Regarding the use of mathematics
Walras thought that “the theory of value in exchange is really a branch of mathematics which mathematicians have hitherto neglected and left undeveloped” (Walras 1954: 70). Since the exchange value is a mathematical fact, resorting to mathematics for pure economics purposes is indeed possible and even necessary for science to make progress.
Formal language is clearer and more specific; it is indispensable on account of its heuristic value, and allows distinguishing true from false with certainty. Indeed, only formal language makes it possible to account for the complexity of the general interdependence of economic equilibrium, whereas natural language strays into apparent tautologies. Through the use of mathematics, it is possible to replace some of economists’ simple dogmatic assertions with rigorous demonstrations and achieve new results. Like all those who advocate applying mathematics to economics, Pareto shared Walras’s views on its formal advantages, but, unlike the latter, he did not believe it could guarantee, beyond mere reasoning consistency, the substantial truth of findings.