# Prove $2^e$ is transcendental

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?

• I like Niven, Irrational Numbers – Will Jagy May 29 '17 at 2:59
• well, I don't see anything that would imply your idea, i think you have remembered it incorrectly. – Will Jagy May 29 '17 at 3:09
• @WillJagy It's an open question if $2^e$ is irrational... – Dair May 29 '17 at 3:18
• A Russian mathematician proved that $2^\sqrt2$ is transcendental, but that's another story. – Ivan Neretin May 29 '17 at 7:52

It is unknown if $2^e$ is irrational. See here (under Open questions).
It is not known whether πe, π/e, $2^e$, ee, $e^{e^e}$, πe, $π\sqrt{2}$, ln π, Catalan's constant, or the Euler–Mascheroni gamma constant γ are irrational.