Who is leopold kronecker

Only in , when Kummer retired from the University , was Kronecker invited to succeed him and became an ordinary professor. Interestingly, the topics Kronecker studied were restricted by the fact that he believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps.

Kronecker believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs. It appears that, from the early s , Kronecker was opposed to the use of irrational numbers , upper and lower limits , and the Bolzano-Weierstrass theorem , because of their non-constructive nature.

Another consequence of his philosophy of mathematics was that to Kronecker transcendental numbers could not exist. When he became math chair of the University of Berlin , Weierstrass planned to move to Switzerland but changed his mind when he decided that someone needed to oppose the views of Kronecker. In he was elected a member of the Leopoldina. Leopold Kronecker died of bronchitis on 29 December References and Further Reading:. Your email address will not be published.

Related Posts. Peter Stumpp — the Werewolf of Bedburg. Karl Nessler and the Invention of Permanent Waves. Richard Dedekind and the Real Numbers. Leave a Reply Cancel reply Your email address will not be published. He helped to manage the banking business of his mother's brother and, in , he married the daughter of this uncle, Fanny Prausnitzer.

He also managed a family estate but still found the time to continue working on mathematics, although he did this entirely for his own enjoyment. Certainly Kronecker did not need to take on paid employment since he was by now a wealthy man. His enjoyment of mathematics meant, however, that when circumstances changed in and he no longer needed to live on the estate outside Liegnitz, he returned to Berlin.

He did not wish a university post, rather he wanted to take part in the mathematical life of the university and undertake research interacting with the other mathematicians.

Borchardt had lectured at Berlin since and, in late , he took over the editorship of Crelle's Journal on Crelle 's death. In Weierstrass came to Berlin, so within a year of Kronecker returning to Berlin, the remarkable team of Kummer , Borchardt , Weierstrass and Kronecker was in place in Berlin. Of course since Kronecker did not hold a university appointment, he did not lecture at this time but was remarkably active in research publishing a large number of works in quick succession.

These were on number theory , elliptic functions and algebra, but, more importantly, he explored the interconnections between these topics. Kummer proposed Kronecker for election to the Berlin Academy in , and the proposal was seconded by Borchardt and Weierstrass.

On 23 January Kronecker was elected to the Academy and this had a surprising benefit. Members of the Berlin Academy had a right to lecture at Berlin University.

Although Kronecker was not employed by the University, or any other organisation for that matter, Kummer suggested that Kronecker exercise his right to lecture at the University and this he did beginning in October The topics on which he lectured were very much related to his research: number theory, the theory of equations, the theory of determinants , and the theory of integrals.

In his lectures [ 1 ] :- He attempted to simplify and refine existing theories and to present them from new perspectives. For the best students his lectures were demanding but stimulating. However, he was not a popular teacher with the average students [ 1 ] :- Kronecker did not attract great numbers of students.

Only a few of his auditors were able to follow the flights of his thought, and only a few persevered until the end of the semester. He did accept honours such as election to the Paris Academy in that year and for many years he enjoyed good relations with his colleagues in Berlin and elsewhere. In order to understand why relations began to deteriorate in the s we need to examine Kronecker's mathematical contributions more closely.

We have already indicated that Kronecker's primary contributions were in the theory of equations and higher algebra, with his major contributions in elliptic functions, the theory of algebraic equations, and the theory of algebraic numbers. However the topics he studied were restricted by the fact that he believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps.

Kronecker is well known for his remark:- God created the integers, all else is the work of man. Kronecker believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs. It appears that, from the early s, Kronecker was opposed to the use of irrational numbers, upper and lower limits, and the Bolzano - Weierstrass theorem, because of their non-constructive nature.

Another consequence of his philosophy of mathematics was that to Kronecker transcendental numbers could not exist. In Heine published a paper On trigonometric series in Crelle's Journal , but Kronecker had tried to persuade Heine to withdraw the paper. Again in Kronecker tried to prevent publication of Cantor 's work in Crelle's Journal , not because of any personal feelings against Cantor which has been suggested by some biographers of Cantor but rather because Kronecker believed that Cantor 's paper was meaningless, since it proved results about mathematical objects which Kronecker believed did not exist.

Kronecker was on the editorial staff of Crelle's Journal which is why he had a particularly strong influence on what was published in that journal. After Borchardt died in , Kronecker took over control of Crelle's Journal as the editor and his influence on which papers would be published increased.

The mathematical seminar in Berlin had been jointly founded in by Kummer and Weierstrass and, when Kummer retired in , Kronecker became a codirector of the seminar. This increased Kronecker's influence in Berlin. Kronecker's international fame also spread, and he was honoured by being elected a foreign member of the Royal Society of London on 31 January He was also a very influential figure within German mathematics [ 1 ] :- He established other contacts with foreign scientists in numerous travels abroad and in extending to them the hospitality of his Berlin home.

For this reason his advice was often solicited in regard to filling mathematical professorships both in Germany and elsewhere; his recommendations were probably as significant as those of his erstwhile friend Weierstrass. Although Kronecker's view of mathematics was well known to his colleagues throughout the s and s, it was not until that he made these views public.

In that year he argued against the theory of irrational numbers used by Dedekind , Cantor and Heine giving the arguments by which he opposed Even the concept of an infinite series, for example one which increases according to definite powers of variables, is in my opinion only permissible with the reservation that in every special case, on the basis of the arithmetic laws of constructing terms or coefficients , So Kronecker was consistent in his arguments and his beliefs, but many mathematicians, proud of their hard earned results, felt that Kronecker was attempting to change the course of mathematics and write their line of research out of future developments.

Another feature of Kronecker's personality was that he tended to fall out personally with those whom he disagreed with mathematically. Of course, given his belief that only finitely constructible mathematical objects existed, he was completely opposed to Cantor 's developing ideas in set theory. Not only Dedekind , Heine and Cantor 's mathematics was unacceptable to this way of thinking, and Weierstrass also came to feel that Kronecker was trying to convince the next generation of mathematicians that Weierstrass 's work on analysis was of no value.