How do we know numbers like “e” & “pi” are transcendental? If its true, how do people calculate all those digits of them, down to the millions of digits?

Question

Thank you in advance, im dumbfounded how we are able to calculate these numbers as if they are truely transcendental, there would be no way to express them as a true fraction.

In: Mathematics

Answer 1

Although it goes beyond ELI5, since no one has actually provided a proof yet, this video does the best job explaining it that I’ve seen:

He covers both the transcendence of e and Pi in a relatively straightforward way.