Euler's Number is Transcendental/Proof 2

Theorem

Euler's Number $e$ is transcendental.

Proof

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$\blacksquare$

Historical Note

The transcendental nature of Euler's number $e$ was conjectured by Joseph Liouville in $1844$, after he had proved that it was not the root of a quadratic equation with integer coefficients.

The proof that $e$ is transcendental was first achieved by Charles Hermite in $1873$.

Sources

• 2004: Ian Stewart: Galois Theory (3rd ed.)