"The basic rule (that multiplication has precedence over addition)
appears to have arisen naturally and without much disagreement as
algebraic notation was being developed in the 1600s and the need for
such conventions arose. Even though there were numerous competing
systems of symbols, forcing each author to state his conventions at
the start of a book, they seem not to have had to say much in this
area. This is probably because the distributive property implies a
natural hierarchy in which multiplication is more powerful than
addition, and makes it desirable to be able to write polynomials with
as few parentheses as possible"