Hermite-Lindemann Theorem

The expression

$$A_1e^{\alpha_1}+A_2e^{\alpha_2}+A_3e^{\alpha_3}+\ldots,$$

in which the Coefficients $A_i$ differ from zero and in which the exponents $\alpha_i$ are Algebraic Numbers differing from each other, cannot equal zero.

See also Algebraic Number, Constant Problem, Integer Relation, Lindemann-Weierstraß Theorem

References

Dörrie, H. ``The Hermite-Lindemann Transcendence Theorem.'' §26 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 128-137, 1965.