Not my type
At MindYourDecisions, Presh Talwalkar explains the correct answer to the following problem:
8÷2(2+2) = ?
I knew the answer just looking at the video's thumbnail; of course, it's 1. I smugly watched the video anyway, almost immediately to find that the answer is, in fact, 16. Oh!
What I didn't know, or had forgotten, is that when applying the order of operations, those operations that are of equal precedence are read from left to right. But it was not always so.
Let's travel back in time, a hundred years. I actually found an academic paper discussing this very ambiguity in 1917. How would they solve this problem? They also would start with the parentheses, and 2 plus 2 would be equal to 4. But then they would interpret this expression a little bit differently. At that time, mathematical typesetting was limited, so if you had something like x divided by 2y you would understand it's x over the quantity 2y. So for this expression we would take 8 divided by 2 multiplied by 4. That's because it would be hard to write this expression in the limited typesetting of the time. So they would complete this as 2 multiplied by 4, this will be equal to 8, and then we have 8 over 8 which is equal to 1. This is not the correct answer today.
Presh Talwalkar, 8÷2(2+2) = ? Mathematician Explains The Correct Answer, MindYourDecisions
So, the correct
answer to this mathematical problem depends on advances in typesetting? (confused)
One thing that I did learn from all of this, is that I was born about 100 years too late.