Arnold Sommerfeld was among the most important students of the so-called ‘older’ quantum theory. His many contributions included papers in 1915 and 1916 extending Niels Bohr’s ‘planetary’ model of the atom beyond circular orbits and his incorporation of relativistic corrections in order to explain hydrogenic fine structure. Originally a realist in his use of Bohr’s model, Sommerfeld became increasingly disillusioned with model-building in general in the late nineteen-teens and early nineteen-twenties. This paper explores Sommerfeld’s use of the term Zahlenmysterium as (...) a self-description of his physical methodology. Rather than reading talk of mysticism as mere pandering to irrationalist forces in Weimar Germany, as some have suggested, I argue that one should see it as a genuine description of the scientific method Sommerfeld increasingly advocated throughout this period. That is, Sommerfeld drew upon and modified talk of Mystik as a means of expressing his own ideas on the importance of aesthetics in what might otherwise be cast as mere guesswork in his phenomenological spectroscopy. Mysticism, properly defined, was an integral part of what Sommerfeld termed die Technik der Quanten.Keywords: Quantum theory; Arnold Sommerfeld; Theoretical physics; Spectroscopy; Phenomenology; Theoretical practice. (shrink)