Someone has posted a paper to the Web purporting to solve the Collatz problem, sometimes known as the 3x+1 conjecture: Abstract: Berg and Meinardus, 1994, 1995, introduced a pair of linear functional equations, acting on a space of holomorphic functions H, deļ¬ned on the open unit disk D. The simultaneous solutions of the two functional equations contain a simple two dimensional space, denoted by delta 2, and if one could show that delta 2 is the only solution, the Collatz conjecture would be true. Berg and Meinardus already presented the general solutions of the two individual functional equations. The present author reformulates the pair of functional equations in form of two linear operators, denoted by U and V . Thus, K := {h in H : U[h] = 0, V [h] = 0} is of main interest. Since the general solutions of U[h] = 0, V [h] = 0, denoted by KU , KV , respectively, are already known, we compute U[h] for h in KV and study the consequences of U[h] = 0. We show, that, indeed delta 2 = K follows, which implies that the Collatz conjecture is true." < http://preprint.math.uni-hamburg.de/public/papers/hbam/hbam2011-09.pdf > I haven't heard anything yet about expert opinion of its validity. --Dan Sometimes the brain has a mind of its own.