The Quickest Way to an Existential Crisis in Your Math Education

... is to skip over computational practice and lose touch with the concrete meaning of things.

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Famous last words of math learners before they fall off the rails in higher math:

“I don’t need to practice computations. That’s what abstraction is for.”

Sure, proofs involving eigenvalues/eigenvectors might just use Av = λv and that’s it. You might just replace A with PDP^-1 and not have to actually calculate a diagonalization.

But you know what these proofs are going to feel like if you have no experience calculating these things?

Pushing meaningless symbols around, in arbitrary patterns of allowed manipulations, without really knowing what you’re talking about.

The quickest way to an existential crisis in your math education is to skip over computational practice and lose touch with the concrete meaning of things.

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