from https://en.wikipedia.org/wiki/Gelfond%27s_constantSince âˆ’i is algebraic but not rational, eÏ€ is transcendental
if anyone uses, maple, their facility for checking that a number 'x' is algebraic is called by:
and if you do so for x=-i you will note that this Boolean returns false, where as if you check the Eulerâ€“Mascheroni constant for this or the same for it's rationality, it will return FAIL since is not known as yet.
So does anyone know why this difference of opinion exists? surely the most basic non-real should have a straight forward proof regarding its algebraicity.