He also developed independently a method of successive approximations for the solution of differential equations and developed the idea of the cluster point of a function. He was also an early supporter of the use of recursive functions and vectors. Peano's greatest contributions, however, were in the fields of axiomatization of mathematics and mathematical logic . His most famous set, known as Peano's postulates, put forth the axioms of natural numbers. In addition, he also developed a related set for geometry.
Mathematical logic is the use of symbols instead of words to write mathematical statements.
The idea had be raised over a century earlier by Leibniz who had suggested a universal language. By using symbols, the equations are simplified and made easily understood to anyone, no matter what language they speak. Mathematical logic quickly became the focus of his work. In 1889, Peano published his first version of a system of mathematical logic in his work Arithmetics principia , which included his famous axioms of natural numbers. Two years later, he established a journal, the Rivista , in which he proposed the symbolizing of all mathematical propositions into his system.