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
Christina Grossack
@hallasurvivor@sunny.garden
mastodon
4.5.9
math/music. she/they.
I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory.
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Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
@hallasurvivor@sunny.garden
·
16h ago
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Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
@hallasurvivor@sunny.garden
·
6d ago
@highergeometer @MartinEscardo
I would also like to read the paper (actually both papers) if they're available
I would also like to read the paper (actually both papers) if they're available
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Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
@hallasurvivor@sunny.garden
·
Apr 07, 2026
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 most n roots" we must have used commutativity somewhere... Can you find where? (I couldn't!)
I'll post solutions in a few days, but as always I'm curious to see how people approach this! Please reply with your thoughts, and boost if you think other people might be interested ^_^
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 most n roots" we must have used commutativity somewhere... Can you find where? (I couldn't!)
I'll post solutions in a few days, but as always I'm curious to see how people approach this! Please reply with your thoughts, and boost if you think other people might be interested ^_^
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Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
Christina Grossack
@hallasurvivor@sunny.garden
math/music. she/they. I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory. Leftist
sunny.garden
@hallasurvivor@sunny.garden
·
Mar 23, 2026
@francisbrb @highergeometer
I agree with this! Ryan O'Donnell used to do this for some of his papers (see here: https://www.youtube.com/@RyanODonnellTeaching/videos) and I loved watching them!
Also, if you recorded some videos explaining the basics of higher geometry I would ABSOLUTELY watch them (what are gerbes? what problem do they solve? how do you compute with them? etc. of course, for any topic you like -- gerbes are just an example).
I agree with this! Ryan O'Donnell used to do this for some of his papers (see here: https://www.youtube.com/@RyanODonnellTeaching/videos) and I loved watching them!
Also, if you recorded some videos explaining the basics of higher geometry I would ABSOLUTELY watch them (what are gerbes? what problem do they solve? how do you compute with them? etc. of course, for any topic you like -- gerbes are just an example).
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