His study of mathematics and the application of these studies led him to invent compound pulley systems, the planetarium and several war machines that were used in defending Syracuse from enemies. It is also possible that he was involved in the invention of the water organ and the water screw.
He did not just study existing literature involving mathematics, but he also initiated and pioneered a number of fields of science such as hydrostatics, pycnometry and static mechanics. He also did a lot for integral calculus and mathematical physics, so much so that he is called “the father of integral calculus" and “the father of mathematical physics". His findings, theories and results of his studies are forever preserved in his published works that include The Sandreckoner, On Spirals, On Conoids and Spheroids, Quadrature of the Parabola, On Plane Equilibriums, On Floating Bodies and Measurement of a Circle.