Over the last seventy years, a range of criticisms has been levelled at the mathematization of economics. While particular criticisms have been pursued extensively, for example, that the mathematics of classical physics provides an insecure base for economics, few general overviews of the critique of mathematical economics have been made. This is the focus here where seven objections to the mathematization of economics are identified. They range from the claim that the axioms of mathematical economics do not correspond to real world behaviour to the assertion that mathematics has often been an unnecessary adornment to economic discovery about the real world but is promoted because it serves unstated social and political purposes. While no determinate answers can be provided to each of the seven criticisms raised, it does appear that the case for the mathematization of economics is not without its limitations.