He goes on to talk about exact sequences, cohomology, and more. Admittedly, the audience is relatively niche, since it assumes you already know about those topics, but for the right person it certainly scratches an itch!
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All images below were produced by AI, with me feeding it the quoted prompt. I was most curious about how helpful such a tool might be in creative work.
"A sloth playing a guitar, photograph 35mm lens"
It seems to try hard to keep an image consistent, often making creative choices to do so. I didn't ask for the cloud to be a wad of yarn, but given the prompt, it actually makes a ton of sense.
“Photo of a thunderstorm where lightning is made of yarn and raindrops are needles”
Likewise here, having a campfire warm the coffee also makes sense conceptually, even if it wasn't explicitly mentioned in the prompt.
"brewing a cup of coffee in the middle of the woods at midnight"
I'd like to tell you about a game/puzzle to help celebrate today.
We'll call it "Death's Dice".
(1/9)
Death finds you. You plead with him that it's too soon, and he agrees to a concession. Every year, he'll roll a set of dice, and if it turns up snake eyes (both 1's) he'll take your life, otherwise, you get one more year.
But it's not necessarily a normal pair of dice.
(2/9)
On the first year, both "dice" will only have two sides, numbered 1 and 2. So in that first year, there's a 25% chance of rolling snake eyes and ending things there.
There are so many people who have some great idea for a video or blog post or interactive experience that might help others learn a tricky topic, but who aren't sure where to start.
Going by the philosophy that the best way to start is to just start, this is a place to trade tips and ask questions of others in the same boat, and potentially find collaborators for what you're working on.
It's a very good question! What follows are many tweets attempting to answer in a possibly way-too-verbose manner. No pictures (sorry), but I'll trust in the readers' mind's eye.
Commentary from mathematicians is more than welcome at the bottom of the thread, which includes scattered thoughts on whether there's a purely geometric reason to expect any rotation to have complex eigenvalues, i.e. one that doesn't appeal to the fundamental theorem of algebra.
First, just answering the question, let's review the basics: What it means for an operator to have an eigenvector with eigenvalue λ is that the way this operator acts on that vector is to simply scale it by λ.