It’s basically impossible to know all of the important concepts and results in mathematics. It’s impossible to even have *heard* of all of the important concepts and results in mathematics. For example, I’d never heard of expander graphs, which apparently have widespread applications in combinatorics and computer science, and even have an interpretation in terms of group representations.

Michael Nielsen has a series of posts on expander graphs beginning here. For more background, he links to lecture notes on the subject by Linial and Wigderson.

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