James Propp @JimPropp
I'm a professor at UMass Lowell. I write a monthly blog called Mathematical Enchantments (https://t.co/8oUk5ueVoN). Sometimes I’m facetious w/o using smileys. Joined December 2015-
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Here's a more symmetric and satisfying one.
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Here's another dynamic Hamiltonian circuit. This one visits 16 moving points on 8 circles; the points form diameters of the 8 incircles of the faces of an octahedron. The circles alternate rotation direction around each vertex. The circuit has constant length!
I was mistaken. "Nested Loops" does indeed have the property that the length doesn't change. (Though perhaps I'm still mistaken; I'm modeling it as a single loop, but the title of the piece suggests that there are several.)
The inspiration for this came from Chuck Hoberman's "Nested Loops" exhibit. I used ChatGPT to search the space of possible solutions in which total length doesn't change (I'm pretty sure that "Nested Loops" lacks this property). youtube.com/watch?v=e4sARe…
A loop joins eight moving points on four circles in such a way that the length of the loop remains constant.
Here's another constant-length dynamic Hamiltonian path using six circles.
My latest Mathematical Enchantment, "Solving the Flat Cube", describes a new puzzle devised by Oskar van Deventer, Dmitry Andreev, and me, and shows how sometimes you can solve a math problem by adding a dimension OR by throwing a dimension away. mathenchant.wordpress.com/2026/08/19/sol…
"Nested Loops" is on display at the National Museum of Mathematics in New York City. The exhibit in an easily-overlooked spot, so if you have trouble finding it, ask a docent.
David Kelly is no longer with us (see mathenchant.wordpress.com/2025/06/17/rem…) but Yellow Pig Seventeen lives on!
The world's worst way of writing the integer four just dropped. See my latest Mathematical Enchantment, "What Bad Bases Are Good For": mathenchant.wordpress.com/2026/07/19/wha…
Watch a cancer cell drink itself to death, thanks to Dr. Louise Chow’s work on catastrophic macropinocytosis and my daughter Eliana’s animation. If you like it, please Like it! youtu.be/jC1R8hSzAqs
In my latest Mathematical Enchantments essay, Seventeen Camels and Where They Can Take You, six seemingly unrelated brain-teasers can be solved using a single elegant trick. mathenchant.wordpress.com/2026/06/15/sev…
To take it a step farther, consider joining the \begin{proof} community: begin-proof.com
Consider signing the Leiden Declaration: leidendeclaration.ai
I'm delighted to report that I've been chosen to be a Radcliffe Institute Fellow for 2026-2027. I'll spend the year conducting research on tilings and completing a first draft of my book "What Can Numbers Be?". radcliffe.harvard.edu/news-and-ideas…
The first half is a mathematically correct discussion of models of growth (exponential vs. logistic) in a fictional context. The second half uses the same scenario to show that sometimes there are more important things than being mathematically correct.
In this month's Mathematical Enchantment, a math-and-science writer named Jim Propp, inhabiting a variant of the fictional Project Hail Mary universe, confesses to his pivotal role in the impending end of all life on Earth, and kind-of sort-of apologizes. mathenchant.wordpress.com/2026/04/18/sor…
Learn how a stupid question led to an interesting, albeit spectacularly useless, way to estimate pi by tossing a coin many, many times, in this month's Mathematical Enchantments essay, "In Praise of Stupid Questions". mathenchant.wordpress.com/2026/03/12/in-…
Hexagons in Harvard Square, #6. Who knows where I took this photo?
Writing in The New Yorker earlier this month, Stephen Witt said matrix multiplication is ugly. Is he right? Check out my take at mathenchant.wordpress.com/2025/11/21/is-…
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