Atomic theory and mechanics, Nature, Vol. 116, 1925, p. 852.
This article arose out of an address that Niels Bohr delivered, on 30 August 1925, to the sixth Scandinavian Mathematical Congress in Copenhagen.
The quote is used an an epigraph on p. 276 in Operator Commutation Relations by Palle E. T. Jorgensen and Robert T. Moore, D. Reidel, Dordrecht / Boston / Lancaster, 1984.
This quote from Niels Bohr is also reproduced in vol. 3 of The Historical Development of Quantum Theory, Vol. 3: The Formulation of Matrix Mechanics and Its Modifications, 1925-1926 by Jagdish Mehra and Helmut Rechenberg, Springer-Verlag, New York, 1982, the volume about Max Born and his times. The quote is on the first page of the Introduction, i.e., page 3 in vol. 3 of the Mehra-Rechenberg work. This even constitutes the opening sentences of the Introduction, Mehra describing how Bohr saw the developments from 1925 on as a revival of the long-established connection between mathematics and physical theory. The Bohr quote is from a Scandinavian conference, which is carefully referenced by Mehra and Rechenberg. They also relied on recorded conversations, and on the Bohr archives.
Some interesting links for Niels Bohr:
Bohr_Niels [in the MacTutor History of Mathematics archive at the University of St Andrews]
Niels Bohr Archive
to Quotes selected by Palle Jorgensen