 He was rector of the university (1914–1915), chairman of the German Committee for Mathematical and Scientific Teaching (1908–1913), member of the Academy of Sciences Leopoldina from 1900 and his president from 1921.At the International Congress of Mathematicians he was an invited speaker in 1904 in Heidelberg and in 1908 in Rome.Gutzmer published more than forty works; among them, the reports about the activities of the teaching committee are specially relevant.