Definition:Elliptic Function/Historical Note

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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