George Walford: Beyond Mathematics

The success attending physical science has won enormous prestige not only for the activity itself but also for the mathematics that plays such a large part in it. So much so that the sciences are sometimes arranged according to their degree of mathematisation, mathematical economics for example being ranked above researches in the same field expressed in words. Other people, well qualified to speak, hold different views. Here is J. M. Keynes reporting the views of Arthur Marshall, one foremost economic authority speaking about another:

Marshall, as one who had been Second Wrangler and had nourished ambitions to explore nuclear physics, always felt a slight contempt from the intellectual or aesthetic point of view for the rather “potty” scraps of elementary algebra, geometry, and differential calculus which make up mathematical economics. Unlike physics, for example, such parts of the bare bones of economic theory as are expressible in mathematical form are extremely easy compared with the economic interpretation of the complex and incompletely known facts of experience, and lead one but a very little way towards establishing useful results.

A footnote extends the theme:

Professor Planck, of Berlin, the famous originator of the Quantum Theory, once remarked to me that in early life he had thought of studying economics, but had found it too difficult! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts, most of which are not precise, which is required for economic interpretation in its highest form is, quite truly, overwhelmingly difficult for those whose gift mainly consists in the power to imagine, and pursue to their furthest points the implications and prior conditions of comparatively simple facts which are known with a high degree of precision. [1]

Very consoling to people struggling with a study which presents these difficulties in an even higher degree!

[1] Keynes J. M. 1961 (1951) Essays in Biography London: Mercury Books 157/8)

from Ideological Commentary 62, November 1993.