Articles

Leopold Kronecker


Leopold Kronecker (1823 - 1891) was born in Germany to Jewish parents although he opted for Protestantism. He was a very prosperous businessman who had strong connections with professors at the University of Berlin, where he accepted a post in 1883. In contact with Weierstrass, Dirichlet, Jacobi, and Steiner obtained his doctorate in 1845 with a thesis on algebraic number theory. According to Weierstrass, he endorsed the universal arithmeticization of analysis but advocated a finite arithmetic, in conflict with Cantor.

He insisted on the idea that Arithmetic and Analysis should be based on integers, which he considered to be God-given meaning and rejected the construction of real numbers because it could not be done by finite processes. He thought irrational numbers did not exist, fighting for their extinction. He is said to ask Lindemann what his proof was that p is not algebraic, since irrational numbers did not exist.

Kronecker contributed significantly to Algebra although his ideas at the time were considered metaphysical. His finitism even embarrassed Weierstrass but it was Cantor who attacked most severely, opposing being given a position at the University of Berlin and, moreover, trying to defeat and extinguish the branch of mathematics that Cantor was creating about the existence of numbers. transfinites.

Cantor defended himself in one of his articles by saying that definite numbers can be made with infinite sets as well as finites, but Kronecker continued his attacks and criticisms. This conflict between Cantor and Kronecker is considered to be the strongest controversy of the nineteenth century. In 1881, with his domain of rationality, he proved that the set of numbers of the form a + b Ö 2 where a and b are rational is a body.

It is sometimes said that his movement on finitism died of starvation but would reappear in a new form in the work of Poincaré and Brouwer.

Source: Fundamentals of Elementary Mathematics, Gelson Iezzi - Current Publisher