Real-world setting --->>> formulation of mathematical model [science knowledge or hypothesis]and mathematics concerns the "theory" part of the second step. A typical theorem-proof mathematician might agree that their job is

formulation of mathematical model ---->>> predictions from model [mathematics: theory or simulation]

predictions from model ---->>> compare with experimental/observational data [statistics, if needed]

(I saw this quote in a thought-provoking 2018 U.K. report The Era of Mathematics, which decried such a "passive" attitude). My experience is that when mathematicians say "science" they usually think "physics", as having precise mathematical laws.Mathematics can be seen as a big warehouse full of shelves. Mathematicians put things on the shelves and guarantee that they are true. They also explain how to use them and how to reconstruct them. Other sciences come and help themselves from the shelves; mathematicians are not concerned with what they do or with what they have taken.Jean-Pierre Serre.

Turning to *probability* models, even though the only mention of probability in Hilbert's
problems was
in the context of statistical mechanics,
most uses of probability models are in contexts outside physics where we do not expect the model to be precisely accurate.
In mathematical probability, even the part called applied probability,
a model is generally a set of stated
rules for how some *hypothetical* system might vary in some random way, and one seeks to
study the resulting behavior of that system.
While parts of theory often have names (*diffusion processes* or *birth-and-death processes*)
reflecting their origin, amongst the 3,500 papers a year on such theory in MathSciNet
very few have any relation with actual data.
So this activity matches the Serre quote above, and perhaps also the following well-known quote.

The famous statistics quote isAs a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" ..... there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities.von Neumann, in The Mathematician.

(Though memorable, this quote strikes me as silly, in that in implicitly treatsAll models are wrong, but some are useful.Box and Draper.

because fiction has a spectrum from pure fantasy to literary realism, and analogously probability models lie on a spectrum from fantasy to toy models, which we don't pretend will give numerically accurate predictions, to models with verifiable numerical predictions. The latter I will callprobability models arefiction

Also, the culture of academic research in quantitative disciplines
often encourages theoretical modeling which is never seriously compared with data.
This is emphasized both by Taleb in
The Black Swan and Piketty in
Capital in the Twenty-First Century.
Individual papers of this *unanchored* style can be interesting, but
when a whole topic is unanchored it is unlikely to be of lasting value.