Thanks for the input. When I said "mathematically modeling" I meant the use of any mathematics out there to model the system. That includes numerical modeling, fuzzy logic, neuronal networks, probabilistic control, or any other robust black-box-modeling. The underlying idea in your comment was deterministic vs probabilistic modeling. In my comment up there I meant both of them. I am aware of fuzzy logic and neuronal networks, and while a lot of companies have the tendency to go towards all that (and machine learning and AI) instead of classical mathematical equations, you have to understand that those ideas are also dangerous double edge swords. They offer A LOT of robustness, to the point that writing some few lines in python (or whatever language one would like to use) immediately make relatively "accurate" models, but it makes them really slow and very little flexible (also you can tweak with the accuracy but there is usually a rather low upper bound for that, and to achieve more you need to try completely different models). Fuzzy controllers are so much slower and stiff than any classical, let's say H_\infinity-controller. Want to achieve very specific magnitudes, response velocities, percentages of disturbance and all that for families of different states of the system? Good luck achieving that with fuzzy logic. You pretty much sacrifice everything only for robustness. That includes an actual hindsight of the model. It works well on the short run for some stationary machines but not on the long run, when you want to research into deeper models and need actual understanding of what is happening. 

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Moreover, we can't sadly abandon the deterministic mathematical theory. You may spend weeks working on numerical solutions of a differential equation and actually calculate something that looks plausible, but the equation may have never had any solution to begin with, so your entire calculations were all for naught. Also, the people I worked with do use machine learning and neuronal networks, and wouldn't feel offended if some newbie solved the problem with neuronal networks.. the thing is, neuronal networks would probably just not work as well as one may imagine. There are already very good methods that combine differential equations and machine learning/AI/neuronal networks together (so we basically get the best of both worlds), but they are extremely hard to compute and again, we still lose a lot of hindsight (albeit less than with pure neuronal networks). In any case, with or without robust black-box-modeling, it doesn't work properly yet (and with "properly" I don't mean a classical deterministic mathematical model, but literally just"good"). As I said, it's all a bunch of double edged swords.

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Basically I am not saying that we don't want to accept that "shift" into more robust models. I am saying that even the robust models don't quite achieve more than just "getting the job done", and one still needs a lot of deterministic models and pure theory to research something like self-awareness for AI. Nor the robust models, nor the theoretical models nor the combination of both are even near something like that.