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If you're wondering what a Hilbert space, know that you're in good company.

> Dr. von Neumann, ich möchte gerne wissen, was ist denn eigentlich ein Hilbertscher Raum? (Dr. von Neumann, I'd would really like to know, just what exactly is a Hilbert space?)

Asked to John von Neumann to David Hilbert at a lecture.

https://ncatlab.org/nlab/show/Hilbert+space#fn:1

I'd like to add, as a physicist by training, that anything can be a Hilbert space if you wish hard enough. You can even use results about countable vector spaces if you need them!