Christian Wiener attended school in Darmstadt, then studied engineering and architecture at the University of Giessen from 1843 to 1847. In 1848 he became a teacher of physics, mechanics, hydraulics and descriptive geometry at the Technische Hochschule in Darmstadt. (It was called the Höhere Gewerbeschule at that time.)
Wiener obtained a doctorate in 1850 and taught at the University of Giessen. After working at the Technical University of Karlsruhe for a year he returned to Giessen in 1851. In 1852 he was appointed to the chair of descriptive geometry at the Technical University of Karlsruhe.
Wiener's chief work is a 2 volume book on geometry Lehrbuch der darstellenden Geometrie which supplements Chasles's work and contains important historical information.
Wiener extended work on descriptive geometry to physics and calculated the amount of solar radiation received at different latitudes during the varying lengths of days in the course of the uear. This work was important in atmospheric studies and climatic studies.
At Clebsch's suggestion Wiener constructed plaster of Paris models of mathematical surfaces which were exhibited in London, Munich and Chicago.