Key methodological differences between Austrians were highlighted in Milton Friedman's "The Methodology of Positive Economics." A key piece of conflict: Friedman's focus on prediction rather than explanation.
The impossibility theorem, developed by Nobel-winning economist Robert Mundell, paints a false tradeoff between the free movement of capital, fixed exchange rates, and effective monetary policy. Under a gold standard, all three are a possibility.
Proponents of modern monetary theory have come up with their own idiosyncratic definition of savings in support of their theory. But the common usage of the term shows MMT doesn't work the way its supporters think it does.