Arnie:

I think part of the allure is the chase. Rarely is there ever an unsolved mystery with such a big bounty. I think that people are drawn to both the mystery and the award. the same is true for unsolvable math problems. If you solve them you get fame and glory, but you also get the satisfaction of solving something that nobody on earth has solved before. I think another part of the Beale cipher is that you don't necessarily have to be an expert cryptoanalyst to solve it if it is a book cipher. If anyone guesses what the book or text the cipher is based on, they will be able to solve the cipher with ease. This means that there is not a huge advantage to having an extensive background in cryptoanalysis. I think that there is also an advantage when something is unsolvable to have an outside perspective. It is entirely possible that all the cryptoanalysts approach the problem in a very similar manner, and they negate other ways to solve the problem. Someone with an outside view on the field may have an advantage because they might come up with a completely original way to solve a problem. This is why there is still a large allure to trying to solve an unsolvable problem like the Beale cipher.