Marshall had the fear that mathematical concepts were more likely to become the Ricardian vice. He warned that while mathematics is good, mathematical economics and mathematical theory were not likely to yield good economics. He argued that mathematical methods were only a good tool if it was to be used as shorthand rather than an engine that drives economic inquiry. This means that mathematics should be used to shorten long theoretical expressions that naturally occur from microeconomic formulations.
Marshall had the desire to improve the use of mathematical rigor to transform how analysis of economics was done at the time. He claimed that mathematical economics was capable of being transformed into a more scientific profession capable of remaining relevant to those for whom it concerned. Although Marshall pursued mathematical economics to a more advanced and rigorous level, he was of the idea that mathematics should not at any given time overshadow economics and thus render economic theory irrelevant to an average person. He hoped to reconcile the classical approaches that were likely to make economics an abstract subject. His views have since been supported by later economics, including contemporary economists of modern economics.
Antoine-Augustine Cournot, a French economist, attempted to bring out economic concepts using mathematical relations in their strictest sense. He is considered the first economist who had the knowledge of both subjects (mathematics and economics) and who treated economic theory as a product of mathematical relations. His main work concerned how mathematical principles related to the theory of wealth. He used mathematical concepts as tools to analyze the partial market equilibrium in which he relied on the assumption that players in the process were either producer whose main objective was to maximize profits. In his discussions, he abandoned the concept of utility and rather concentrated on the mathematical functions of demand and supply in different types of markets.