**Hermann Wiener**'s parents were Ludwig Christian Wiener and Pauline Hausrath. At the time of Hermann's birth, Christian Wiener was professor of descriptive geometry at the Technische Hochschule of Karlsruhe, having moved there five years earlier when appointed to the chair. Hermann entered the Gymnasium in Karlsruhe in 1866 and he took his final examinations ten years later. Then, in 1876, he entered the Technische Hochschule in Karlsruhe where his father taught, studying there mathematics and the natural sciences.

After graduating from the Technische Hochschule in Karlsruhe in 1879, Wiener went to the Technische Hochschule in Munich to study for his doctorate. After submitting his doctoral thesis *Über Involutionen auf ebenen Curven* Ⓣ to the University of Munich in 1881, he spent some time at the University of Leipzig. He returned to Karlsruhe in the following year to take the state examinations which qualified him to teach in high schools and, following this, he taught as a trainee teacher for a year in the Gymnasium in Karlsruhe. In addition to teacher training, Wiener was also undertaking research for his habilitation thesis with his father at the Technische Hochschule in Karlsruhe.

Wiener submitted his habilitation thesis *Rein geometrische Theorie der Darstellung binärer Formen durch Punktgruppen auf der Geraden* Ⓣ to the University of Halle in 1885. His habilitation thesis formed the first part of the monograph *Rein geometrische Theorie der Darstellung binärer Formen* Ⓣ published in 1885. For the following nine years he worked as a Privatdozent at the University of Halle.

The German Mathematical Society (Deutsche Mathematiker-Vereinigung) was founded in 1890 at a meeting of the Society of German Scientists and Physicians which took place in Bremen from 15 to 20 September. Wiener was a founder member of the German Mathematical Society, as were Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber who all gave lectures at the Bremen meeting. Also in 1890 Wiener published three papers: *Die Zusammensetzung zweier endlichen Schraubungen zu einer einzigen* Ⓣ; *Zur Theorie der Umwendungen* Ⓣ; and *Über geometrische Analysen* Ⓣ. In the following year he published two further papers: *Über geometrische Analysen. Fortsetzung* Ⓣ; and *Über die aus zwei Spiegelungen zusammengesetzten Verwandtschaften* Ⓣ.

In 1894 Wiener was appointed as an ordinary professor of mathematics at the Technische Hochschule in Darmstadt. His most important publication after his appointment to the chair at Darmstadt was the book *Die Einteilung der ebenen Kurven und Kegel dritter Ordnung* Ⓣ which was published in 1904. He retired from his duties in 1927, at the age of seventy. His health slowly deteriorated and he died after a long illness.

Although Wiener is not explicitly credited with influencing Hilbert in his championing of the axiomatic method, it is still worth noting that he gave the talk *Über Grundlagen und Aufbau der Geometrie* Ⓣ to the German Mathematical Society which was published in the first volume of the *Jahresberichte der Deutschen Mathematiker vereinigung* Ⓣ (1892). Wiener proposed that geometry be studied without using visual images, but rather by abstract axiomatic methods. He also joined his father in the creation of mathematical models of geometric surfaces, constructed from plaster and wire.

Among the honours that Wiener received was election to the German Academy of Scientists Leopoldina in 1895.

**Article by:** *J J O'Connor* and *E F Robertson*

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