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.

Is the Catalan constant $G = \sum_{n=0}^∞ (-1)^n / (2n + 1)^2 \approx 0.91596$ irrational?

$\zeta(5)$ is irrational.

$\zeta(7)$ is irrational.

$\zeta(9)$ is irrational.

$\zeta(11)$ is irrational.

$\zeta(2n + 1)$ is irrational for any $n\in\mathbb{N}^{+}$.

Given any set of $n$ complex numbers $\{z_1, ..., z_n\}$ that are linearly independent over $\mathbb{Q}$, the field extension $\mathbb{Q}(z_1, ..., z_n, e^{z_1}, ..., e^{z_n})$ has transcendence degree at least $n$ over $\mathbb{Q}$.

$e + \pi$ is transcendental.

$e\pi$ is transcendental.