[mr_mitm]

You are complaining that you study the simple cases or simplified cases first before you study near unsolvable systems?

Besides, very often the simplified case gets you surprisingly far because the difference between idealized situations and reality is often negligible or at least easily describable - see perturbation theory. The simplified cases are well worth studying.

[sfink]

If I understand correctly, or at least if I map it to my own similar complaint: the problem is not that they have you study simple or simplified cases, it's that the ignored complexity is unacknowledged and sometimes even denied. Which makes a lot of sense in primary school, where even mentioning it might cause some kids to ignore everything because "it's not really how it works" or whatever. But by the time you've made it past the basics, sweeping complexity under the rug is harmful. You still want to be studying the simplified scenarios, but it would be much better if you had some sense of the range of things that meaningfully differ from realistic scenarios. Not so you can take them into account in your solutions, but so you have the appropriate level of humility about what your solutions mean and the limits of their applicability.

I guess I didn't do that much physics, because for me it comes up more in other fields. In statistics, for example, it is critically important to understand the limitations of your results. For example, you might assume that error is normally distributed. You don't want to forget about that assumption, because it is very commonly violated, and it can make a large difference in your conclusions. Yet in school, it was almost always handwaved aside with "Law of Large Numbers mumble mumble mumble". Even when the law didn't apply, or the definition of "Large" happened to be "way bigger than your pathetic number of data points".

It's also why there's often such a gulf between academia and industry. Academic results walk a tightrope of assumptions and preconditions, and trying to put them into practice always finds places where those don't hold. Sometimes they even start out holding, but then everybody takes advantage of it until competition drives everyone into optimizing the residuals. If there's a space where things make sense, competition will always drive you to the edge of that space. Or beyond; competitive pressure does not care about keeping your equations simple and pure. Back to the point, you might study a field for years and then land a job in exactly that field, only to discover that everybody is looking at it completely differently because they've exhausted the simplified space and are deep in the land of heuristics, guesswork, and approximation. The market for spherical steaks was saturated years before.

[BlueTemplar]

Well for physics, the three-body problem, you see it in the first year, the Roche limit - in second. (Specifically two spheres coming close does NOT result in infinities, pointlike objects do - but then you also learn around the same time that atoms aren't pointlike objects and at nanometer-short ranges you have to start to deal with other forces than gravitation too...)

(I have my own beef with the "sweeping under the rug" which happens with (electromagnetic) pseudovectors, but I do realize that requires a LOT of effort to fix.)

[mr_mitm]

Sounds like an individual experience then. It's a bit of a stretch to blame "the physicists" for this. All of my teachers were very open about the short comings of our assumptions and solutions, and while it may be true that not every one and sometimes even none of "the physicists" is able to handle the complexity of realistic scenarios, I see no shame in working your way up until you get stuck. I can't remember a teacher that was too proud to say that something was too complicated.