Georg Cantor
Cantor thought that infinite numbers really existed, and used ideas from ancient and medieval philosophy to prove his point.  Kronecker disagreed with him.  He thought that only integers existed.  Kronecker said that “God made integers and all the rest is the work of man”.  Kronecker stopped Cantor from being offered a professorship in Berlin, a position he ought to have had since he was one of the greatest mathematicians in the world.  Cantor stayed at Halle and continued to work into his old age, although he often suffered from fits of depression.  He often lost his temper, but he was also a very kind man.  He always gave encouragement to young mathematicians with new ideas.  He did not want them to suffer like he had because of older mathematicians who felt threatened by new ideas.  A lot of Cantor’s work led eventually to what is called “new mathematics” in schools today.