Ibn al-Haytham's work on optics was deeply rooted in geometric principles. He employed geometry extensively to analyze the paths of light rays, the formation of images, and the properties of lenses and mirrors. His geometric analyses were crucial for developing his theories on refraction and reflection.

Ibn al-Haytham was a pioneer in using analytical methods to solve geometric problems. He employed algebraic techniques to analyze and solve geometric problems, a step towards the development of analytic geometry.

Ibn al-Haytham made contributions to number theory, including studies on perfect numbers (numbers equal to the sum of their proper divisors) and amicable numbers (pairs of numbers where each is the sum of the proper divisors of the other).

Ibn al-Haytham posed and solved Alhazen's problem: given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer. This problem, which has applications in optics and geometry, requires solving a quartic equation (an equation of degree four).