During the late 1860s Neumann was one of the best chess players in the world. In tournaments he was first at Berlin 1865 (+34 –0 =0; first perfect score), first at Elberfeld 1865, first at Dundee 1867 Scotland International, second place went to Steinitz. Neumann reached fourth at Paris 1867 (Ignatz von Kolisch won), third/fourth at Baden-Baden 1870 (Adolf Anderssen won), and second, behind Anderssen, at Altona 1872. However, severe mental illness stopped him playing after 1872.
In 1864–1867, together with Anderssen, he founded and edited the Neue Berliner Schachzeitung. He died in Wehlau in East Prussia.