Please reply in the comments with things you understood recently. The only condition is that they have to be useless in your daily life. For example, "I found this idea that defeats procrastination" doesn't count, because it sounds useful and you might be deluded about its truth. Whereas "I figured out how construction cranes are constructed" qualifies, because you aren't likely to use it and it will stay true tomorrow.
I'll start. Today I understood how Heyting algebras work as a model for intuitionistic logic. The main idea is that you represent sentences as shapes. So you might have two sentences A and B shown as two circles, then "A and B" is their intersection, "A or B" is their union, etc. But "A implies B" doesn't mean one circle lies inside the other, as you might think! Instead it's a shape too, consisting of all points that lie outside A or inside B (or both). There were some other details about closed and open sets, but these didn't cause a problem for me, while "A implies B" made me stumble for some reason. I probably won't use Heyting algebras for anything ever, but it was pretty fun to figure out.
Your turn!
PS: please don't feel pressured to post something super advanced. It's really, honestly okay to post basic things, like why a stream of tap water narrows as it falls, or why the sky is blue (though I don't claim to understand that one :-))
...and Leonid Andreyev's The Black Masks. (I'm on the phone, so have not Googled it, sorry.) 'The God our Lord placed the sword in my hands, and with death I punished the mad Lorenzo, and yet he was a knight'...
There's quite a lot of Andreyev's work available in English. Some translations are apparently in the public domain as they are available for free on Amazon in ebook form. I don't really enjoy reading plays as a rule (The Black Masks is a play, I believe), so I downloaded the novella The Seven Who Were Hanged. It'll be a while before I get around to reading it, as my reading list is fairly long (and getting longer, thanks to your great suggestions!).
Is The Seven Who Were Hanged a good introduction to Andreyev?