How does anyone learn linear algebra taught via matrices? Like, I don't think I could understand what was going on in 18.06 if I hadn't taken Math 55a first, and I have a PhD in math. I can't imagine how confused the poor undergraduates must be.
I appreciate papers like Bluffing in Scrabble, arXiv:2509.10471:
It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the optimal strategy involves bluffing, or even a Scrabble position in which the optimal strategy is a mixed (i.e., randomized) strategy. We present a carefully constructed Scrabble position, that could actually arise in a tournament game with no invalid words played, in which the optimal strategy (assuming that a tied score leads to the point being split equally, with no recourse to so-called "spread points" as a tie-breaking mechanism) is to make Move A with probability 1/3 and to make Move B with probability 2/3. Move B can reasonably be called a bluff, in the sense that it sets up a threat which the player cannot in fact execute, but which the opponent may not be able to rule out.
After all these years, there are some MO problems for which I don't remember anymore how I came up with the solution, and others for which I definitely do. I like it when my students ask me about the latter and not the former, because I'm lazy and it's less work for me to answer their question.
Wouldn't it be convenient if those also turned out to be the more instructive problems? I'm secretly hoping that this laziness happens to causes me to have better taste in problems, but I don't think I'd be able to test that.
So Claude Code actually outputted reasonably good Asymptote code for me today, which is a surprise to me, because usually the LLM's are really bad at Asymptote.
I was trying to convert the following into Asymptote:
\begin{circuitikz}[american]
\node (P) at (0,0) [left] {$P$};
\node (Q) at (13,0) [right] {$Q$};
\draw (P) to[short] (1,0);
\draw (1,0) to[short] (1,1) to[R=$x\,\Omega$] (3,1) to[short] (3,0);
\draw (1,0) to[short] (1,-1) to[R=$\frac{1}{3}\,\Omega$] (3,-1) to[short] (3,0);
\draw (3,0) to[short] (4,0);
\draw (4,0) to[short] (4,1) to[R=$y\,\Omega$] (8,1) to[short] (8,0);
\draw (4,0) to[short] (4,-1) to[R=$\frac{1}{3}\,\Omega$] (6,-1) to[R=$\frac{1}{3}\,\Omega$] (8,-1) to[short] (8,0);
\draw (8,0) to[short] (9,0);
\draw (9,0) to[short] (9,1) to[R=$z\,\Omega$] (11,1) to[short] (11,0);
\draw (9,0) to[short] (9,-1) to[short] (9,-2) to[R=$\frac{1}{3}\,\Omega$] (11,-2) to[short] (11,0);
\draw (9,-1) to[R=$\frac{1}{3}\,\Omega$] (11,-1);
\draw (11,0) to[short] (13,0);
\end{circuitikz}
The output from Claude
actually worked.
Though the most jarring part is probably the presence of import olympiad; at the top.
A lot of Asymptote users from the AoPS math contest community... it shows.
I cleaned up the output and posted it here.
Some real Ace Attorney material here:
In one of nature’s most remarkable convergent evolutions, koalas have developed fingerprints that are virtually indistinguishable from human fingerprints, even under electron microscopes. ... Each koala possesses unique fingerprints, just as humans do, with distinctive whorls, loops, and arches.
Snopes says this doesn't seem to have happened yet.