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Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1conjecture. I agree, but very soon it will be! With the exponential growth ofcomputer-generated mathematics, we (or rather our silicon brethrern) would havea shot at it. Of course, not by number crunching, but by symbol crunching andautomatic deduction. In the present article, I taught my computer how to usethe brilliant ideas of four human beings (Amal Amleh, Ed Grove, Candy Kent, andGerry Ladas) to prove two-dimensional analogs of this notorious conjecture.Once programmed (using my Maple package LADAS) it reproduced their tentheorems, and generated 134 new ones, complete with proofs. All by itself! Ibelieve that the proof of the original 3x+1 conjecture would be in the samevein, but one would need a couple of extra human ideas, and better computers.

Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture