Alhazen's problem

[1] It is named for the 11th-century Arab mathematician Alhazen (Ibn al-Haytham), who presented a geometric solution in his Book of Optics.

Later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow, and many others attempted to find an algebraic solution to the problem, using various methods, including analytic methods of geometry and derivation by complex numbers.

[3][4][5][6][7] An algebraic solution to the problem was finally found first in 1965 by Jack M. Elkin (an actuary), by means of a quartic polynomial.

[8] Other solutions were rediscovered later: in 1989, by Harald Riede;[9] in 1990 (submitted in 1988), by Miller and Vegh;[10] and in 1992, by John D. Smith[3] and also by Jörg Waldvogel.

[14] They showed that the mirror reflection point can be computed by solving an eighth-degree equation in the most general case.