Why is economics so mathematical?

As a physicist, it seems to me that economics is even more mathematical than physics. Now, I have barely more than a layman's knowledge of economics, but from reading descriptions of economics research and from skimming over a few random papers, it seems economics involves a lot more serious proof-based math than physics. In terms of background knowledge, it seems that economics research requires analysis, topology, probability, etc. at the level taught in graduate level math department courses, while much of physics research (even theoretical physics) requires little more than calculus and linear algebra. (Yes, some particle theory/string theory involves impressively high levels of math, but that is only a tiny minority in the field of physics as a whole). Okay, maybe economics is not really more mathematical than physics, but in any case it is quite mathematical, and it certainly goes against the stereotypical view that the social sciences are less mathematical than the natural sciences. So why is this the case? One cynical view is that economics doesn't really need much math and that all the fancy math is just a charade, for example as discussed in this popular question on this site, but I'm willing to give you guys the benefit of the doubt. Here are some of my thoughts on this question (please correct me if I am wrong!) In physics, the gold standard of any theory is comparison to experiment, and experiments are (relatively) cheap. On the other hand, economists can't really conduct experiments, and real world data is messy. So the gold standard is instead mathematical proof. For example, for physicists the ideal project would be coming up with some theory that uses math in a loose, "hand-wavy" way, say only 70% rigorous, but matches the experimental data 95%. While for economists, the ideal case would be to come up with some theory that is 95% mathematically rigorous, but only fits the real world data 70% (because the data is so messy that any better fit is impos