Gelfond-Schneider Constant is Transcendental/Historical Note

Historical Note on Gelfond-Schneider Constant is Transcendental

The question of the transcendental nature of the Gelfond-Schneider constant $2^{\sqrt 2}$ was raised in the context of the $7$th problem of the Hilbert $23$.

That the Gelfond-Schneider Constant is Transcendental was established in $1930$ by Rodion Osievich Kuzmin.

It was since determined to be a special case of the Gelfond-Schneider Theorem, established $\text {1934}$ – $\text {1935}$.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 665 \, 144 \ldots$
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 \cdotp 66514 \, 4 \ldots$
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