Definition:Elliptic Function/Historical Note
Historical Note on Elliptic Function
Elliptic functions were first explored by Niels Henrik Abel in $1827$, after his discovery of them as the inverses 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.
Charles Hermite used elliptic functions in $1858$ in his solution of the general quintic equation.
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 ($\text {1815}$ – $\text {1897}$)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): elliptic functions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elliptic functions