Born in 1833 near Bleckede at the Elbe as the son of a forester, he attended Realschule ("Johanneum") in Lüneburg from 1845 to 1850, where he already showed a certain talent for mathematics.

Following a fondness of mathematics and physics, in 1852, at the age of 19, he moved on to study in Göttingen, attending classes by Gauß, Weber, Dirichlet, Stern and Riemann.

From 1860 onwards he was also appointed by the Göttingen Academy to edit the works of Gauß, of which he eventually completed six volumes.

His wife, Maria Heliodora, whom he married in 1876, was the daughter of the Swedish mathematician Carl Johan Malmsten.

They had one daughter and two sons, one of which, physicist Harald Schering, would later become professor of electrical engineering at the Technische Hochschule Hannover.