How Pi Almost Wasn’t

Since you’re reading this essay, you probably already know about the mathematical holiday called Pi Day held on March 14th of each year in honor of the mystical quantity π = 3.14…. Pi isn’t just a universal constant; it’s trans-universal in the sense that, even in an alternate un … | Continue reading


@mathenchant.wordpress.com | 1 day ago

Dedekind’s Subtle Knife

“Think about the knife tip. That is where you are. Now feel with it, very gently. You’re looking for a gap so small you could never see it with your eyes, but the knife tip will find it, if you put your mind there. Feel along the air till you sense the smallest little gap […] | Continue reading


@mathenchant.wordpress.com | 25 days ago

The Real Line versus the Fakes

There’s a pretty thought experiment that’s sometimes attributed to Democritus though it’s actually due to a later popularizer of the atomic hypothesis1 and it goes like this: Suppose we use the world’s sharpest knife to cut a block of cheese in half, leaving two small blocks wher … | Continue reading


@mathenchant.wordpress.com | 1 month ago

When 1+1+1 Equals 1

There are mathematical operations of all kinds with the property that doing the operation twice is tantamount to not doing anything at all. Such operations are called involutions, and you can find them all over the place in math: taking the negative of a number, taking the recipr … | Continue reading


@mathenchant.wordpress.com | 2 months ago

Can Math Save Your Soul?

“No simplicity of mind, no obscurity of station, can escape the universal duty of questioning all that we believe.” — William K. Clifford “Nobody knew math could be so complicated.”— nobody ever The most truthful — and, to me, the most infuriating — thing a certain public figure1 … | Continue reading


@mathenchant.wordpress.com | 3 months ago

Industrious Dice

I’m a professional mathematician. That means somebody pays me to do math. I’m also a recreational mathematician. That means you might have to pay me to get me to stop. Wearing my recreational mathematician hat – quite literally, as you’ll see – I gave a talk earlier this year on … | Continue reading


@mathenchant.wordpress.com | 4 months ago

Our Fractional Universe

(by this month’s guest-columnist, Jeff Glibb) An esoteric branch of math called fraction theory may hold the answers to science’s deepest mysteries You may think you know what numbers are. Chances are, you learned to count before you entered kindergarten, and number-names like “o … | Continue reading


@mathenchant.wordpress.com | 5 months ago

Math for English Majors and Everybody Else

Ben Orlin’s charming new book Math for English Majors: A Human Take on the Universal Language is a welcome addition to the growing fold of books about math for non-mathematicians – though I have to say, speaking here as an ally of English majors everywhere, that I vehemently prot … | Continue reading


@mathenchant.wordpress.com | 6 months ago

When 1+1 Equals 1

dedicated to Norman Skliar and Sidney Cahn In an earlier blog-essay, When 1+1 Equals 0, I explained how 1 + 1 = 0 makes sense in mod 2 arithmetic; today I’ll tell you how the equation 1 + 1 = 1 makes sense in Boolean arithmetic and became a tool for designing the complex digital … | Continue reading


@mathenchant.wordpress.com | 7 months ago

Math’s Mutable Rules

John McWhorter, one of my favorite public intellectuals, writes (in his recent essay “Lets chill out about apostrophes”), “Writing does not entail immutable rules in the way that mathematics does.” I think he’d be happy to know that some of the rules that govern mathematical form … | Continue reading


@mathenchant.wordpress.com | 8 months ago

Zero-to-the-Zero and the Do-Nothing Machine

I’m sure you know how to add and multiply counting numbers, but did you ever add or multiply sets of things? Did you ever raise one set of things to the power of another set of things? If you never did, you should. These things are fun, and fun is good. And, if you’ve ever wonder … | Continue reading


@mathenchant.wordpress.com | 10 months ago

The Muffin Curse

Here’s a small puzzle that opens the door to a surprisingly tricky general problem: How can a teacher divide 24 muffins among 25 students so that everyone gets the same amount to eat but nobo… | Continue reading


@mathenchant.wordpress.com | 4 years ago

Between the World and the Mind

The wizard’s-cap graphic that appears at the top of my blog as part of the logo is a piece of an infinite mathematical surface called the pseudosphere. I don’t study the pseudosphere in… | Continue reading


@mathenchant.wordpress.com | 5 years ago

Calculus Is Deeply Irrational

You’re lying on a beautiful beach when you feel a tap on your shoulder, and suddenly you’re not at the beach at all — you’re in a classroom. The student who woke you looks apologe… | Continue reading


@mathenchant.wordpress.com | 5 years ago

Stance and distance in popular writing about math

Here’s something you’ll never see in popular writing about musicians: Music. For most of us, the mere word conjures up memories of metronomes and endless scales, the student’s nev… | Continue reading


@mathenchant.wordpress.com | 6 years ago

Why Does Exploding Dots Work?

A few months from now, if James Tanton and his Global Math Project co-conspirators have their way, ten million schoolchildren will take a huge mathematical step from the twenty-first century all th… | Continue reading


@mathenchant.wordpress.com | 6 years ago

How to Be Wrong

“To be wrong, or not to be wrong?” That is the wrong question.  You are going to spend a lot of your time being wrong, especially if you become a scientist or mathematician.  The question is, are y… | Continue reading


@mathenchant.wordpress.com | 6 years ago

“Really Big Numbers”

A few years back I was disconcerted to hear a kid at my son’s preschool mention googol and googolplex. But what really shocked me was when, a year later, one of his kindergarten classmates dr… | Continue reading


@mathenchant.wordpress.com | 6 years ago

Prof Engel's marvelously improbable machines

When the path from a simple question to a simple answer leads you through swamps of computation, you can accept that some amount of tromping through swamps is unavoidable in math and in life, or yo… | Continue reading


@mathenchant.wordpress.com | 6 years ago