# Lagrange's Four Square Theorem/Historical Note

< Lagrange's Four Square Theorem(Redirected from Hilbert-Waring Theorem/Particular Cases/2/Historical Note)

Jump to navigation
Jump to search
## Historical Note on Lagrange's Four Square Theorem

It is suggested by some sources that the result of Lagrange's Four Square Theorem was known, at least empirically, by Diophantus of Alexandria.

Some sources suggest that the theorem was originally stated formally by Pierre de Fermat.

However, it appears that Claude Gaspard Bachet de Méziriac published the results of his having tested it thoroughly up to $120$, and stated the theorem in his $1621$ translation of the *Arithmetica* of Diophantus.

Fermat read about it in his copy of that work, and studied it, but appears to have failed to find a proof, as no proof of his can be found.

Some sources claim that its first proof was by Leonhard Paul Euler, but this is questionable.

It was finally proved by Joseph Louis Lagrange in $1770$.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $4$ - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $4$