In the mid 1960s American mathematician Stephen Schanuel devised a complex mathematical conjecture regarding the 'transcendence degree' of certain 'field extensions' of the rational numbers.

Formally stated :

Given any n complex numbers z₁, …, z_n that are linearly independent over the rational numbers Q, the field extension Q (z₁, …, z_n, e^z₁ , …, e^z_n) has transcendence degree at least n over Q

Source :Wikipedia

At present, the conjecture has neither been proved or disproved.

If it is eventually proved, it could have profound implications for exploring the nature of π and the natural logarithm e.