Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture
| dc.creator | Zeilberger, Doron | |
| dc.date | 2009-03-24 | |
| dc.date.accessioned | 2026-07-07T12:56:04Z | |
| dc.date.available | 2026-07-07T12:56:04Z | |
| dc.description | Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1 conjecture. I agree, but very soon it will be! With the exponential growth of computer-generated mathematics, we (or rather our silicon brethrern) would have a shot at it. Of course, not by number crunching, but by symbol crunching and automatic deduction. In the present article, I taught my computer how to use the brilliant ideas of four human beings (Amal Amleh, Ed Grove, Candy Kent, and Gerry Ladas) to prove two-dimensional analogs of this notorious conjecture. Once programmed (using my Maple package LADAS) it reproduced their ten theorems, and generated 134 new ones, complete with proofs. All by itself! I believe that the proof of the original 3x+1 conjecture would be in the same vein, but one would need a couple of extra human ideas, and better computers. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0903.4050 | |
| dc.identifier | http://arxiv.org/abs/0903.4050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224462 | |
| dc.subject | Combinatorics | |
| dc.subject | Dynamical Systems | |
| dc.title | Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture | |
| dc.type | text |