Recently I studied about the Napier's constant $e$ and learned that it is known as the formula$$ e=\lim_{x\to 0} (1+x)^{\frac{1}{x}} $$
But why can't we express it in terms of $\pi$, for example?
Also for other constants, for example, there is an expression for $\zeta(2)$ in terms of the constant $\pi$, but we cannot do that with $\zeta(3)$.
Same thing with $\text{Li}_4\left(\frac{1}{2}\right) $ and Catalan's constant $C$ and also Glaisher–Kinkelin constant $A$... etc
Can it be proven impossible, or will scientists find out one day?