What’s true is that the sensation of mathematical understanding—of suddenly knowing what’s going on, with total certainty, all the way to the bottom—is a special thing, attainable in few if any other places in life. You feel you’ve reached into the universe’s guts and put your hand on the wire. It’s hard to describe to people who haven’t experienced it. We are not free to say whatever we like about the wild entities we make up. They require definition, and having been defined, they are no more psychedelic than trees and fish; they are what they are. To do mathematics is to be, at once, touched
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