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Biography of George Cantor

Georg Kantor is an authoritative mathematician who introduced the concepts of quantitative and ordinal numerals.

Childhood and youth

Georg Ferdinand Ludwig Philip Kantor was born on March 4, 1845 in St. Petersburg. His parents were Georg-Waldemar Cantor and Maria Anna Boim. Cantor was raised as a convinced Protestant, and love of art was passed on to him from his parents. It is believed that he was an outstanding violinist. His father was a German, and his mother was a Russian woman who attended the Roman Catholic Church. From an early age, Kantor had a private teacher, he also attended a school in St. Petersburg. In 1856, when Cantor was eleven years old, his family moved to Germany, which Kantor had never been able to love.

The health of Cantor’s father began to deteriorate, because of which the family again moved, this time to Frankfurt, because of the warm climate. In Frankfurt, Cantor studied at the gymnasium, which he graduated with honors in 1960.

His teachers noted that he was well mathematics, especially trigonometry. After the gymnasium in 1962, Kantor entered the Federal University of Zurich, where he studied mathematics. After receiving the approval of his parents, he studied there for a couple of years, until the death of his father put an end to his studies. After the death of his father, Kantor moved to the University of Berlin, where he became friends with Herman Schwartz and attended lectures by Kronecker, Weierstrass and Kummer. In the summer, he also studied at the University of Gottingen, and in 1867 completed his first thesis on numbers entitled “De aequationibus secondi gradus indeterminatis”.

Career

At the beginning of his career, Kantor was an active member of mathematical unions and communities. He became president of one of the communities in 1865 and 1868. He also took part in the Shelbach conference on mathematics. In 1869, he was appointed professor at the University of Halle. He continued to work on various dissertations in number theory and analysis. At the same time, Cantor decided to continue the study of trigonometry

and began to reflect on the uniqueness of the geometric representation of the trigonometric series, which he introduced to his older colleague, Heine.

By 1870, Cantor coped with the task, proving the uniqueness of the geometric image, much to Heine’s amazement. In 1873 he proved that rational numbers are calculable and can come in accordance with natural numbers. By the end of 1873, Cantor proved that both real and relative numbers are also countable. He was promoted to the position of extraordinary professor in 1872, and in 1879 he took the position of professor of the highest category. He was grateful for the appointment, but still wanted to get a position in a more prestigious university.

In 1882, Cantor began to correspond with Geest Mittag-Leffler, and soon began to publish his works in the journal Leffler – “Acta Mathematica.” Kronecker, a contemporary of Kant, constantly mocked and oppressed Cantor’s theory.

Kantor continued to publish his works, but in 1884 he suffered a nervous breakdown, from which he soon recovered and decided to teach philosophy. Soon he began to study the literature of the Elizabethan period.

In 1890, he founded the German Mathematical Society, in which he first published diagonal cross-sectional drawings, thus slightly adjusting his relations with Kronecker. But, despite the fact that scientists began to communicate, they never reconciled, because of which the tension in their relationship was present until the end of Cantor’s life.

Personal life

In 1874, Cantor married Vallee Guttman; the couple had six children. It is believed that Cantor, despite the status of a famous mathematician, could not support his family. In the presence of free time, he played the violin and immersed himself in art and literature. He was awarded the Sylvester Medal for his research in mathematics. In 1913, Kantor retired because he was mentally unstable, suffered from permanent mental disorders and eventually he ended up in a health resort where he stayed until his death.

Death and heritage

Georg Kantor died on January 6, 1918 in Halle, after a prolonged mental illness. About Cantor came a lot of publications, one of which was a publication in the book “The Creators of Mathematics” and a note in “The History of Mathematics.” He founded the German Mathematical Society, and most of his scientific work is still used.

Basic work

“Infinite sets”
“Uncountable sets”
“Cantor set”
“Cardinals and Ordinals”
“The Continuum hypothesis”
“Number theory and function theories”
“Infinitesimals”
“Convergent series”
“Transcendental numbers”
“Diagonal argument”
“Cantor-Bernstein-Schroeder theorem ”
” Continuum hypothesis “

Publications

“On a Property of the Collection of All Real Algebraic Numbers”
”
Mathematica Annalen”
“Grundlagen einer allgemeinen Mannigfaltigkeitslehre”
“De aequationibus secondi gradus indeterminatis”