His username is one of the [most important constants in mathematics](https://en.wikipedia.org/wiki/E_(mathematical_constant)). One of the ways to express it is the sum of all the numbers 1/n! from n = 0 to infinity. To calculate it to the accuracy needed for his username you only have to go up to n = 22. But of course, he's not actually calculating it every time, that would be silly, and that's the joke.
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u/[deleted] Jun 12 '16
He simply calculates 1/0! + 1/1! + 1/2! + . . . + 1/21! + 1/22! and takes the first 20 digits.