Prove $2^e$ is transcendental

Question

I remembered that a Russian mathematician proved this, but now I cannot find it again.

Could you please recommend a book on these kinds of problems?

Answer 1

It is unknown if $2^e$ is irrational. See here (under Open questions).

It is not known whether $\pi e, \frac\pi e, 2^e, e^e, e^{e^e}, π^\sqrt{2}, \ln π$, Catalan's constant, or the Euler–Mascheroni gamma constant γ are irrational.

(Remark: All real numbers that are transcendental are irrational.)