Page "Elliptic function" Paragraph 1

Historically, elliptic functions were first discovered by Carl Gustav Jacobi as inverse functions of elliptic integrals ; these in turn were studied in connection with the problem of the arc length of an ellipse, whence the name derives.

Jacobi's elliptic functions have found numerous applications in physics, and were used by Jacobi to prove some results in elementary number theory.

A more complete study of elliptic functions was later undertaken by Karl Weierstrass, who found a simple elliptic function in terms of which all the others could be expressed.

Besides their practical use in the evaluation of integrals and the explicit solution of certain differential equations, they have deep connections with elliptic curves and modular forms.