Comments by "Scum42" (@Scum42) on "A Lifelong Mathematical Obsession" video.

One of my favorite things about this video is your description of where you gave up when you tried this post-grad. You gave up during the most complex step (how many ways can a permutation contain at least k forbidden pairs) with the thought "this is getting ridiculous, there must be an easier way to solve this." Well, as the rest of this video shows, there really isn't. This was only solved by rolling up your sleeves and diving into that mess head first, keeping track of everything as best as you can along the way. This is a really great lesson on the fact that while striving for elegance and simplicity is usually a good idea, and can often lead you to the right answer, it isn't always possible. Sometimes a problem really is a mess but is solvable through pure perseverance. And as a consequence of that complexity, the final formula is messy as well.
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