Math Without Numbers (With Big Ideas)
This delightful book, written by a young mathematician, explores deep mathematical ideas with zero equations and plenty of imagination.
Hello and Happy Wednesday, Friends!
Today’s resource is a delightful math book that explores deep math ideas with zero equations and lots of playful illustrations.
Grant Sanderson, create of 3blue1brown, had this to say:
Math Without Numbers offers an accessible and whimsically illustrated glimpse of what pure mathematicians study, all while capturing the playful spirit with which they do it.
While writing this post, I looked at what the publisher had to say about it, and this quote made me laugh:
The only numbers in this book are the page numbers
This should give you an idea of what type of math book it really is.
Let’s dive in.
I. Resource of the Week: “Math Without Numbers” by Milo Beckman
If your kid loves thinking big but isn’t a fan of drills or worksheets, this is a book worth exploring together.
Title: Math Without Numbers
Author: Milo Beckman (a former “child prodigy” who captained the NYC math team at age 13 and went to Harvard at 15)
Target Age: 4th grade and above (younger kids might need some definitions explained)
Resource Type: Popular Math book for the general public
Here’s the publisher’s description of the book:
Math Without Numbers is a vivid and wholly original guide to the three main branches of abstract math - topology, analysis, and algebra - which turn out to be surprisingly easy to grasp. Milo Beckeman upends the conventional approach to mathematics, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. How many shapes are there? Is anything bigger than infinity? And can mathematics even be described as ‘true’?
And here’s a picture of the table of contents:
The author’s online presence is here:
Book: Penguin USA Website
Milo’s webpage: https://milobeckman.com
Milo’s YouTube Channel: https://www.youtube.com/channel/UCURP6q1VjGEFfy7GPP3Tm0w
II. What It Is
Per the photo of the table of contents above, this book covers College-level mathematical topics in a way that young people and non-math people can understand.
The book is broken into five parts covering Topology, Analysis, Algebra (not your high school kind), Foundations (of math), and Modeling.
To help you get a sense of where the book is going, the following illustration gives you a sense of how things are going to shape up:
Because there are no formulas, no computations, and no problem sets, Milo focuses on the big ideas with clever illustrations that give you a taste of the topic without getting bogged down in Definitions, Theorems, and Examples.
It reads like an immensely engaging TED Talk for math-curious Teens.
III. How We Used It at Home
We used it as an introduction to the mathematical subjects people study in college and beyond.
A postcard from a distant place you might visit someday, filled with fun and wondrous sights to see.
We wanted to get the kids excited about what comes next and show them that math keeps getting stranger and more exciting.
We did some chapter read-alouds as well as family “math discussions”.
We also had the kids explain back to us what they took away from it.
The only downside was the inevitable question of “when will we get to see this?” as the answer is mostly, “Well, in a few to many years, as you need to learn a whole bunch more math between now and then.”
This didn’t feel like a great answer, but we haven’t found any resources that bridge the gap between this book and the college or graduate-level classes/topics it covers, outside of doing the actual math in between.
That said, it did expose them to a whole range of math words and concepts they hadn’t seen before, and now they can discuss them.
And as they have gotten into Calculus, limits and Infinity start to pop up all over the place, so they have something to reference.
Here’s another photo from the book, this time talking about Infinity in the context of “Analysis” (which is a subject that studies the foundational underpinnings of calculus, exploring the “why” and “how” behind the computations)
Overall, a great read.
That said, what we didn’t do was watch the YouTube videos, so we’re going to be diving into that this week.
IV. Questions for Your Math Kid
How would you explain the math you’re learning without numbers?
If you had to use pictures to illustrate your math problems, what would you draw?
Can you draw a “map” of the math ideas you’ve recently learned?
V. Why I like This Resource
This book introduces kids (and adults) to the areas of mathematics that show up once you get past the calculus sequence.
This shows that math isn’t only about numbers, rules, and worksheets.
It shows us that math can be playful and visual.
On a meta level, I also really like the idea of being able to communicate what you’ve learned in a different way than you’ve learned it.
We often ask each other, “What would be another way to explain it?”, so you can imagine how much enjoyment we got out of this book.
If you’re looking for a book that gives your math kid something deeper to chew on, this one is worth checking out.
That’s all for today :) For more Kids Who Love Math treats, check out our archives.
Stay Mathy!
Talk soon,
Sebastian