Gustav Conrad Bauer (18 November 1820, Augsburg – 3 April 1906, Munich) was a German mathematician, known for the Bauer-Muir transformation and Bauer's conic sections. He earned a footnote in the history of science as the doctoral advisor (Doktorvater) of Heinrich Burkhardt, who became one of the two referees of Albert Einstein's doctoral dissertation.
Gustav Bauer passed in 1837 his Abitur at Augsburg's Gymnasium bei St. Anna. He continued his studies of mathematics at the Polytechnischen Schule Augsburg and also the universities of Erlangen, Vienna and Berlin. At Humboldt University in Berlin, Bauer received in 1842 his Promotierung under Peter Gustav Lejeune Dirichlet. From 1842 Gustav Bauer continued his studies in Paris under Joseph Liouville, as well as other mathematicians.
In 1862 Gustav Bauer married Amalie, daughter of the Archivrat and Professor Honorarius Nathanael von Schlichtegroll. The marriage produced two daughters and a son Gustav junior, who became a well-known engineer.
At the beginning of his professional employment, Bauer applied for a civil service position as a schoolteacher but became a private tutor from 1845 to 1853 in the royal house of Prince Mihail Sturdza and his successor Prince Grigore Alexandru Ghica in what is now Rumania. In 1857 Bauer spent three months in England and upon his return to Germany became a Privatdozent for the Mathematics Faculty of the Ludwig Maximilian University of Munich. There he received his Habilitation and became in 1865 professor extraordinarius, in 1869 professor ordinarius, and in 1900 professor emeritus.