The advanced research in the basic theory of mathematics has produced many famous Arab mathematicians. Many famous astronomers are also outstanding mathematicians. Hua Lazimi not only made great contributions in astronomy, but also made great achievements in mathematics. The book Calculations of Integrals and Equations demonstrates the basic method of understanding linear equations and quadratic equations and the calculation formula of finding quadratic roots, and puts forward many concepts such as algebra, known number, unknown number, root, shift term, union term and irrational number, thus making algebra a basic branch of mathematics. The two basic methods of solving equations, "reduction" and "elimination", demonstrated by Hua Lazimi, had great influence on western mathematics until they evolved into algebraic algorithms "shifting terms" and "merging similar terms" commonly used in modern mathematics. Therefore, Hua Lazimi was praised as "the father of algebra" by later generations. Abu Wafa is very accomplished in trigonometry, especially in demonstrating the functional relationship among chords, tangents and tangents, and determining the trigonometric calculation formula and trigonometric function table, which made trigonometry break away from astronomy and gradually become a branch of mathematics. Umar al-Khayyam wrote Algebra, focusing on the solution of linear equations with one variable and the geometric drawing method of roots of multivariate equations, systematically expounding the theory of finding roots with conic curve, and solving cubic equations with conic curve transfer method, which laid an important foundation for analytic geometry.