From a lecture by Paul Adrien Maurice Dirac titled ‘The Relation Between Mathematics and Physics’, on presentation of the JAMES SCOTT prize, February 6, 1939

*P**ublished originally in: Proceedings of the Royal Society (Edinburgh) Vol. 59, 1938-39, Part II pp. 122-129*

Reposted at http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html

“I would like to put forward a suggestion as to how such a scheme might be realized. If we express the present epoch … in terms of a unit of time defined by the atomic constants, we get a number of the order 10^{39}, which characterizes the present in an absolute sense. Might it not be that all present events correspond to properties of this large number, and, more generally, that the whole history of the universe corresponds to properties of the whole sequence of natural numbers? At first sight it would seem that the universe is far too complex for such a correspondence to be possible. But I think this objection cannot be maintained, since a number of the order 10^{39}^{ }is excessively complicated, just because it is so enormous. We have a brief way of writing it down, but this should not blind us to the fact that it must have excessivly complicated properties.

There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.”