> The purpose of [mathematical] models that are built thoughtfully is to explain why complex systems are the way they are, with data and algorithms, however imperfectly.

Nope. The main purpose of the whole endeavor is usually to predict the behavior of a complex system, because that's actually what we care about. If we can predict it, we can adapt to it, and eventually use it to our advantage.

Explaining why a complex system is the way it is, is merely nice-to-have. Models are opinions. All of them are wrong, but some are useful, and we rank them by how useful they are. The models and explanations are important because, beyond their elegance and convenience, it's also the case that more accurate models give you better predictions across larger domains, meaning we get better at getting something useful out of the complex system.

People get fixated on modern theoretical science, with bottom-up mathematical explanations traced through seas of empirical data, with whole magical rituals of peer review and double-blind studies and statistical significance around them. But they forget that the core of empirical science is literally throwing shit at a wall to see what sticks. That is the guiding principle, everything else is just making the process more efficient.

Understanding complex natural systems (or even engineered ones that got too complex) always starts with tests - tests on the real thing, then on approximate models that we poke and prod and bash into shape until they start acting similarly to the real thing. It's through the poking and bashing, and how they affect our proxy model, that we glean insights into nature of the simulated phenomena, and eventually formulate general theories - but more importantly, the models give us useful predictions from the start, before we have any theories explaining why.