Teichmüller was born in Braunschweig in the Duchy of Brunswick. He taught as a professor at the Basel University (since 1868) and the Imperial University of Dorpat (since 1871). He died in Dorpat, Russian Empire (now Tartu, Estonia).
In his philosophical work he argued for personalism.
- Die aristotelische Eintheilung der Verwaltungsformen (St. Peterburg 1859)
- Studien zur Geschichte der Begriffe, 1874
- Darwinismus und Philosophie, 1877
- Meyers Großes Konversationslexikon, 6th reprint (1909).
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