“The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.”
Alexander Grothendieck
Recently, I came across a paper by Dan Isaksen, which I find very interesting. It shows that even incredibly basic math, such as the way we learned to add integers in elementary school, could be seen from a much deeper and beautifully illuminating light of group cohomology. The original paper is very accessibe, but I still wanted to share this with you in my own exposition. We begin by revisiting the classic algorthim for adding and subtracting non-negative whole numbers: we align the numbers vertically, we do the operation digit-by-digit, and carrying a \(1\) when the digits add to \(10\) or more. The “carrying” here is the essence, we will see that this could be interpreted as 2-cocycles in a certain group cohomology.