# Definition:Elliptic Function/Historical Note

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## Historical Note on Elliptic Function

Elliptic functions were first explored by Niels Henrik Abelâ€Ž in $1827$, after his discovery of them as the inverse of elliptic integrals.

Carl Gustav Jacob Jacobi then continued the work in $\text {1828}$ – $\text {1829}$.

However, it turned out that Carl Friedrich Gauss had actually got there first, but had never got round to publishing his work.

Jacobi noticed a passage in Gauss's *Disquisitiones Arithmeticae* (Article $335$) in which it was clear that Gauss' had already arrived at the same results that Jacobi had done, but some $30$ years before.

As Jacobi wrote to his brother:

*Mathematics would be in a very different position if practical astronomy had not diverted this colossal genius from his glorious career.*

Joseph Liouville based his own theory of elliptic functions on his Liouville's Theorem (Complex Analysis).

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.25$: Gauss ($\text {1777}$ – $\text {1855}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.27$: Abel ($\text {1802}$ – $\text {1829}$) - 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 $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)