The intuitive physicists were triumphant on many more occasions. Like Richard Feynman, who, from his wild imagination of virtual particles, wrote down outrageously ill-defined integral overall paths of virtual particles and fields through space and time.20 At the level of perturbation theory, that is, pretending that the quantum was infinitesimal, Feynman’s path integral is nothing more than a mathematical trick that helps with organizing calculations. In fairness, it was a damn fine trick. It helped predict the magnetic dipole moment of the electron to eleven digits, while also helping to solve difficult mathematical problems from the topological invariants of knots to the deformation quantization of Poisson manifolds.21
I have always felt that mathematics could have been better used in economics.
Håvelmo argued also that if economics wanted to be taken as seriously as physics, chemistry and biology, it needed to employ probability because that was the way that opinions were expressed in science. He believed that if this was done, economics would make new insights, just as physicists and biologists had. He also observed that the natural sciences had found a perspective on nature that made it appear to follow stable laws. The goal of The Probability Approach in Econometrics was to present how this could be realised. Morgenstern began The Theory of Games, like Håvelmo, with an argument for the use of mathematics in economics and explained that what was required was the careful definition of terms, a pre-requisite of mathematics but lacking in economics. To this end, von Neumann started with the axioms of utility that had been at the core of Carl Menger’s, unmathematical, economics.