Mathmatician-Georg+Cantor

Georg Cantor was born in 1845 in Denver, Mass. Maria Anna Böhm and Georg Waldemar Cantor were his parents. His father was a merchant and his mother was a very musical Russian. Georg inherited considerable musical and artistic talents from his parents being an outstanding violinist. Georg was brought up a Protestant, this being the religion of his father, while Georg's mother was a Roman Catholic. After early education at home from a private tutor, Cantor attended primary school in St Petersburg, then in 1856 when he was eleven years old the family moved to Germany. Cantor's father had poor health and the move to Germany was to find a warmer climate than the harsh winters of St Petersburg. Cantor studied at the Realschule in Darmstadt where he lived as a boarder. He graduated in 1860 with an outstanding report, which mentioned in particular his exceptional skills in mathematics, in particular trigonometry. After attending the Höhere Gewerbeschule in Darmstadt from 1860 he entered the Polytechnic of Zurich in 1862. After receiving his doctorate in 1867, Cantor taught at a girl's school in Berlin. Then, in 1868, he joined the Schellbach Seminar for mathematics teachers. immediately after being appointed to Halle in 1869, he presented his thesis, again on number theory, and received his habilitation. At Halle the direction of Cantor's research turned away from number theory and towards analysis. This was a difficult problem which had been unsuccessfully attacked by many mathematicians. He published further papers between 1870 and 1872 dealing with trigonometric series and these all show the influence of anothers teachings. Cantor published a paper on trigonometric series in 1872 in which he defined irrational numbers in terms of convergent sequences of rational numbers. In 1873 Cantor proved the rational numbers countable, i.e. they may be placed in one-one correspondence with the natural numbers. He also showed that the algebraic numbers, i.e. the numbers which are roots of polynomial equations with integer coefficients, were countable. However his attempts to decide whether the real numbers were countable proved harder. He had proved that the real numbers were not countable by December 1873 and published this in a paper in 1874. Cantor undertook the exploration of the "infinite", and developed modern theory on infinite sets. which remains conceptually challenging. Cantor's work provided an approach to problems that had beset mathematicians for centuries, including Zeno's ancient paradoxes. He gave the first clear and consistant definition of an infinite set.