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Briefly from wikipedia,

Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior.

In early math courses, we are often taught how to solve mathematics provided models of a scenario, but never quite how theories on how to come with models. The stuff one finds in even the earliest conception of this theory in General System theory, Ludwig von Bertalanffy seems to be quite useful in providing an understanding for this.

Yet, his name or the idea of system theory in general theory is never mentioned Mathematics classes. Hence, my question, how did the system theory as a field fall out of public view?

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    $\begingroup$ I tried to study system theory when I was in grad school, but concluded that this was a case where the totality was far less than the sum of the parts. $\endgroup$
    – Mark Olson
    May 24 at 22:49
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    $\begingroup$ According to the Google Ngram of systems theory, it did not fall out of public view at all. It is just that it's natural home is not mathematics. Heuristic reasoning on how to come up with applicable models is not what mathematics is about, it is about extracting what one can from models that have already come up. $\endgroup$
    – Conifold
    May 25 at 6:07
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    $\begingroup$ Imo, your question as posed is erroneous or, rather, it's applicable and true only for people who don't know, don't understand or reject it. In other words, there are many applied academic and scholarly domains where systems theory is alive, kicking and well, e.g., ecology, logistics and supply chain models, operations research, complexity theory, yada yada. You don't say where your math courses were taught but they sound like purely theoretical programs where ST would not be a natural fit. $\endgroup$
    – DJohnson
    May 25 at 11:00
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    $\begingroup$ As far as I know, at least in my country, System Theory is not studied in mathematics courses, but it is well-known and widespread in engineering courses, there are many courses of engineering named System Theory. Simply, it is not considered a branch of mathematics, even if some important parts as control theory or dynamical systems are part of mathematics. $\endgroup$
    – BakerStreet
    May 30 at 18:14
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    $\begingroup$ I saw your answer, but you speak of a particular field, I was referring to the usual practice of courses at universities, nobody has ever seen courses of System Theory at departments of mathematics, whereas they are normal at departments of engineering. This intersection of category theory and system theory you report could be very interensting, but I guess that few students or professors of mathematics have ever heard of it. The question speaks of 'popularity'. $\endgroup$
    – BakerStreet
    May 30 at 18:25

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Seems so that this has been rediscovered and being worked on under the guise of "Categorical Systems theory". See here

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