He created a large number of algebraic symbols, replaced unknowns with letters, systematically expounded and perfected the solutions of cubic and quartic equations, and pointed out the relationship between roots and coefficients. The triangular solution of irreducible cubic equation is given. He edited and drew many works, such as Introduction to Analytical Methods and Identification and Correction of Equations.
David engaged in mathematical research only out of love, but he accomplished masterpieces in algebra and trigonometry. His "Mathematical Laws Applied to Triangle" is one of David's earliest mathematical monographs, and it may be the first book in Western Europe that systematically discusses six methods of trigonometric functions to solve plane and spherical triangles. He is called the father of modern algebraic symbols. David also specially wrote a paper "Tangent Angle", which preliminarily discussed the general formulas of sine (sin), cosine (cos) and tangent chord, and applied algebraic transformation to trigonometry for the first time. He considered the equation with multiple angles, gave the function of expressing COS(nx) as COS(x), and gave the expression of multiple angles when n≤ 1 1 equals any positive integer.
His book Introduction to Analytical Methods concentrates his previous achievements in algebra, making algebra truly an excellent branch of mathematics. His contribution to equation theory is that he proposed the solutions of quadratic, cubic and quartic equations in the book "Arrangement and Revision of Equations".