It's stated that $\pi$ and $e$ are mathematical constants. But how can they be constants when there is a formula from one to the other, for instance Euler's formula. Since $e^{i \pi}=-1$ then is it true that we can express $e$ as a function of $\pi$ and vice versa? So if we can express $\pi$ in terms of $e$ then only one of these should be considered a mathematical constant since one in fact is a function of the other and therefore a dependence, not a linear dependence but clearly some formula.
There is a formula for the $n$-th digit of $\pi$, then should there also be a formula for the $n$-th digit of $e$? Why not?
Did I misunderstand what we mean when we say mathematical constant?
Thank you
Mathematical constants are not like physical constants. In physics you try to reduce the amount of constants to a minimum, in mathematics constants are just values of major significance (check also this article). Of course for every two mathematical constants you can find a formula that relates the two constants, that doesn't mean you only need one of them.