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 ^_^
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
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Apr 07, 2026
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