Möbius worked mainly on analytical geometry, topology, and theoretical astronomy. He was born at Schulpforta in Germany and held a chair in theoretical astronomy at Leipzig, making numerous contributions to the field with publications on planetary occultations (‘eclipses’) and celestial mechanics. His more purely mathematical work centers on geometry and topology.

Möbius is chiefly famed for his discovery of the Möbius strip, a one-sided surface formed by giving a rectangular strip a half-twist and then joining the ends together. He introduced the use of homogeneous coordinates into analytical geometry and did significant work in projective geometry, inventing the Möbius net, which became of central importance in the future development of the subject.