October | 2025 |
1 post published by jamespropp during October 2025| mathenchant.wordpress.com
I’m a great believer in low-tech math. I don’t like to rely on things a computer tells me; what if there’s a bug in the code? I prefer trusting things that I can check for myself. At the same…| mathenchant.wordpress.com
Quick math-personality quiz: What is seven-and-one-fourth minus three-fourths, expressed as a mixed number (a whole number plus a proper fraction)? What matters isn’t what answer you get but how yo…| mathenchant.wordpress.com
“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…| mathenchant.wordpress.com
As a member of the Advisory Council for the National Museum of Mathematics (“MoMath”) over the past decade, I’ve had a number of unique opportunities, such as the thrilling chance to improve the Museum’s datebase via my smartphone and watch exhibit-content update in real-time, and the less thrilling opportunity to break an exhibit on the […]|
This past week I was saddened to learn of the death of mathematician and teacher David C. Kelly, the founder of the Hampshire College Summer Studies in Mathematics program (HCSSiM). “Kelly”, as everyone called him, had a huge impact not just on my career but on the careers of people spanning several generations. I knew Kelly […]|
“I couldn’t help but wonder…” — Carrie Bradshaw (in every episode of Sex and the City) The best birthday party I ever had as a kid was a trip to the Museum of Natural History in New York City with half a dozen like-minded friends and my indulgent parents. The huge dinosaur skeleton in the […]|
If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance […]|
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 universe with a different geometry than ours, […]|
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 reciprocal of a number, rotating an object by […]|
“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 com…| mathenchant.wordpress.com
monthly writings in and around mathematics by James Propp| mathenchant.wordpress.com
I thought my earlier essay on .999… did a pretty good of explaining why I (along with 99.999…% of mathematicians) say that it equals 1, until I asked some of my students what they got o…| mathenchant.wordpress.com
In ordinary math, the infinite decimal .999… is defined to be the limit of the terminating decimals .9, .99, .999, …; that is, it’s defined to be the real number that the fractions 9/10, 99/1…| mathenchant.wordpress.com
“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…| mathenchant.wordpress.com
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 wor…| mathenchant.wordpress.com
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 mak…| mathenchant.wordpress.com
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.”…| mathenchant.wordpress.com
No reckoning allowed save the marvelous arithmetics of distance (from Smelling the Wind by Audre Lorde) Suppose a child comes up to you and says “I know 1 is odd and 2 is even, but I think 4 is mor…| mathenchant.wordpress.com
How far would you go to save a theorem? Would you invent a new kind of number? That’s what the mid-19th century German mathematician Ernst Eduard Kummer did, and while he was partly driven by the h…| mathenchant.wordpress.com
To err is human; we all make mistakes. But some mistakes have worse consequences than others. According to Greek myth, King Sisyphus of Ephyra made the especially big mistake of cheating Hades, the…| mathenchant.wordpress.com
