# Law of Quadratic Reciprocity/Historical Note

Jump to navigation
Jump to search

## 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