In college my minor was in math. I learned that real mathematicians go to great trouble to formulate their problems and mathematical expressions in a non ambiguous way. They are trying to convey one and only one meaning. That is why you see thing like brackets in their expressions.
I was recently told the same thing by a mathematician. Mathematicians aim to be rigorous and unambiguous. However, engineers tend to be practical and assume others will know what they mean if they use shortcuts or abbreviations.
For instance, engineers may write 1/xy and assume the reader will interpret it as \$\frac{1}{xy}\$ and not as \$\frac{1}{x}y\$
On the other hand, a mathematician would always write 1/(xy) and leave no room for any doubt.
My education was in physics, with lots of mathematics on the side.
I learned the conventional order of operations, but I saw no reason not to be careful and use parentheses to avoid possible confusion.
I only needed to know the conventional order in order to read equations done by those less careful than I.
Incidentally, "Polish notation" (well-known in reverse as RPN, found in good calculators) was invented by Łukasiewicz (whose name is hard to pronounce in reverse order, hence the abbreviation RPN) to avoid ambiguity without recourse to parentheses.
I encountered Łukasiewicz' notation in the forward direction in a class on formal logic; compared with "infix" notation for logical formulae, it also avoids special characters, using only majuscules and miniscules found on a normal typewriter.
https://plato.stanford.edu/entries/lukasiewicz/polish-notation.htmlThere is an example for a formula in propositional calculus half-way through that citation (which does not copy) that requires 43 characters, including 20 parentheses, in "normal" spelling, but only 23 characters in Łukasiewicz' notation, all of which are "active".