Awesome post over on The Big Questions by Steven Landsburg about polynomial equations and correspondences (just isomorphisms) between trees and n-tuples of trees.
There is a isomorphism between, for example, seven-tuples of trees and one-tuples, but not between single trees and pairs, or singles and triples, etc, etc.
Amazingly, it sort of turns out that by thinking of the class of one tree as a variable, writing a polynomial equation using the same variable and solving for its root, you can create some algebraic equations that provide the results of these theorems. Weird!, and definitely worth a read.
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