Wittig was born in Berlin, Germany; shortly after his birth moved with his family to Kassel, where his father was professor at the applied arts high school.

After being an Allied prisoner of war from 1918 until 1919, Wittig found it hard to restart his chemistry studies owing to overcrowding at the universities.

The time in Braunschweig became more and more problematic as the Nazis tried to get rid of Karl Fries and Wittig showed solidarity with him.

The 1956 appointment of the nearly sixty-year-old Wittig as head of the organic chemistry department at the University of Heidelberg as successor of Karl Freudenberg was exceptional even at that time.

Wittig was well known in the chemistry community for being a consummate experimenter and observer of chemical transformations, while caring very little for the theoretical and mechanistic underpinnings of the work he produced.