This Function Solved a Historic Problem 

Given any positive integer, how many ways are there to break it up as the sum of itself or smaller positive integers? For instance, we can break up 4 as 4 itself, 1+3, 2+2, 1+1+2, or 1+1+1+1 (We don't consider the order of the numbers in the sum as a discerning factor). This is a very difficult problem if we didn't use a particular counting superpower!
This video goes in detail about generating functions and how they solved a historically hard problem about partitions of positive integers. I hope you find this video educational and interesting :)
Consider subscribing if you learned something new!