Updated: Dec 16, 2020
Hello everybody! I've been quite busy lately, but I thought I'd write something everybody can enjoy this week! Today's article is going to mirror my series on my favorite math videos (feel free to check out part 1 or part 2 here) but we're focusing on books!
I've actually compiled a lot of my favorite books in the resources section of this site already, and I've written a lot over there about how to find a specific recommendation for a math book you would love, so make sure to check that out after you read this article! (You'll have to become a member if you aren't already to see it, and I welcome all members.)
Even so, I thought I'd dedicate an article to books because the recommendations I've received for math books truly shaped how I think about math and look at the world, and I know these books would be extremely valuable for all of you as well! My math book collection is nearing 100 at this point, and I'd love to share parts of my bookshelf with you. These are mostly books about the fun, exciting work that mathematicians do on a daily basis and about the beauty of math behind that, but I've thrown in my favorite book for math competitions if you're into that kind of thing too.
If you have other recommendations or suggestions, feel free to leave them in the comments. I've limited this article to my top eight books, but I have so many more I love, so again, hop on over to resources for even more of my favorites.
Without further ado, let's begin!
1. Here's Looking at Euclid by Alex Bellos
How better to start than with one of the first full-length math books I ever read? This book is the length of a novel, and it made me fall in love with all the intricacies of the math world, and it pretty much began my math book collection.
Alex Bellos takes us on a journey through various topics of recreational math, including origami, a hotel with infinite rooms, and 4D crochet. Not only are the topics themselves intriguing and thoughtful, but he tells the stories through the words of various interesting people he meets throughout the course of the novel, including the godfather of Sudoku and a man who believes he can predict the future by reading numbers like a crystal ball. It's such a witty and amusing book, and you'll come away from this one with a love of problem-solving and admiration for the world around you.
There's actually a sequel called The Grapes of Math, which has even more compelling stories.
2. How to Bake Pi by Eugenia Cheng
This book explores mathematics through a unique lens: food. It is about category theory, described as the "mathematics of mathematics," which is the study of how math works. Understandably, the "math of math" can get pretty abstract, but Cheng does an incredible job of making it digestible.
Each chapter starts with a recipe, typically for a dessert, and breaks down math into its essence: logical, creative, and sweet. Cheng questions logic itself: can it be too powerful? Can the predictions we make be too strong? She asks about jigsaw puzzles and tourism and crème brûlée.
Not only is category theory a topic so rarely explored, but Cheng attacks it from such a witty direction, and you're sure to enjoy this tasty math book.
Cheng has since written several more books, including Beyond Infinity: An Expedition to the Outer Limits of Mathematics, The Art of Logic in an Illogical World, and even X+y: A Mathematician's Manifesto for Rethinking Gender, which came out just last week and which I'm so excited to read! She's such an accomplished mathematician and author and has even shown up in The New York Times time and time again, and I think all of you would love to read her books!
3. Fermat's Enigma by Simon Singh
This book explores one of history's most compelling problems: Fermat's Last Theorem.
If you know the Pythagorean Theorem, you'll know that there are plenty of solutions for x^2 + y^2 = z^2 where x, y, and z are all integers. Indeed, 3^2 + 4^2 = 5^2. But what if we raise these integers to higher powers?
Fermat's Last Theorem states that there are no solutions to x^n + y^n = z^n for integer x, y, and z with n>2. It's a statement that seems simple enough, but yet, it could not be solved until recently.
The story of Fermat's Last Theorem goes a little something like this: The mathematician Pierre de Fermat claimed to have a proof of the elusive theorem, but nobody could prove it for more than three centuries after his death. Mathematicians searched and searched for centuries, and finally, the now-famous Andrew Wiles managed to prove it in 1993 after seven years toiling in his attic. In fact, when Andrew Wiles' proof was reviewed by other mathematicians, an error was found in the proof, and Andrew Wiles had to live another year in agony—struggling but ultimately succeeding to close the gap.
The interesting thing about this problem is the math that goes into it has only been discovered very recently, involving new types of math in objects called "elliptic curves" and "modular forms," so it is quite possible Fermat never found a proof in the first place—or perhaps, if he did, there's still a simpler one out there somewhere.
Fermat's famous words in the margin of a book when his theorem (along with the claim he proved it) was found, "I have discovered a truly remarkable proof of this theorem which this margin is too small to contain," have become something of mainstream mathematical folklore, and what better place to learn such an amazing story than in the words of Simon Singh, one of the best science journalists out there?
It's a wonderful book, and I think you would all enjoy it! I'm hoping to write a GLeaM article on Fermat's Last Theorem at some point, and I'm excited to tell you more about this incredible story.
For the time being, I'll just happily inform you that there happens to be a musical on Fermat's Last Theorem. Go ahead and search up Fermat's Last Tango on YouTube if you're so inclined!
4. Hidden Figures by Margot Lee Shutterfly
I'm sure most of you know the story of Hidden Figures by now. The popularity of the 2016 movie was able to bring exposure for several black women mathematicians that worked for NASA during the space race and who played a crucial role in completing the calculations that sent men into space in the early Apollo missions.
What you might not know is this movie was a book first!
It's an amazingly well-written book, and the detail Margot Lee Shetterly puts into it is unmatched. There are so many heart-wrenching moments involving the terrible discrimination Katherine Johnson, Dorothy Vaughan, and Mary Jackson experienced, and so many triumphs in the power of the calculations they computed, all of which you can't quite get from the movie.
If you were in any way moved by the movie, I would recommend you check out this book! See if you can watch the movie too if you still haven't seen it.
Katherine Johnson herself recently passed away in February, and I think there is a lot of value in the perspective you would get reading this book after her death, especially given the increasing problem of discrimination against women in STEM in the workplace and even more importantly, the current state of racial relations in America.
5. Love and Math by Edward Frenkel
Love and Math gives such an eye-opening view into what math looks like to mathematicians.
Edward Frenkel, a famous mathematician at UC Berkeley, tells us stories of his personal experiences with math, and he paints pictures of his favorite fields in the subject, all in a labored effort to confront the general public's fear of math and show just how beautiful and essential the subject is.
He argues that math "directs the flow of the universe," and he pulls on the idea of art, comparing the tedious way schools teach math to ignoring the true masterpieces of the subject: "What if at school you had to take an 'art class' in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art?" No, certainly not, in much the same way multiplication tables don't make students appreciate math.
This book reads the most like a novel of all the ones on this list, and Frenkel weaves his personal narrative, some of the most fascinating and applicable gems of math, and his argument about the true nature of math, in such a marvelous way.
It's honestly hard to describe how well-written and compelling this book is. It's such a delightful read, and I'd highly recommend it to anyone.
6. So You Think You've Got Problems? by Alex Bellos
This is a book I actually bought pretty recently, but I absolutely love it! (If you've been reading the recent articles, maybe you've seen how often I've been referencing it.)
It's a collection of the best puzzles and problems out there! Bellos has pulled from so many different sources to bring a book of the most delightful problems to solve and the most intriguing questions to answer.
You can find some examples of these problems that I cited in my last two articles, which were my own compilations of some of my own favorite puzzles, including some from this book! You can check those out here: part 1 and part 2.
This is such a great book if you'd like to try your hand at some problems as you read it, and these are the most clever, mind-blowing puzzles I've ever seen.
7. The Art of Problem Solving, Volume 1: The Basics and Volume 2: and Beyond by Sandor Lehoczky and Richard Rusczyk
I told you I'd throw in my favorite books for math competitions, and here they are! If you're looking to excel in the AMC, MathCounts, or any other math competitions, these two volumes will teach you absolutely everything you need to know! (There are four books pictured because the solutions come separately to the volumes.)
I've talked about how valuable the Art of Problem Solving is in the past, but just in case you still want to know more about all the company AoPS does for the math community, from classes to books to forums that you can participate in, check out www.artofproblemsolving.com.
Volume 1 is great for anybody who has never done math competitions in the past or is just beginning, and Volume 2 is amazing for anybody who wants to hone their skills further.
If you're just starting out in math competitions, I have a lot more advice about how to get started, so just reach out if you want any more help!
8. Things to Make and Do in the Fourth Dimension by Matt Parker
I'm ending on one of my favorites to date! Matt Parker is a wonderful mathematician who does a great job explaining math to a popular audience through his frequent appearances on the YouTube channel Numberphile and his own channel standupmaths, and this book is no exception!
This is a witty, thoughtful exploration of so many fields of math, including shapes of constant width, knot theory, and the domino computer, and of course, the fourth dimension! Written in a casual, anecdotal style, this book is a fun, whimsical introduction to the world of recreational mathematics, and there are so many gems in this book, including exciting concepts, like taxicab numbers, amicable numbers, and triangles which somehow have angles that add up to more than 180 degrees!
Matt Parker has since written a couple of other books, and I'd definitely recommend Humble Pi: When Math Goes Wrong in the Real World as well, which discusses when math errors have immense consequences in day-to-day life—from mistakes in elections to air traffic control to the Internet.
That's it for today! Thanks for reading everybody and have a wonderful day. Leave any questions or comments in the comments section or in the forum, and remember to check out the Resources section for more book recommendations!