Was there a time before Order of Operations in Modern History?

Question

I have twice come upon adults who have stated that Order of Operations is only a part of this "New Math" that is now being taught and wasn't a part when they were growing up. This seems illogical to me as how was such a fundamental part of algebra not included in the curriculum until recent times. One was with one of those infamous facebook mathematics posts where they thought that $$4 + 3 \times 5 = 7 \times 5 = 35 $$ instead of $$4 + 3 \times 5 = 4 + 15 = 19 $$ The second person was arguing that $$ -4^2 = (-4)^2 = 16$$ instead of $$ -4^2 = -(4)^2 = -16$$ While I am unaware of the first person's education, the second person has a Masters in Electrical Engineering which makes me think they got a good education in mathematics yet contradicts what seems logical to me. I've done some research but cannot find any indication that Order of Operations is a new concept. Is it a new concept or are these two adults just mistaken?

Answer 1

According to Earliest Uses of Various Mathematical Symbols:

The convention that multiplication precedes addition and subtraction was in use in the earliest books employing symbolic algebra in the 16th century. The convention that exponentiation precedes multiplication was used in the earliest books in which exponents appeared.