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George Cantor

Picture of George Cantor

Date of Birth: 03/03/1845

Age: 72

Place of birth: St. Petersburg

Citizenship: Germany

The structure of infinity

Family Georg Cantor (1845-1918) moved from Russia to Germany when he was still a child. It was there that he began to study mathematics. Defended in 1868 dissertation on the theory of numbers, he received his doctorate at the University of Berlin. In 27 years, Cantor published an article containing a total solution to a very difficult mathematical problem - and the ideas brought up later in his famous theory - the theory of sets. In 1878 he introduced and formulated a significant number of new concepts, gave a definition of the set and the first definition of the continuum, developed the principles of comparing sets. A systematic exposition of the principles of his doctrine of infinity, he gave in 1879-1884 gg.

Cantor`s insistence to consider this as an infinite something important was at that time the big news. Cantor thought his theory as a completely new calculus of the infinite, "transfinite" (ie "superfinite") mathematics. According to his idea, the creation of such calculation was to revolutionize not only in mathematics but also in metaphysics and theology, which interested Cantor almost more than the actual research. He was the only mathematician and philosopher, who believed that actual infinity is not only there, but in the full sense of understandable human comprehension and it will raise the mathematicians, and after them, and theologians, all of the above - and closer to God. This task he devoted his life. The scientist firmly believed that he was chosen by God to accomplish a great revolution in science, and that his faith was maintained mystical visions. Titanic attempt of Georg Cantor, however, ended in strange: in theory have been found insurmountable paradox, questioning the value and loved the idea of ??Cantor - "ladder Alef", the serial number of ordinals. (These numbers are well known in their adopted notation: the letter Aleph - the first letter of the Hebrew alphabet.)

Surprise and originality egotochki view, despite all the advantages of the approach led to a sharp rejection of his works mostly scientists. For decades, he led a bitter struggle with almost all his contemporaries-philosophers and mathematicians, to deny the legitimacy of building on the foundations of mathematics, true infinite. Some have taken this as a challenge, since Cantor assumed the existence of sets or sequences of numbers with infinitely many elements. The famous mathematician Poincare called the theory of transfinite numbers "disease" from which mathematics should ever be cured. Kronecker - Cantor teacher and one of the most influential mathematicians of Germany - even attacked Cantor, calling him a "charlatan", "renegade" and "seducers of youth!" Only in 1890, when the application of set theory were obtained for analysis and geometry, theory of Cantor has been recognized as an independent branch of mathematics.

It is important to note that Cantor contributed to the creation of the professional association - the German Mathematical Society, which contributed to the development of mathematics in Germany. He believed that his scientific career has suffered from prejudice against his work and hoped that an independent organization will enable young mathematicians independently judge the new ideas and engage in their development. He was the initiator of the convening of the first International Congress of Mathematicians in Zurich.

Cantor was very upset by the contradictions of his theory and the complexity of its adoption. Since 1884, he suffered a deep depression and after a few years moved away from scientific activity. Kantor died of heart failure in a mental hospital in Halle.

Cantor proved the existence of a hierarchy of infinities, each of which "more" prior. His theory of transfinite sets, having gone through years of doubt and attacks, in the end, has grown into a huge revolutionizing force in the 20th century mathematics. and it has become the cornerstone.