Comments by "David Terr" (@dcterr1) on "Why Do Sporadic Groups Exist?" video.

  1. To me, sporadic simple groups are kind of like Fermat primes, of which only five are known, which give rise to all known constructible regular polygons. Do you think there is any connection? And what about classifying semisimple Lie algebras? I know there's a connection between Lie algebras and infinite families of finite simple groups of Lie type, via Dynkin diagrams, though I'm by no means an expert on this! Do sporadic simple groups fit into the theory of Lie groups or Lie algebras, or are they more like the odd men out?
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  2. Wow, fascinating video! For many years, I've also been mystified by sporadic simple groups and have wondered why they exist. Your explanation of Mathieu groups and why they are sporadic makes a lot of sense! At some point, I'll have to try to see if I can understand why the other sporadic groups are sporadic as well. Great job!
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  3. I also understand that simple groups play an imporant role in the theory of solvable and unsolvable Galois groups, both of polynomials (whose Galois groups are finite and thus involve various sequences of finite simple groups) and of nonintegrable functions, like e^x^2, to which a version of Galois theory can also be applied to show that they are nonintegrable for the same reason that the roots of general polynomials of degree 5 or larger cannot be solved in terms of radical expressions. I wonder what roles if any sporadic simple groups play in either of these versions of Galois theory. I'd greatly appreciate any info you can provide on this topic.
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