In details

Giuseppe Peano

Peano He was born on August 27, 1858 in Cuneo, Piemont, Italy, and died on April 20, 1932 in Turin, Italy. He was the founder of symbolic logic and the center of his interests was the foundations of mathematics and the development of a formal logical language.

Peano studied mathematics at the University of Turin and joined staff there in 1880, being assigned to a chair in 1890. In 1889 Peano published his famous axioms, called Peano axioms, which defined natural numbers in terms of sets. In 1891 he founded the Mathematical Rivista, a journal devoted primarily to logic and the foundations of mathematics.

In 1886 Peano proved that if f (x, y) is continuous then the first-order differential equation dy / dx = f (x, y) has a solution. The existence of solutions with strong f hypotheses had been earlier determined by Cauchy and then Lipschitz. Four years later Peano showed that the solutions were not unique, giving as an example the differential equation dy / dx = 3y, with y (0) = 0.

Peano introduced the basic elements of geometric calculation and gave new definitions for the size of an arc and the area of ​​a curved surface. He invented space-filling curves in 1890, these are cartographies of 0.1 on the square unit. Hilbert, in 1891, similarly described space-filling curves.

He produced an axiomatic definition of the natural number system and showed how the real number system can be derived from these postulates.

Peano was also interested in universal or international languages, and created the artificial language Interlingua in 1903. He compiled the vocabulary taking words from English, French, German and Latin. It was further developed by Alexander Gode. However, Peano considered his work in mathematical analysis to be of great significance.

Although Peano is a founder of mathematical logic, the German philosopher and mathematician Gottlob Frege (1848-1925) is considered the father of mathematical logic.