> I have heard that somebody has proven that exp(pi)= e^{\pi} is
> irrational. Please, I would like to know a reference for it.
This follows from the famous theorem of Gelfond and Schneider
that if a and b are algebraic irrationals then a^b is transcendental.
The reason is that one of the values of i^i is exp(-pi), and i
is an algebraic irrational.
John Conway