Georg Cantor
Cantor taught for a time at a girls’ school in Berlin,  then he became a lecturer in Halle where he remained for the rest of his life.  He became full professor there in 1879.  Cantor worked on the theory of numbers, continuum hypothesis and then on trigonometric series, starting with ideas that had been developed by Bernhard Riemann on complex variables.  He sent a paper on algebraic numbers to be published in Crelle's Journal, but Kronecker was against it.  However, Dedekind supported Cantor, and eventually the article was published.  This article showed that Cantor was a great mathematician.