8÷2(2+2) = ? Mathematician Explains The Correct Answer

What is 8÷2(2+2) = ? Everyone is arguing about this problem, so let's figure out the correct answer! The problem involves the order of operations, historical math notation, and binary expression trees. Glad to see the world is passionate about mathematics! (Note: some people write 8/2(2 + 2) = but this has the same answer.)

0:00 Order of operations
1:12 Historical usage
2:11 Common questions
4:08 Binary trees

I studied Mathematics and Economics at Stanford. Press coverage of my work:
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*I get many, many emails about this problem and am unable to reply to them.

Here is a 1917 article from "The American Mathematical Monthly" that explains the usage of the division symbol as an exception to the order of operations
http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents

Google evaluation
https://www.google.com/#q=8÷2(2%2B2)

What is 6÷2(1+2) = ? The Correct Answer Explained
https://youtu.be/URcUvFIUIhQ

9 - 3 ÷ 1/3 + 1 = ? The Correct Answer (Viral Problem In Japan)
https://youtu.be/07Abat5iBbw

Plus Magazine David Linkletter suggests the problem is not well-defined
https://plus.maths.org/content/pemdas-paradox

Harvard's Oliver Knill also says PEMDAS does not resolve the ambiguous problem
http://www.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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