Two interesting articles I ran across recently:
1 . Wikipedia on mathematical coincidence– a list of near-equalities and identities that just do not matter. This is a fascinating way to define a “coincidence”, as something that has no theoretical importance or connection to anything else. Initially I kept an eye on this article thinking it would be a neat way of explaining the 1/998001 decimal expansion, though Leonid Kovalev had a great post relating this identity to a broader theory of power series and generating functions. I find it beautiful and frustrating at the same time how nearly everything in mathematics has some significance. This is a fun page to remember for examples of non-significance.
As an anecdotal aside, there was a great colloquium speaker at Rice a few years ago, and I have forgotten everything about his talk (and even who he was!) except the following: he began the talk by listing 7 integers on the side of the board, and saying that he would describe their pattern later in the talk, but we could try to figure it out ourselves. When the promised moment came, it turned out they were the number of points the Rice football team had scored in their first 7 games (which of course the mathematicians had no hope of recognizing). However, it was interesting to see how many generating functions people in the room had come up with for these scores!
2. Wolfram article on roundoff error, including two stories of floating point arithmetic gone tragically wrong: once with a European Space Agency rocket, and once with a Patriot missile. Puts my series from last week in a bit more perspective.