The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

by Clifford A. Pickover

The Neumann Prize–winning, illustrated exploration of mathematics—from its timeless mysteries to its history of mind-boggling discoveries. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, The Math Book covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic is lavishly illustrated with colorful art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

Genres: Mathematics, Science, Nonfiction, History, Reference, Stem, History Of Science

877 pages, Kindle Edition

First published September 1, 2009

About the author

Clifford Alan Pickover is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research Center in Yorktown, New York, where he was editor-in-chief of the IBM Journal of Research and Development. He has been granted more than 700 U.S. patents, is an elected Fellow for the Committee for Skeptical Inquiry, and is author of more than 50 books, translated into more than a dozen languages.

Reviews

[Sean · Rating 4 out of 5]

The first thing I did when I picked up this book was look up Kovalevskaya in the index. As in Sofia Kovalevksaya, mathematical genius and pioneering female mathematician and academician of the 19th century. And there she was, a full page on one of my heroes. Weierstrass's unsung research partner. The first woman in Europe to obtain a doctorate in mathematics and only the third female full professor. This article and the article on Emmy Noether (a female mathematical genius of even higher stature than Kovalevskaya) almost made me cry at my desk at the library. So inspiring.

This book is gorgeous. The 250 articles, ranging from the pre-mathematics of several thousand years ago to cutting-edge mathematical research, are uniformly light and short and are written at a level that most laypersons would understand. Each is illustrated with a full-page mathematical drawing or rendering, a reproduction of a historical document, or a portrait of the subject.

I find that most people don't understand what mathematics is. They get caught up in the notation and the symbols and the algorithms and the nerdiness and they miss out on the beauty and the wonder of the subject. This book will not actually teach anyone mathematics, but maybe it'll light a spark!

[Jim Leckband · Rating 4 out of 5]

The target audiences for these books must be very selective, but I think they have a strategy that enables them to sell more of them than they would by the subject and writing itself. If this was a book of the author writing on the greatest hits of mathematics with a page devoted to each and where the reader needs to be almost 90% of the way there in terms of being able to understand the subject matter at any level - then very few copies would be sold. The mathematics described in this book are of the highest levels. Pickover does a very good job for the most part of the general gist of each milestone, but sometimes he just misses it - because the point in question is so arcane and indescribable in words.

So back to the strategy. The publishers have each milestone paired with a high quality (almost schmaltzy) illustration of the milestone facing the words. The illustrations are sometimes fascinating to gaze at on their own, but sometimes they are just graphic design placeholders (like 3D type of greek letters - big whoop!). In any case, this strategy puts an arcane math text into a coffee table book - and broadens the audience from solely math geeks, to those who want to show off their intelligence and interests via book bling. It seems the publishers read up on their Venn diagrams among other things!

[Grant · Rating 2 out of 5]

I found the book too much of a tease, where it would explain the most intuitive concepts that didn't need to be explained and then skip over the more interesting complex things. Introducing the most notable mathematical contributions is a great idea, but two hundred is far too many to remember or appreciate given the limited text.

[Aniek Kaasbanaan · Rating 2 out of 5]

Eindelijk uit...
Dit is duidelijk niet het soort boek om als een leesboek te lezen.

[Robert · Rating 3 out of 5]

There were a few quirks in the presentation of this book that annoyed me but might not be noticed by anyone else.

The structure of the book is to have 3 or 4 paragraphs that explain discuss introduce mention a favorite topic of the author on the left page and an illustrative picture on the right. Each picture has an explanatory blurb at the bottom of the left page. Here is the annoyance: Most of the time the blurb simply repeated a few sentences from the 3 or 4 paragraphs of text above. I thought that was lazy.

I have a background in engineering and finance so I have taken lots and lots of math and statistics courses. This book was interesting because so many of the topics dealt with number theory and topology, two topics that are not covered in engineering or finance. Problems in number theory are often easy to state, since they normally only involve positive integers, but difficult to solve. I would guess that 90% or so of these topics involved prime numbers. Here is the thing that bugged me: Every single time he mentioned prime numbers, he explained what prime numbers are using the exact same sentences. Every time. I thought that was lazy too. If there was one thing you could actually learn from this book, it is how to recognize a prime number.

On the other hand, even problem statement in topology involves a lot of opaque language about abstruse concepts. Annoyance #3: When he introduced topology problems, he breezily threw around "invariant," "Hilbert space," and "n-dimensional symmetry" like they were every day topics at lunch. Maybe they are, but I don't hang out with that crowd. I'm only annoyed because I did not feel like going to another source to try to understand what he was talking about. Brian Greene would have found a way to explain it.

Annoyance #4: The author had a tendency to involve religion more than I would have thought to be strictly necessary. For example, if a mathematician under discussion was Jewish, he mentioned it. He did not comment on any other religions unless it was because a mathematician was Jewish and then converted. He also used angels as the actors in his examples instead of, for instance, "person A" or "John."

There are lots of glossy pictures and it is a nice jumping off point for a lot of topics that you've never heard of before 3/5 stars.

[Derek Donahue · Rating 2 out of 5]

Pros:
every other page has a picture.
A diverse selection of math milestones.

Cons:
Every milestone is only a page and what the author writes can sometimes be highly interesting and cool, but most of the time it wasn't. The author has a poor sense of what should make it into a book.

[Eric Hamilton · Rating 2 out of 5]

More of a history book than a useful dive into actual math topics. Would have been more interesting if each topic was a few pages long (and less topics overall) - with each topic making an attempt to describe and/or teach the reader about the topic. Instead every page is a brief overview of the topic and how it helped our lives - which is interesting, but not interesting enough for a book of this size.

[Richard Holmes · Rating 2 out of 5]

Way too superficial bits about too many topics. I'd rather read a full discussion of one tenth as many subjects.

[Will Seith · Rating 2 out of 5]

This is nothing more than a coffee table book for people with a degree in mathmatics

[Moloy De · Rating 3 out of 5]

Ok

[Lthmath · Rating 4 out of 5]

The author has set a big goal for this book: discussing different mathematical breakthroughs from B.C up to 2007. It is hard to briefly describe them and make it interesting for the general public, but the book is delivering it.

It is very interesting how the author decided to attach an image to every aspect. You will find everything from paintings, graphs, photos, drawings. I consider that the images for each topic are so good and they just give so much more to the text-description. With this book, it just shows how much an image does to understanding mathematics and its applications.

Moreover, this book does such a good job at talking about the applications of different mathematical concepts into other fields. Even if there are just a short mention at the end of a page or something, I observed that the author didn't stop at the basic examples and gave full on details about some aspects.

On the other hand, the book might seem boring from time to time if you are not completely griped by the topic described. Short descriptions are important for getting the general idea, but they might seem a little dry from time to time. I recommend you give yourself some time in between seatings for this book. Read a couple of pages at a time and them do some research on your own for the most interesting aspect you discovered (check the "Notes and Further Reading" at the end) and so on. You might bet more from the book if you do it this way.

[Eric · Rating 4 out of 5]

Awesome book for anyone interested in the history of mathematics and its major breakthroughs. A great tribute to the immense impact mathematics has had on society. It’s presented in bite-sized chapters, which some may not like since it only really scratches the surface of most of the topics covered, but in my opinion it offers an ideal jumping off point for any topics that the reader wants to take a deeper dive into.

[A J · Rating 5 out of 5]

i really like this

[David · Rating 5 out of 5]

Un libro impresionante. He tardado medio año en leerlo, por que a cada página tienes un montón de información para indagar e investigar en profundidad. Hay ciertos temas que son bastante complejos de entender si no eres matemático o tienes conocimientos muy avanzados, aún así Clifford Pickover lo redacta de la forma más simple y fácil de comprender.

[Edward Wendt · Rating 4 out of 5]

An excellent introduction to the history of mathematics and what it holds for our future. I have previously read another book in this series, The Space Book, and this book is a bit harder to grasp, though maybe rightfully so as the concepts here are often deeper than what the average reader will know. With a decent though uneducated appreciation of mathematics, this book was hard at times to grasp as the author leads into the unknown through the presentation of formulas only. It is still a fascinating read, just one that might be easier a little bit at a time, as it takes some time to digest.

[Steve · Rating 5 out of 5]

Do you like Math? Do you like History? Do you like Math History?

If the answer to any of the above was "no", then this is a book with a serious chance of changing your mind.


This book is essentially a highlight reel of math history. With a quick page-long summary (coupled with some interesting art), the author briefly explains some mathematical development, how it happened, who did it, and occasionally an amusing little side note to the history as well.

The topics covered range from the fairly well known (Pythagorean Theorem, Euclidian Geometry, Invention of the Abacus...) to things that sound made up (Hairy Ball Theorem, for one). Generally explained in a straightforward, easily comprehensible manner, most readers should gain at least a modicum of understanding, aside from perhaps the most obtuse topics in the book.

Highly recommended.

[Matt · Rating 2 out of 5]

I read The Math Book cover to cover, but perhaps a better experience would be just to flip through and find topics that look interesting. If you go through chronologically, it's very dull. I was hoping to get more of a sense of the historical development of mathematical ideas and concepts. I also wish it had more on practical applications of concepts.
In my opinion, Pickover doesn’t do a great job of conveying a sense of wonder or excitement about these mathematical topics. The Math Book didn’t make me interested in anything I was not already aware of and interested in. This will be a nice addition to my classroom library (I'm a high school math teacher) because it's best experienced in short doses.

[Liezie · Rating 4 out of 5]

After 1 year, 1 week and a lot of toilet visits it is finally finished. :)

I'm very glad I bought it. I found it very interesting.

The writer doesn't always succeed to explain the complex matter into terms I understood, but most of the time he does. And it doesn't always stick to the theories, often it just tells about the scientists behind the science, the times they lived in, what practical fields it is used in, why it is important, ...

You do not have to have a scientific background to like this book, you only have to be interested in science.

[Brian Bohmueller · Rating 3 out of 5]

An enjoyable glimpse of math history, though lacking in enough detail too often. Thanks youtube for more in depth explanations of the more interesting vignettes.

I was a bit dismayed at the author's antiquated use of AD and BC vice CE and BCE...pure math is universal and at should be its temporal reference points.

[Scottekim]

Fabulous math book, one of the best. What a great format: gorgeous picture on one page, one-page essay on facing page, chronicling 250 milestones in math history. Far ranging, very deep, yet coffeetable book accessible. I learned a lot from this book, and I'm an experienced mathematician.

[Jessica · Rating 4 out of 5]

Fantastic collection of topics and beautiful illustrations. Warning: If you are looking for a book that gives in-depth explanations of mathematical concepts, this isn't for you: each topic is only given a page of rather large text, so the explanations are often shallow.

[Juan Fuentes · Rating 3 out of 5]

Recorrido de la historia de las matemáticas a través de 250 hitos cronológicamente ordenados. Desde el podómetro de las hormigas hasta el universo matemático. Pasando por los clásicos: espiral de Arquímedes, teorema de Fermat, teoría de grupos, axiomas de Peano, transfinitos

[Abhishek Shekhar · Rating 4 out of 5]

A good book for references to all important Math works. Must for those who like or used to like Maths :)

[Álvaro (Alvy) · Rating 5 out of 5]

One of the best math books I've ever read. Every chapter is deeply interesting, many are not too well-known and is a complete history of maths from the very beginnings.

[ניקאָלע · Rating 5 out of 5]

Amazing, but could do without the explanations of what prime numbers are every four pages.

[Prabidhik KC · Rating 5 out of 5]

This book is a must-read for any Math lovers. The earlier you read, the better it is. It amazingly shows the beauty of mathematics from its history to till date.

[Behrooz Parhami · Rating 4 out of 5]

This is a great book, with many strengths and a few weaknesses. As the author readily admits on p. 15: "This is not a comprehensive or scholarly dissertation, but rather it is intended as recreational reading for students of science and mathematics and interested laypeople." The "recreational-reading" objective explains the blending of some lightweight material with deep results. The book consists of self-contained articles, presented in chronological order, each consisting of one page of text and one page of graphics. In a majority of instances, however, the graphics are decorative, providing little in way of illustrating the concepts or making them easier to understand.

Having discussed the weaknesses, let me shift my focus to the book's strengths. Pickover, the prolific author of 40+ books, has a gift for describing mathematical concepts in accessible form. On p. 14, the author whets the reader's appetite by promising answers to a number of intriguing questions:

- Why was the first female mathematician murdered?

- Who was the "Number Pope"?

- Who was the earliest named individual in the history of mathematics?

The very first idea ("Ant Odometer," p. 15), dating back 150 million years, concerns the way ants have evolved to be able to return home along a straight line, after traveling along a winding path in search of food. They accomplish this feat using their sense of direction and their ability to count steps. If an ant's legs are artificially shortened or lengthened before its return trip, it either does not reach its nest or overshoots it.

The final entry in the book, "Mathematical Universe Hypothesis" (p. 516), describes the work of MIT Physics Professor Max Tegmark, who hypothesized in 2007 that our universe isn't just described by mathematics—it is mathematics! "[W]e don't invent mathematical structures—we discover them, and invent only the notation for describing them."

From among the other 248 entries, let me describe just one: "Andrica's Conjecture" (p. 482). If p(n) is the nth prime number and g(n) = p(n+1) – p(n) is the gap between p(n) and the next prime p(n+1), then g(n) < 2 sqrt(p(n)) + 1. Put another way, sqrt(p(n+1)) – sqrt(p(n)) < 1. This relationship remains an unproven conjecture, but it is believed to be true based on empirical evidence.

I was particularly intrigued by three entries describing ideas from Persian mathematicians/philosophers. On p. 84, we read about "Al-Khwarizmi's Algebra" (830 CE), the first book on the systematic solution of linear and quadratic equations. Then, on p. 94, "Omar Khayyam's Treatise" (1070 CE), having to do with solving third-degree and some higher-order equations, is discussed, as well as his writings on properties of non-Euclidean geometries, an area that did not flourish until the 1800s. Ghiyath al-Din Jamshid al-Kashi's "Law of Cosine" (ca. 1427 CE), which relates the side lengths of a triangle and the cosine of the angle opposite to the side of length c by the identity c^2 = a^2 + b^2 – 2ab cos(C). The latter identity includes the Pythagorean theorem c^2 = a^2 + b^2 as a special case corresponding to C = 90 degrees.

Pickover's fascinating book ends with 8 pages of notes, providing details and references for the entries, a 2-page index, and one page of photo credits.

[Max McKinnon · Rating 4 out of 5]

Fun book. Not as good as the physics one, namely because it’s even harder to describe math in laymans terms than it is physics. Same author.

The psychology and philosophy ones from this series were awful. Was glad this one was decent.

My biggest complaint is the summaries almost never contain math. Sometimes a bit of math and a bit of english is way simpler than trying to dumb it all down for the reader.

Lots of cool things I learned through this that spawned hour long googling sessions to read more, such as Sprouts, game of life, lie group, non-euclidian geometry (interesting Einstein claims his familiarity here was key to general relativity, the warpage of space time), gauge geometry, Erdös’s crazy but uniquely awesome lifestyle, Gödel’s proof for god (but he didn’t publish it for a while, because he didn’t want his peers to think he was an idiot that believed in god! Hahaha), Penrose tiles, knots, chaos, public key cryptography, attractor, quaternions (if you put General Relativity into quaternion form, apparently Maxwell’s equations come out of it!), Mandelbrot, group theory, instant insanity, ulam spiral, sierpinski numbers, newcomb’s paradox, Turing (what a badass, way ahead of his time - really sad what happened to him. His Turing test being a metaphor for a homosexuality test while at the same time having so much notoriety for the mark of ai is just so genius.), Noether’s Idealtheorie

The best part of this book I am using from now on are amphibious numbers. You know, the solution to the poly x2 + 1? (Descartes popularized the term imaginary number as an insult to the idea - boo!)

[Joaquin Armijo · Rating 4 out of 5]

Gran libro. El autor nos lleva por un camino en donde nos introduce y nos enseña la mayoría de los descubrimientos mas importantes de las matemáticas durante la historia de la especie humana. Me gustó mucho que haya temas muy variados, a pesar de que el libro "solo" sea de matemáticas y que tenga mas de 500 páginas, no se te hace tan repetitivo, ya que, abarca un gran abanico de las ramas de la matemáticas. Creo que fue una muy buena idea que cada concepto tenga su propia ilustración o imagen, ya que, se hace mucho mas fácil enteren todo. El autor trata de explicar desde la forma mas básica distintos conceptos matemáticos, pero a pesar de esto, hay algunos capítulos en donde encontré que el nivel requerido era muy alto, única rozan por la que no le puse 5 estrellas. En conclusión, es una lectura que recomiendo mucho a todas las personas que tengan un conocimiento básico y que les gustan las matemáticas, porque se van a encontrar con cosas que los fascinarán.

[Paulo García · Rating 5 out of 5]

Este libro, en una bonita edición, nos presenta 250 acontecimientos relacionados con la matemática, con una ordenación cronológica y de áreas distintas de esta disciplina. Hubo unos temas que me resultaron más conocidos que otros y, en general, me parece clara la exposición que realiza de cada uno. Básicamente dedica dos páginas a cada uno, en la primera presenta aspectos relacionados con un objeto, concepto, teorema o conjetura, entre otros y en la siguiente una imagen alusiva al tema que aborda. Lo anterior genera que, posiblemente, los temas puedan seguirse profundizando más (al final el autor menciona fuentes de información para los temas, aunque también se pueden investigar en otras fuentes).

Lo veo más como un libro para ir disfrutándolo poco a poco que para ser leído de "corrido". A su vez, es un esfuerzo por divulgar la belleza de las matemáticas, su relación con otras disciplinas y acercar a las personas a esta área del conocimiento.