Law of Quadratic Reciprocity/Historical Note

Historical Note on Law of Quadratic Reciprocity

The Law of Quadratic Reciprocity was investigated by Leonhard Paul Euler who stated it imperfectly and failed to find a proof.

Adrien-Marie Legendre first stated it correctly, but his attempted $\text {1785}$ proof of it was incorrect.

Carl Friedrich Gauss first became aware of this result, and found a correct proof. He wrote this up in $\text {1798}$ and published it in his Disquisitiones Arithmeticae in $\text {1801}$.

The proof as given here was found by Ferdinand Eisenstein and published in $\text {1844}$.


Sources

  • 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.25$: Gauss ($\text {1777}$ – $\text {1855}$)
  • 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Gauss
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