The English Wikipedia article about Turing machine opens with:
A Turing machine is a mathematical model of computation that defines an abstract machine,
As a Hebrew speaker, I read a similar explanation in Hebrew Wikipedia:
מכונת טיורינג היא מודל חישובי מתמטי אשר באמצעותו ניתן לתאר באופן מופשט את פעולתו של מחשב (כולל מחשב מודרני).
I understand this term as reflecting a scientific theory in CS or Math, but interestingly, none of the two opening sentences presented this concept as a scientific theory in either CS or Math.
By scientific theory I meant:
An idea or set of ideas that can be falsified by principle (falsifiability as a condition for it to be real) and that one or more reinforcements can make it somewhat more plausible in reality.
If it's a theory in Math, maybe my approach is wrong, because, as far as I understand, in Math the paradigm is different so something is either true or false (i.e, not true).
Is Turing machine a scientific theory in CS?
In comment section, Yuval Filmus said (minor paraphrase):
Turing machines are a mathematical abstraction.
They're neither a scientific theory nor a practical engineering idea;
Actual computers are much better modeled using a different abstraction → RAM machines;
The relevant scientific theory is the Church-Turing thesis.
This made me wonder "what is the difference between a mathematical model and a mathematical abstraction and does the former or the latter or both, can be based in a "scientific theory"?
This isn't the main question, but you are welcome to explain this in an answer as I think it's relevant.