Paul Daniel Hahn was the youngest son of the Rhenish missionary Johannes Samuel Hahn and his wife Helene Langenbeck, and a brother of J. Theophilus Hahn. He graduated as Master of Arts (MA) and Doctor of Philosophy (PhD) in March 1874. His doctoral thesis consisted of two papers which dealt with the phosphorescence of minerals and the chemical constitution of natural silicates respectively. On 28 June 1875 he married Marie N.A. Aneck at Gotha, with whom he had six children. In September 1875 he was appointed Jamison professor of experimental physics and practical chemistry at the South African College, Cape Town. From 1893 his post was changed to professor of chemistry (which later included metallurgy), a position he retained with distinction to his death in 1918.