**August Möbius** is best known for his work in topology, especially for his conception of the Möbius strip, a two dimensional surface with only one side.

- Möbius was educated at home until he was 13 years old when, already showing an interest in mathematics, he went to the College in Schulpforta in 1803.
- In 1809 Möbius graduated from his College and he became a student at the University of Leipzig.
- The teacher who influenced Möbius most during his time at Leipzig was his astronomy teacher Karl Mollweide.
- In 1813 Möbius travelled to Göttingen where he studied astronomy under Gauss.
- Gauss was the director of the Observatory in Göttingen but of course the greatest mathematician of his day, so again Möbius studied under an astronomer whose interests were mathematical.
- From Göttingen Möbius went to Halle where he studied under Johann Pfaff, Gauss's teacher.
- Under Pfaff he studied mathematics rather than astronomy so by this stage Möbius was very firmly working in both fields.
- In 1815 Möbius wrote his doctoral thesis on The occultation of fixed stars and began work on his Habilitation thesis.
- Mollweide's interest in mathematics was such that he had moved from astronomy to the chair of mathematics at Leipzig so Möbius had high hopes that he might be appointed to a professorship in astronomy at Leipzig.
- However Möbius did not receive quick promotion to full professor.
- In 1825 Mollweide died and Möbius hoped to transfer to his chair of mathematics taking the route Mollweide had taken earlier.
- By 1844 Möbius's reputation as a researcher led to an invitation from the University of Jena and at this stage the University of Leipzig gave him the Full Professorship in astronomy which he clearly deserved.
- From the time of his first appointment at Leipzig Möbius had also held the post of Observer at the Observatory at Leipzig.
- In 1844 Grassmann visited Möbius.
- He asked Möbius to review his major work Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik Ⓣ(The linear theory of extension, a new branch of mathematics) (1844) which contained many results similar to Möbius's work.
- However Möbius did not understand the significance of Grassmann's work and did not review it.
- He did however persuade Grassmann to submit work for a prize and, after Grassmann won the prize, Möbius did write a review of his winning entry in 1847.
- Although his most famous work is in mathematics, Möbius did publish important work on astronomy.
- Möbius's mathematical publications, although not always original, were effective and clear presentations.
- Almost all Möbius's work was published in Crelle's Journal, the first journal devoted exclusively to publishing mathematics.
- Möbius's 1827 work Der barycentrische Calcul Ⓣ(The barycentric calculus), on analytical geometry, became a classic and includes many of his results on projective and affine geometry.
- He introduced a configuration now called a Möbius net, which was to play an important role in the development of projective geometry.
- Möbius's name is attached to many important mathematical objects such as the Möbius function which he introduced in the 1831 paper Über eine besondere Art von Umkehrung der Reihen Ⓣ(On a special type of reversal of the rows) and the Möbius inversion formula.
- Before the question on the four colouring of maps had been asked by Francis Guthrie, Möbius had posed the following, rather easy, problem in 1840.
- However it does illustrate Möbius's interest in topological ideas, an area in which he is most remembered as a pioneer.
- In a memoir, presented to the Académie des Sciences and only discovered after his death, he discussed the properties of one-sided surfaces including the Möbius strip which he had discovered in 1858.
- This discovery was made as Möbius worked on a question on the geometric theory of polyhedra posed by the Académie.
- Although we know this as a Möbius strip today it was not Möbius who first described this object, rather by any criterion, either publication date or date of first discovery, precedence goes to Listing.
- A Möbius strip is a two-dimensional surface with only one side.

Born 17 November 1790, Schulpforta, Saxony (now Germany). Died 26 September 1868, Leipzig, Germany.

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Algebra, Astronomy, Group Theory, Origin Germany, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive