What were two remarkable advancements made by Arabs?

1. Algebra: Arabs made significant contributions to the field of algebra, particularly through the works of mathematicians like al-Khwarizmi. Al-Khwarizmi's book, "Al-Kitab al-Jabr wa al-Muqabalah" ("The Compendious Book on Calculation by Completion and Balancing"), introduced the concept of algebra as a systematic method for solving equations. He also developed the concept of the algorithm, which is a set of rules or procedures for solving a particular type of problem.

2. Optics: Arabs made notable advancements in the field of optics, primarily due to the contributions of scientists like Ibn al-Haytham (Alhazen). Ibn al-Haytham conducted extensive experiments and wrote several influential works, including "Kitab al-Manazir" ("Book of Optics"). He challenged the prevailing Greek theories of vision, proposing that vision occurs when light enters the eye rather than being emitted by it. His work influenced later Western scientists, such as Roger Bacon and Johannes Kepler.