If the 3x+1 problem is intractable, why should one bother to study it? One answer is provided by the following aphorism: ``No problem is so intractable that something interesting cannot be said about it.'' Study of the 3x+1 problem has uncovered a number of interesting phenomena; I believe further study of it may be rewarded by the discovery of other new phenomena. It also serves as a benchmark to measure the progress of general mathematical theories. For example, future developments in solving exponential Diophantine equations may lead to the resolution of the Finite Cycles Conjecture.
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