Can anyone define for me the \(\textit{heart}\) [over field k of a group acting on a thing that's probably regarded as a vector space at the moment]? I'm not familiar with the term and it's a bit tough to search for.

The OEIS tags certain sequences as "nice" (and I generally agree with it) but I think that "dull," "rotten," and "notniceatall" could also be useful.

"Twisty Puzzle" seems to be common parlance for Rubik's cube and its many descendents, but I think we need to start using the term "scrambly puzzle" for stuff like the 15-puzzle, Segerman's 15+4 puzzle, and other stuff where you mix up pieces but the mechanism isn't twisting.

There was a link on MetaFilter to Quazel, a site which promises to let you practice conversation in the language of your choice with an AI bot. Here's as far as I went:

Quazel [speaking aloud]: "Hallo! Mein Name ist Unterstrich Unterstrich Unterstrich Unterstrich Unterstrich Unterstrich Unterstrich. Wie ist dein Name?"
Me [through mic]: "Bitte duzen Sie mich nicht."
Quazel: "Es tut mir leid, ich wollte dich nicht verärgern."

Puzzle/Problem: An \(n\times n\) square grid is filled with the numbers 1 through \(n^2\). A cell in the grid is a local maximum if its value is greater than all of its orthogonally-adjacent neighbors. Let \(M(n)\) denote the expected value for the number of local maxima when the grid is filled randomly.
(a) Compute \(M(4)\)
(b) Evaluate \(\displaystyle\lim_{n\to \infty} M(n)/n^2\)

(I decided this was too easy to send off to journals, but I don't think it's a total no-brainer.)

Working on implementing a tile-sliding game that I researched with students a while back. It's a little twist on the usual 15-puzzle type of thing, which you can play on your favorite 3-regular graph.

Perhaps one should distribute the ordinal over the addition and say "nth plus 1st"

(I have, in practice, settled on writing (n+1)-st because saying "one-th" aloud is just too abrasive for me.)

How do you "ordinalize" the expression (n+1)? Do you say (n+1)st, or (n+1)th, or... what?

It's a heartbreakingly beautiful day outside; once I would have set work aside and jumped on my bike for the afternoon, without a care.

One has more cares these days.

Are... are these images GENUINELY related to a search for ["142/13" random walk] somehow?

Spot the image that was thrown into this (quite interesting) article solely to distract any border collies who might be trying to learn enough mathematics to start publishing.

I'm not sure there's any better feeling than going back to a project you had to shelve for a long time and finding that your past self LEFT THINGS WELL-DOCUMENTED AND ORGANIZED for future self to pick up and resume without friction.

Nice problem from Mathematics Magazine (#2150): Find the maximum area of a triangle whose vertices lie on the cardiod \(r=1+\cos \theta\)

Installed manim today.

"Dad, can we get 3blue1brown?"
"No, we have 3blue1brown at home"

Neat discussion of colors on the Commodore 64 (happy 40th anniversary year) and other 8-bit computers.

I would assume that's someone who specializes in forging rings of power.

Topologists: Don't bore us, get to the torus

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