Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther.

From there, he went to study with Carl Gauss's instructor, Johann Pfaff, at the University of Halle, where he completed his doctoral thesis The occultation of fixed stars in 1815.

He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space.

[4] Before 1853 and Schläfli's discovery of the 4-polytopes, Möbius (with Cayley and Grassmann) was one of only three other people who had also conceived of the possibility of geometry in more than three dimensions.

In Euclidean geometry, he systematically developed the use of signed angles and line segments as a way of simplifying and unifying results.