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Schanuel's conjecture

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, …, zn that are linearly independent over the rational numbers Q, the field extension Q (z1, …, zn, ez1 , …, ezn) 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.


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