Georg Cantor

History of Mathematics Portfolio Standard 1 Discrete Mathematics Georg Ferdinand Ludwig Phillip cantor (1845 1918) the transfinite species are just as much at the disposal of the intentions of the manufacturing business and His absolute boundless will as the finite numbers. Georg precentor Georg Cantor was born on March 3, 1845 in Saint Petersburg, Russia. Georg lived in the metropolis until age eleven, when his have became sick and the family moved to Germany to get away from the astringent winters in Russia. Throughout his youth, Georg played the violin and showed smashing gift, a talent he inherited from his musical parents.Georg graduated in 1860 from Realschule in Darmstadt. He was given praise for his outstanding skills in mathematics, especially trigonometry. He keep his studies at the Federal Polytechnic Institute in Zurich, where he stayed until his fathers death in 1863. At this time, he was given a considerable inheritance, and decided to transfer his studies to t he University of Berlin. While at the University, Georg attended canes by prominent mathematicians such as Leopold Kr iodincker, Karl Weierstrass, and Ernst Kummer.In the summer of 1966, Georg attended the University of Gottingen, which was and still is an authorised mathematical research center. He received his Ph. D. in 1867 for his thesis on number theory, De aequationibus secundi gradus indeterminatis. After receiving his Ph. D. , Georg began work uping at an all-girls school in Berlin. He quickly left this position to take up another one at the University of Halle, where he remained for the rest of his course. In 1874, after Georgs career began, he met and married Vally Guttmann.Between 1874 and 1886, Georg and Vally had six children. Thanks to his fathers inheritance he was able to care and provide for such a extended family while qualification a modest salary in academia. The ten dollar bill of 1874 to 1884 proved to be Georgs finest mathematical time. It was during t his time that Cantor began his work on set theory. He was able to prove that there are (infinitely) many possible sizes for infinite sets, which were not trivial and needed to be studied. Before this proof, infinite was a philosophical discussion, not a mathematical one.In one of Georgs first papers, he proved that the set of true numbers is more numerous than the set of natural numbers. He alike showed the necessity of one-to-one correspondence in set theory. He apply this concept to define finite and infinite sets, subdividing the latter into denumerable sets and uncountable sets. Georg overly pioneered using fundamental counting in set theory. This discovery lead to Cantors theorem the size of the power set of A is strictly larger than the size of A, even when A is an infinite set.Georg had many triumphs during his career, making him one of the great discrete mathematicians in history, but he excessively suffered because of his career. He was hospitalized several times thr oughout his life, which until his death, was contributed to depression. He would sever ties with friends and colleagues if they criticized his work. He once became so depressed from criticism by Leopold Kronecker that he began applying himself to lecture on philosophy instead of mathematics. He spent a great deal of time trying to prove that Francis Bacon wrote the plays attributed to Shakespeare, even writing ii pamphlets on it.All of his correspondence with friend and publisher Gosta Mittag-Leffler attacked Kronecker and displayed how much of his confidence he lost due to Kroneckers critiques of his work. Georg retired in 1913, still battling chronic depression. He suffered from poverty and malnourishment during World War I. He passed his final social class of life in the sanatorium, where he died on January 6, 1918. After his death, Georg was diagnosed with bipolarity, which is attributed for his erratic expression and depression.