Leopold Kronecker | Biography

Leopold Kronecker's approach to mathematics can best be described in perhaps his most famous words, spoken in 1886 in Berlin: "The integer numbers were made by God, everything else is the work of man." Kronecker believed that all mathematics could be reduced to and explained by finite whole numbers only, and that irrational and transcendental numbers and any related proofs and theories involving them did not exist.

Kronecker was born into a well-to-do family, and through inheritance and business interests, he remained independently wealthy throughout his life. He developed a keen interest in mathematics when in school at the Liegnitz Gymnasium (secondary school). Here, he met teacher Ernst Kummer, whom he would work with for the greater part of his mathematical career.

In 1841, Kronecker enrolled at Berlin University to study mathematics, philosophy, and astronomy. After a brief stint at the University of Breslau, where he once again studied under Kummer, Kronecker returned to Berlin to earn his doctorate in mathematics in 1845, studying under Peter Dirichlet and writing his final dissertation on algebraic number theory.

Instead of pursuing his academic career after earning his doctorate, Kronecker left Berlin for the family estate, assisting in business affairs and managing the family property for the next decade. He continued to work on mathematical theory, but as a hobby rather than a serious academic pursuit. However, in 1855, Kronecker returned to Berlin to once again work with his mentor, Kummer, who had taken a position at the University of Berlin. Kronecker did not seek a teaching position in Berlin, and financially, did not need one. He instead spent his time on mathematical studies and research. It was here that he also met and worked with respected mathematician Karl Weierstrass.

During this period, Kronecker published a large body of research on number theory, elliptic functions, and algebraic equations. After Kummer nominated him to the Berlin Academy in 1860, he began to lecture at the University. Although he would by choice remain a lecturer and researcher with no official teaching position for over twenty years, Kronecker's reputation as a serious and respected mathematical researcher grew amongst his colleagues, as did his influence in the mathematical community. In addition to the Berlin Academy, he was elected to a number of prominent mathematical societies, including the Paris Academy and the Royal Society of London. He was also appointed to the editorial staff of Crelle's Journal, a high profile German mathematical journal. In 1880, Kronecker took over as editor of the journal, expanding his sphere of influence even further.

Kronecker was extremely vocal in his views on number theory and what he perceived to be the invalidity of the use of anything other than finite numbers in number theory. He used his considerable influence to speak out against the views of mathematicians such as Heine, Cantor, Dedekind, and even colleague Weierstrass, and may have been responsible for blocking the publication of some of their work in Crelle's Journal. It is thought that Kronecker also used his influence at the University to block the appointment of Cantor to a teaching position in Berlin because of the mathematician's ideas about set theory and irrational numbers.

Upon Kummer's retirement in 1883, Kronecker was appointed to the chair of mathematics in Berlin, his first official teaching position, and to the position of codirector of Berlin's mathematical seminar. He died in 1891 at the age of 68, several months after his wife Fanny was killed in a climbing accident.