Now wait until someone asks the author to prove that e or π exist. The whole reasoning they used for √2 is based on the fact that √2 is a root of a simple equation x²-2=0 which has rational coefficients; with e or π no such equation exists.
the argument for the existence of pi or e doesn't connect as easily to something as "tangible" as a polynomial equation, but the arguments are still out there
I know, it's just less obvious and probably not at all convincing for a person with no mathematical knowledge. Even talking about (1+1/n)ⁿ is not easy without a bunch of calculus.
I think the argument for pi should be somewhat straightforward since people usually do trigonometry in high school? I don't know an argument for e that doesn't involve some kind of calculus.