Open-problem statements, with their sources attached.

Four exponentials conjecture* Let $x_0, x_1$ and $y_0, y_1$ be $\mathbb Q$-linearly independent pairs of complex numbers, then some $e^{x_i y_j}$ is transcendental.

Are $e$ and $\pi$ algebraically independent?

Is $e + \pi$ irrational?

Is $e \pi$ irrational?

Is $e ^ e$ irrational?

Is $\pi ^ e$ irrational?

Is $\pi ^ \pi$ irrational?

Is $\ln(\pi)$ irrational?

Is the Euler-Mascheroni constant $\gamma$ irrational?

The Gompertz constant $\delta$ is transcendental.

$\Gamma(1/n)$ for n ≥ 2 is transcendental.