Rothbard (1993, pp. 638–45) refuted the important economic fallacy that excess capacity is a normal consequence of profit maximizing behavior by businesses in some industries when they are in long-run equilibrium.
What is certain is that mathematics cannot possibly be a valid means (to advances in economic understanding) unless and until it is used properly. That means that dimensions must be used consistently and correctly.
Neoclassical utility functions are an invalid means of analyzing consumer behavior for three reasons: first, and most important, because such functions, and their attendant rankings, are cardinal, not ordinal in nature;