If you haven't stumbled across [Fields medalist] Richard Borcherds' YouTube channel yet, it's a trove of mathematical lectures at various levels.
Grid Paint (https://grid-paint.com/) is annoying in requiring a sign-in, but is otherwise a delightful and minimal browser-based tool for playing with polyforms, among other uses.
I often use unsolved/open problems in math as a discussion point with, especially, younger students (late elementary or middle school), but also college-age students with little math exploration outside the calculus-focused school curriculum). Too many of my examples are from number theory. So I'm soliciting problems that are comprehensible to young students, invite play and curiosity, but aren't primarily about integers.
Nice little bit of card-shuffling mathematics, but also an excellent presentation that takes advantage of the medium.
The ninth of my A-to-Z topics this year was Imaginary Numbers. Yes, I found the Peanuts strip where Sally Brown imagines "overly-eight".
Also the one where that plush tiger has some suggestions.
Maybe Mandelbrot images are clichéd by now, but these videos from Maths Town are a pleasant way to space out and calm down for a few minutes.
Oh, according to the appendix, that one is actually proven, not just conjectured.
Interesting paper on computer-generated conjectures regarding continued fraction representations of mathematical constants.
In particular, Figure 2 shows a really splendid (conjectural) representation of \(e\). I gave up trying to figure out how to type it readably here.
Note, looking into this is officially preparation for one of my fall classes. Work work work.
Matthew Seymour has done more incredible work in service of the connection game Hex, this time in the form of a beautifully-implemented collection of 500 "white/black to play and win" puzzles of the sort that chess and go enthusiasts take for granted as study tools:
The most recent Mathematical Gazette has some really lovely articles. If you have access to the Gazette at all, I can recommend these two:
Herzlich Willkommen in Minnesota!
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