It was certainly a severe blow to Cantor when Dedekind declined the offer in the early , and the blow was only made worse by Heinrich Weber and then Mertens declining too. After a new list had been drawn up, Wangerin was appointed but he never formed a close relationship with Cantor. The rich mathematical correspondence between Cantor and Dedekind ended later in Almost the same time as the Cantor- Dedekind correspondence ended, Cantor began another important correspondence with Mittag-Leffler.
Soon Cantor was publishing in Mittag-Leffler 's journal Acta Mathematica but his important series of six papers in Mathematische Annalen also continued to appear. Firstly Cantor realised that his theory of sets was not finding the acceptance that he had hoped and the Grundlagen was designed to reply to the criticisms. Secondly [ 3 ] :- The major achievement of the Grundlagen was its presentation of the transfinite numbers as an autonomous and systematic extension of the natural numbers.
Cantor himself states quite clearly in the paper that he realises the strength of the opposition to his ideas I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers. At the end of May Cantor had the first recorded attack of depression. He recovered after a few weeks but now seemed less confident. He wrote to Mittag-Leffler at the end of June [ 3 ] I don't know when I shall return to the continuation of my scientific work.
At the moment I can do absolutely nothing with it, and limit myself to the most necessary duty of my lectures; how much happier I would be to be scientifically active, if only I had the necessary mental freshness. At one time it was thought that his depression was caused by mathematical worries and as a result of difficulties of his relationship with Kronecker in particular. Recently, however, a better understanding of mental illness has meant that we can now be certain that Cantor's mathematical worries and his difficult relationships were greatly magnified by his depression but were not its cause see for example [ 3 ] and [ 21 ].
After this mental illness of [ 3 ] Kronecker accepted the gesture, but it must have been difficult for both of them to forget their enmities and the philosophical disagreements between them remained unaffected. Mathematical worries began to trouble Cantor at this time, in particular he began to worry that he could not prove the continuum hypothesis , namely that the order of infinity of the real numbers was the next after that of the natural numbers.
In fact he thought he had proved it false, then the next day found his mistake. Again he thought he had proved it true only again to quickly find his error. All was not going well in other ways too, for in Mittag-Leffler persuaded Cantor to withdraw one of his papers from Acta Mathematica when it had reached the proof stage because he thought it " Cantor joked about it but was clearly hurt:- Had Mittag-Leffler had his way, I should have to wait until the year , which to me seemed too great a demand!
But of course I never want to know anything again about Acta Mathematica. Mittag-Leffler meant this as a kindness but it does show a lack of appreciation of the importance of Cantor's work. The correspondence between Mittag-Leffler and Cantor all but stopped shortly after this event and the flood of new ideas which had led to Cantor's rapid development of set theory over about 12 years seems to have almost stopped. Before the end of the year a son was born, completing his family of six children.
He turned from the mathematical development of set theory towards two new directions, firstly discussing the philosophical aspects of his theory with many philosophers he published these letters in and secondly taking over after Clebsch 's death his idea of founding the Deutsche Mathematiker-Vereinigung which he achieved in Cantor chaired the first meeting of the Association in Halle in September , and despite the bitter antagonism between himself and Kronecker , Cantor invited Kronecker to address the first meeting.
Kronecker never addressed the meeting, however, since his wife was seriously injured in a climbing accident in the late summer and died shortly afterwards. Cantor was elected president of the Deutsche Mathematiker-Vereinigung at the first meeting and held this post until He helped to organise the meeting of the Association held in Munich in September , but he took ill again before the meeting and could not attend. Cantor published a rather strange paper in which listed the way that all even numbers up to could be written as the sum of two primes.
Since a verification of Goldbach's conjecture up to had been done 40 years before, it is likely that this strange paper says more about Cantor's state of mind than it does about Goldbach's conjecture. His last major papers on set theory appeared in and , again in Mathematische Annalen under Klein 's editorship, and are fine surveys of transfinite arithmetic. The rather long gap between the two papers is due to the fact that although Cantor finished writing the second part six months after the first part was published, he hoped to include a proof of the continuum hypothesis in the second part.
However, it was not to be, but the second paper describes his theory of well-ordered sets and ordinal numbers. In their lectures at the Congress [ 4 ] Hurwitz openly expressed his great admiration of Cantor and proclaimed him as one by whom the theory of functions has been enriched.
Jacques Hadamard expressed his opinion that the notions of the theory of sets were known and indispensable instruments. At the Congress Cantor met Dedekind and they renewed their friendship. By the time of the Congress, however, Cantor had discovered the first of the paradoxes in the theory of sets.
He discovered the paradoxes while working on his survey papers of and and he wrote to Hilbert in explaining the paradox to him.
Burali-Forti discovered the paradox independently and published it in Cantor began a correspondence with Dedekind to try to understand how to solve the problems but recurring bouts of his mental illness forced him to stop writing to Dedekind in Whenever Cantor suffered from periods of depression he tended to turn away from mathematics and turn towards philosophy and his big literary interest which was a belief that Francis Bacon wrote Shakespeare's plays.
Georg Cantor was a popular German mathematician. He is best known as the inventor of set theory that later became a fundamental theory in mathematics. He was able to establish the importance of one-to-one correspondence between members of two sets, well-ordered sets, and defined infinite sets. These proved that real numbers are much more numerous than natural numbers. Georg Cantor was born on March 3, in St. Petersburg, Russian Empire. He was brought up in the city until he turned He was the oldest of six children and was regarded as a great violinist.
His grandfather was a famous musician and the soloist in the Russian Empire in an imperial orchestra. His dad had been a member of the St. Petersburg stock exchange. They first went to Wiesbaden before going to Frankfurt. They were seeking winters milder than those in St.
In , Georg graduated with a distinction from Realschule in Darmstadt. His great skills in mathematics and trigonometry were noted. In , he enrolled at the University of Zurich. This was after receiving his inheritance after his father passed way in He later shifted to the University of Berlin.
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