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If I had to associate a place with Elon Musk, LA would probably be it. SpaceX is based in the LA area, and IIRC Musk does live down there somewhere (although I don't think it's in LA proper). Musk has also captured quite a lot of attention lately for his various antics and ventures.

The problem that LA has is that there are a lot of very famous people you might associate with it. It seems like a nearly impossible problem to solve.

I do agree that birthplace would be a more interesting map, but I think it would be more interesting for tiny places. I think LA would suffer from the exact same problem.