The relationship between the social sciences and the natural sciences has always been a little strained, with social sciences constantly seeking the approval of the natural sciences. The social sciences cannot use the same methodology as the natural sciences, which causes too many natural scientists to look on the social sciences as having little to value.
That is not to say that all social sciences suffer from this problem. The sciences of anthropology and archaeology are quite well accepted, and psychology mostly so, but too far beyond that and the value, as seen by a natural scientist, diminishes rapidly.
Some of the fault for this does lie in the social sciences themselves. If one is to study psychology, the basic courses are more of a history of psychology, where each theory is studied, and then the refutation by the competing school is offered. An equivalent in the natural sciences would be for a physicist to have to study phlogiston and for a biologist to have to study the four humours. They are valuable in a history of science class, but have no actual value to someone seeking to learn science now.
Some in the social sciences feel the problem is that the issues studied aren't expressed mathematically. This is the solution adopted by Keynesians, and since that ideology is currently dominant other economists who wish official approval adopt the practice of trying to express everything in number. This includes some factors that cannot accurately be measured, such as "consumer confidence" or "satisfaction."
There is an aspect to Keynesian economics that would appeal to engineers, in that the Keynesian economic model present society as a machine, and if a certain input is inserted at one end a certain end result comes out of the other. But that alone doesn’t make Keynesian economics scientific.
The underlying basis of science is "does it work." That may sound like a strange stipulation to a person who read "Pragmatic Politics" but unlike the pseudo-pragmatists, when a scientist says "does it work" the scientist is operating from a specific premise. "Pragmatic Politics" also argued that any time someone asks that question they person asking it is acting from a particular premise of what goal the person asking it is trying to achieve. In the case of the scientist, the goal is a theory that accurately describes the real world and can be used to make accurate predictions.
It is said that when Einstein had finished developing his theories, he was quite distressed that as a consequence of his formulas black holes were predicted. He checked his work many times, but eventually came to the conclusion that the data said what the data said. As much as he personally disliked the idea of black holes, the theory was meant to reflect the world and he had to accept it as it was. Later on corroborating evidence was found that showed the mathematics were correct.
That is what made his theories scientific. They were designed to reflect the world, not the way he wished the world to be. They made predictions that could be tested. And unlike the theories that were replaced by Einstein’s theories, the tests showed that the theories accurately modeled the world.
All the currently competing schools of economics make predictions. Keynesian economics predicts that manipulation of aggregate demand can lead to a prosperous economy. Monetarist economics predicts that manipulation of the money supply can lead to a prosperous economy. And both of those have been discredited by events. If a theory is supposed to model the real world, then neither Keynesianism nor Monetarism are theories.
Once a theory has been discredited by the data, continuing to hold to that theory is no longer scientific but an act of faith.
Austrian economics, however, has been validated by events. Although it lacks the mathematics that many consider to be necessary for a scientific theory, an honest analysis shows that the predictions have been accurate. Since it is not the mathematics but the predictive power of a theory that makes it scientific, that means that Austrian economics is indeed a scientific theory of economics.
Although there are those scientists who might initially find it unappealing, if they emulate Einstein they will reluctantly embrace it because of its verified predictive power in spite of whatever political ideology they hold.