Is 2 to the power of Euler's Number Rational?

Open Question

It is not known whether $2$ to the power of Euler's number $e$:

$2^e$

is rational or irrational.

Progress

See Schanuel's Conjecture Implies Transcendence of 2 to the power of Euler's Number.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental