Most Austrians tend to say that the problem with the modern mainstream of economic science is that they use the standards of intellectual inquiry that are dominant in physics. The mainstream economists are thus guilty of what Hayek (if I am not mistaken) called ‘physics envy’.
According to those Austrians, mathematical modelers attempt to make unrealistic models of reality and then test them, like physicists do. But do physicists (at least classical physicists from whose work much of the modern mathematical methods in economics were borrowed) really do what they are charged with?
Let us take the theory from which the indifference curves were borrowed, the isotherms of the Carnot cycle of thermodynamics. Now, of course the theory makes a somewhat unrealistic assumption that the reservoir that is used to maintain the temperature constant throughout the experiment is infinite. But I think the infiniteness can be thought of as a harmless approximation in measurement.
Another retort would be to say that the thermodynamic description of the Carnot cyckle utilizes averages like say macroeconomics does. In particular, temperature is nothing but certain average of the kinetic energy of the molecules inside the closed system multiplied by a constant. Why then not say that physicists are as unrealistic as macroeconomists who utilize the constructs like price levels?
The answer is that not all averages are made equal. It is possible to average over the same units. And in physics speed is kinetic energy is kinetic energy, regardless of the object.*
Kinetic energy is an objective mathematical dimension that can indeed be averaged. But what about price. Is price really a measure like speed is? The answer is an obvious no. The prices are not actually 2$ and 3$, they are 2$/banana and 3$/orange. Dollars are thus not units of some measure of a good. They are just units of money. Averaging over such units does not give a price, it gives the average amount of units of money that changed hands which, however subtle this idea might be, is a wholly different thing from price.
Thus, the stake can be turned against mainstream economists. The creators of thermodynamics did not do the unrealistic modeling, they stayed faithful to the elements of the world which they were describing. So should economists.
*A question may be asked how we can know it. There is clearly no experiment that could prove this idea. Thus the hypothetico-deductive conception of physics is clearly wanting. Classical physics at bottom is clearly based on fundamental bits of experience but not on experiments.