What is this "order of operation" cult now with math?

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For me it seems that this confusion or split have become true when people started to interface with computers (parsing classic paper infix notation with hidden brackets and many times 2-dimensions for computer 1-dimensional entry) and then with bedacocy justification some group got the idea that pupils should be prepared for computers, because computers are scary and stupid. Soup was set.

Now it seems that there is loosely a two and half groups.
The ones that read one line expressions like computer (but adding hidden symbols, which compilers do not do)
The ones that read one line expression like it was a print paper.
The last half that try to deduct the right aproach from content or say directly that something is ambiqyous. (Most math. uni. Profs seems to be on this group, which is wise I must admit[/b].)