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Mathematicians could do a better job of conveying their topics, but this is really not the case. Some things are just genuinely hard, and the research frontier in mathematics is one of these. If you could produce a 5-page proof of an important theorem that currently has a 100-page proof, you would be hailed as a hero.

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There’s really a lot more to it than that. There is a notion of “polite mathematics” which is independent of the difficulty of the proof.

If every step clearly follows from the prior steps it’s rather immaterial how long the proof is. Similarly a short proof with enough rabbits can achieve a kind of incomprehensibility.

What is "polite mathematics"? That sounds like "logic".

What's a "rabbit"?

A rabbit is when the mathematician presents the next step in a proof as a magician pulls a rabbit from a hat; leaving his reader to puzzle out how the trick was performed. For shorter proofs this can be delightful, but for longer ones it becomes tedious or even unmanageable.

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