In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one.
Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann.
Their third child, Fritz Noether, was born in 1884, and like Emmy, found prominence as a mathematician; he was executed in the Soviet Union in 1941.
In birational geometry, Noether introduced the fundamental technique of blowing up in order to prove resolution of singularities for plane curves.
The Noether-Lefschetz theorem (proved by Lefschetz) says that the Picard group of a very general surface of degree at least 4 in P3 is generated by the restriction of the line bundle O(1).