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Today, many members of the YouTube math community are getting together to make videos about their favorite numbers over 1,000,000, and were encouraging you - the viewers to do the same. Take a look at the description for details. My own choice is considerably larger than a 1,000,000, roughly 810^53. For a sense of scale, thats around the number of atoms in the planet Jupiter, so it might seem completely arbitrary, but what I love is that if you were to talk with an alien civilization or a super-intelligent AI that invented math for itself without any connection to our particular culture or experiences, I think both would agree this number is something very peculiar and that it reflects something fundamental. What is it, exactly? Well, its the size of the monster, but to explain what that means, were gonna need to back up and talk about group theory. This field is all about codifying the idea of symmetry. For example, when we say a face is symmetric, what we mean, is that you can
