In order to make clear the foundations of arithmetic, the fields of mathematical logic and set theory have been developed. Mathematical logic includes the mathematical research of logic and the purposes of formal logic to different areas of mathematics; set concept is the branch of mathematics that studies units or collections of objects. The phrase “crisis of foundations” describes the search for a rigorous basis for arithmetic that occurred from roughly 1900 to 1930. Some disagreement in regards to the foundations of mathematics continues to the current day.
The Arithmetica had a significant influence on later mathematicians, corresponding to Pierre de Fermat, who arrived at his well-known Last Theorem after attempting to generalize a problem he had read within the Arithmetica (that of dividing a square into two squares). Diophantus also made vital advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation.