Euler's Number is Transcendental/Historical Note

Historical Note on $e$ is Transcendental

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

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 718 \, 281 \, 828 \, 459 \, 045 \, 235 \, 360 \, 287 \, 471 \, 352 \, 662 \, 497 \, 757 \, 247 \, 093 \, 699 \ldots$
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.30$: Hermite ($\text {1822}$ – $\text {1901}$)
  • 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): $2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ \ldots$
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