It is surprising that in the very period when modern ‘mathematical economies’ was burgeoning forth so auspiciously as a novel science, there was, it appears, only one occasion on which Henri Poincaré (1858–1912), universally acclaimed for his versatility in applied as well as pure mathematics, brought his genius directly to bear on the application of mathematics to economics. His single passing glance in this direction is, nonetheless, of considerable interest, revealing, as it does, a profound insight on Poincaré's part into the economic implications of the question he was called upon to examine. This occurred when Léon Walras invited Poincaré to pronounce upon his controverted assumption of cardinal measurement of utility when it ran into more serious opposition than usual.

Walras had first made this assumption in 1873, in his maiden analytical paper, ‘Principe d'une théorie mathématique de l'échange,’, which he read in August of that year before the Académie des sciences morales et politiques in Paris. The relevant passage reads: