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  In case you haven't seen it, here's a SUPER cool video where someone builds puzzles based on sporadic groups. In particular, the M12 puzzle looks VERY clean! I'm sure lots of people would find this interesting, but I think that @henryseg in particular would be REALLY interested! There's one based on M24 as well, which I'll leave as a surprise for those who watch the video 👀 https://www.youtube.com/watch?v=xwQ5dx4dE9g

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  Hmmm... Wondering if I should try and learn some condensed matter physics, lol

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  Just learned that the theory of generating functions can be seen as harmonic analysis on Z?? Then the usual way we use generating functions to solve recurrence relations is a special case of Fourier transforms turning translation into multiplication, which turns the recurrence relation into an algebraic equation! If you haven't seen this before, it's really fun to work out for yourself ^_^. Whether or not you've seen this before, post your thoughts here! If you alread...

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  It's kind of funny, I remember learning algebraic geometry and wondering why people would care about the derived pushforward R*f. I don't think I ever got an answer to that specific question -- I just learned so many reasons to care about derived functors broadly that now R*f seems inevitable... BUT ☝️ I finally have a 𝑟𝑒𝑎𝑙𝑙𝑦 good reason that I think would have satisfied younger me! If you're interested in sheaves then you're interested in their global sections, a...

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  It's finally done! Have a 3 part series on the topological topos First, let's talk about some fundamentals. How do we think of objects in the topos? How do we compute with them? How do they relate to objects in "the real world"? https://grossack.site/2024/07/03/life-in-johnstones-topological-topos Then, since post 1 is loooong, a little palate cleanser. It's a short post about how we can use the topological topos to more effectively study algebraic s...

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  I have a friend visiting me from out of town and he gave me this fun puzzle which COMPLETELY broke my brain! The quaternions are a "skew-field" in the sense that they satisfy all the axioms of a field, except they're not commutative. In the quaternions, we have a crazy fact: x²+1 has uncountably many roots! Puzzle 1: Can you find uncountably many roots of x²+1 in the quaternions? Puzzle 2: This means that in the proof of "a polynomial of degree n has at mo...

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  Just said "the situation is worse in the absence of inequality" in a meeting, lol. I was talking about the theory of an object vs the theory of a 𝑑𝑒𝑐𝑖𝑑𝑎𝑏𝑙𝑒 object, but I had to chuckle at how that sounds out of context, haha