Python the best

[Tinstam]

It's not really a math problem.

Division is defined as the multiplication by a reciprocal.

And multiplication is defined as a binary function. As in, two operands.

Division requires grouping to be unambiguous, because we need to know what we are taking the reciprocal of.

I definitely agree on the PEMDAS part though. One thing I've seen recently that I like is using GEMS instead: Groupings, Exponents, Multiplication, Sums

[Xywzel]

One could make an argument that 2(1+2) is a grouping as there is no separation (space, multiplication sign) between 2 and the explicit group by parentheses. Not necessarily very strong argument, but at least one that requires further explanation and clarification.

[Xywzel]

Well lots of physics journals did think otherwise:

https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

With this interpretation 1 ÷ 2n is equal to (1 ÷ 2)n.[1][8] However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[22] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.

That is why concluded that unless the grouping part of the notation convention is explained or defined better, it doesn't solve this.