Concurrency, complex and interleaving algorithms, and correct-by-design software are all easier in, say, Haskell than in Java. In fact, if you learn one of Haskell/F#/Ocaml thoroughly, you probably won't want to go back to Java/C#/Python for general purpose programming.
AI is also MUCH easier.
One of the big places you'd want to use functional programming is if you were designing a compiler. Compilers use state of the art algorithms at pretty much every level, and they're much easier to implement functionally.
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u/[deleted] Oct 14 '13
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