As said, mathematics is just a language to say things precisely. To disregard math in, say economics, is to say precise formulation of statements is not valued. All science is based on testing hypothesis or statements. Precisely formulated hypothesis yields precise theories, vague hypothesis yields vague theories. Vague theory is almost useless as base to make predictions, which happens to be the essence of science. From this basis I find austrian school of economics handicapped for their avoidance of math, altough it has its virtues.
Any mathematician will tell you that to be valid, mathematics must proceed from valid premises. Without that foundation, it might as well be astrology.
This is obviously true for any practical application of math. (Math itself isn't that picky; any system of axioms and premises is in a sense valid, even contradicting systems, altough those are not useful in other than philospohical sense). Anyway, as said, to model economics properly you have to use sound premises. After that math by definition is very precise tool. And to find those premises scientific method is what prevails. Even if value is created from consciusnes, its modelable.
As social science economics is very slippery and have to be approached accordingly with, say statistical tools. In my opinion the main problem in modeling (macro)economics accurately is that if you are able to catch the peoples behaviour in a set of equations, when it becomes widely know, people will try to take advantage of it and the trend disappears or becomes unpredictable. Nevertheless, that is far cry from making math useless.
Hmm, good interview. He's right that, at a practical level, most mathematics in economics is useless. Worse than useless, actually. But at a certain level there are mathematical relationships that do hold, and will always hold. And a theoretical framework can be built up from there.
I couldn't disagree more. If you ingore the part of economics which is infested with values and opinions the math is very useful. Think of interest for example.