Number Theory is what truly fascinates me about maths. Because it is

*deep*, I suppose. Numbers are everywhere. Numbers are universal. As in universe-al perhaps ( ... ). Imagine an intelligent civilization on a distant planet in the universe. If they are intelligent than they must have numbers and thus prime numbers. The movie 'Contact' based on the book of Carl Sagan was about how we would establish contact with extra-terrestrial life. Almost inevitably prime numbers are involved. There is a short paper written by a number theorist that explains how this communication might work, 'Prime numbers and the search for E.T.' ( pdf )

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