Is Schanuel's conjecture true?

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Schanuel's conjecture states that, for any complex numbers z₁,..., zₙ that are linearly independent over the rational numbers, the field extention ℚ(z₁,..., zₙ, e^z₁,..., e^zₙ) has transcendence degree at least n.

Note that the transcendence degree of a field extension is the size of the largest subset of the extension that is algebraically independent over the original field. So in this case, the theorem means that there is a set of at least n elements of ℚ(z₁,..., zₙ, e^z₁,..., e^zₙ) that are algebraically independent over ℚ.

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