, my 9-year old son saw me reading this book and drifted over and for a while we read together. This is one of those books where, after you've read it, you feel you've learned something, you feel you've become smarter. I would be hard pressed to pinpoint what exactly I've learned -I am certainly no closer to understand the Fast Fourier Transform than I was before - but it's a lovely feeling to have. So in my opinion this book deserves four stars.
January 18, 2014
This was a perfect introduction book done even better with illustrations & photographs. The closest thing I've come to a mathematics coffee table book, the tome went through 101 different areas and aspects of mathematics and illustrated them. At no point is any of the introductions enough to whet anyone's whistle, but they're there enough for you to note the ones that interest you for further reading. Very well done!
May 26, 2020
A good selection of topics and not a bad book overall, but I did spot a couple of factual errors regarding some of the content I know a lot about, leaving me less convinced that the content I don't know so much about is trustworthy. With a bit of proofreading and an update to correct the mistakes this would be a lovely addition to any coffee table.
January 9, 2015
This is an excellent introductory book to mathematics. However it really is introductory and doesn't have enough explanations or graphs beyond fairly short descriptions. For example: on the topic of Poisson's distribution, the book doesn't even include a sample graph.
June 16, 2013
NIce little coffee book covering the history of mathematics.
July 1, 2013
I love it when my boys are an interest for what I do. Each of us are finding things that is interesting and cool for ourselves as we read it iget her. ;-) this book has became our summer family read.
July 23, 2013
Beautiful illustrations. Very factoid driven and superficial but a great simple overview.
Displaying 1 - 30 of 33 reviews