The indifference curve model: the Austrians are wrong about it.

We all know we cannot cardinally measure our utilities. Does that mean the indifference curve model is inappropriate? Obviously, the Austrians think so:
http://mises.org/daily/926
However, does it matter how much my utilities are exactly? Probably not. Consider my utility function between two goods, X and Y:
U=f(X,Y)
Since marginal utility of X is mathematically defined the derivative of U with respect to X, its equation is:
dU/dX=df/dX+(df/dY)(dY/dX)
Here is a thing: whether or not I know what my utilities are, I know on the same indifference curve it never changes, so dU/dX is always zero as long as I'm on the same indifference curve.
Does that mean my marginal utilities are always zero? Not really. If my income increases I can buy more goods and services, so my utilities will increase. In this case my marginal utilities may not be zero. However, in that case, I will be on another indifference curve a bit more outward from the origin.
Unlike the Austrian criticism above, the indifference curve model was not intended to calculate our utilities in the first place. Regardless of its ability to measure the exact utilities of an individual, the model does predict economic behaviour pretty well.
If you want to criticize mainstream economics using too much math, it is fine. However, please, do not bring a scarecrow criticism.

PS. The author of the post above argues that some 'prominent(?)' Austrian economists know math pretty well. However, how can I be convinced so as long as they never publish their works with mathematical analysis?

Mathematics in Social Science

I dug up this one at Mankiw's blog and more than agree with it.
http://gregmankiw.blogspot.ca/2006/09/why-aspiring-economists-need-math.html?m=1
What about non-economists who have jobs related to politics or social issues, for example, political scientists or policy analysts? I still think they (I mean 'we' by 'they') need to learn math. One reason. Political science and policy studies (or policy science, sometimes) are scientific disciplines. As long as 'science' is attached to their names, they need to quantify information analyze it systematically.
Why is it necessary to quantify information and analyze it systematically in science? That is probably the best way to replicate and evaluate the results using the theories involved. If you fail it, you may not be well-recognized in the field. Even in Poli-Sci, with the rise of social choice theory, mathematical thinking has become more and more important.
Thus, study math as hard as you can.