I don't know what mathematicians think. But I have been struck by inconsistencies in terminology and by disagreement about fundamental concepts among experts in statistics.
For example, I was watching a video in which a professor kept mentioning "scatter". I had no idea what he was talking about, but eventually it became clear that "scatter" was the same thing as "variation" -- which is also known as "variability", "dispersion", and "spread". That's 5 terms for one concept.
Here's another example: in the equation y = f(x), y is variously known as the
SST = SSR (Sum of Squares Regression) + SSE (Sum of Squares Error)
But one author (at least) uses "SST" (Sum of Squares Treatment) instead of "SSR" -- which is very confusing. (I forget what they renamed Sum of Squares Total.)
And experts disagree about some very basic concepts. For example:
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.