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
    Commented May 24, 2023 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
    Commented May 25, 2023 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
    Commented May 25, 2023 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. $\endgroup$ Commented May 30, 2023 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'. $\endgroup$ Commented May 30, 2023 at 18:25

1 Answer 1


This is perhaps a comment rather than an answer but too long for a comment.

Your question points to a general problem that I might call the "unitary model of scientific knowledge", in that there is a singular position in a historical moment that describe what is "discovered", "known", and "rediscovered". The missing question or variable is "to whom?".

As numerous commenters have pointed out, "system theory" never become unpopular or forgotten in engineering. Linear system theory is the core of virtually any engineering program, similarly can be said about other aspects of systems theory such as network theory and it's models (graph theory). This stands in no contradiction at all with some notion of "the mainstream of mathematics researchers show little to no awareness of system theory during a time period" and that in this sense "some mathematics researchers rediscovered systems theory in the guise of categorical systems theory", the the hypothetical at least.

Sadly even on the last statement I consider this ahistorical. Many practicioners in applied category theory have training in engineering disciplines (computer science etc) are very aware of ideas and developments in applied fields such as network theory, so it is in my view not even correct to say that this is a rediscovery. At current categorical systems theory has the status of a category-theoretic reformulation of applied models that have not categorified before.

So the fundamental question here is "what is known to whom" and what constitutes "forgotten" and "rediscovered". The most important step here is to "desingularize" knowledge. What may be unknown to a fresh pure math PhD may be well known to a fresh engineering PhD and vice versa. There may in fact even be differences in knowledge inside these groups and it might further be made more complicated as cohorts of working scientists further mature.

For example, Gabriel Kron provided work in systems theory from the perspective of decompositions of analogue machines, but with the intent of general applicability. I think it is fair to say that much of Kron's work has in substance been forgotten by most engineers and mathematicians, but stuck around as a kind of folklore history (people may know Gabriel Kron as a historical figure). But here too it is important to be precise. Kron's work is much more cited in analogue machine theory today than in other branches of engineering. In digital signal processing some of his ideas have reemerged (Kron reduction) recently. So it is important even on these examples to be specific whose knowledge we are referring to.


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