Georg Cantor, with a life span astride the nineteenth and twentieth centuries, is the last mathematician to be considered in detail here. He was born in St. Petersburg in 1845 , moved with his parents to Germany in 1856, studied at the University of Berlin (where he came under the influence of Weierstrass ) from 1863 to 1869 , taught in the University of Halle from 1869 until 1905, and died in a mental hospital in Halle in 1918 .His early interests were in number theory, indeterminat equations, and trigonmetric series.