Dynamical systems workgroup

New Findings on the Collatz Conjecture Reveal Hidden Global Stability - a possible road to a proof

Orion Haunstrup

Friday, February 14th, 2020
4:15 PM - 5:30 PM

The Collatz Conjecture is one of the most insurmountable math problems on the market today. The famous mathematician Paul Erdös once state, “Mathematics is not yet ready for such problems.” I am not sure I believe this anymore. I have spent the last three years intensely researching the Collatz problem. I have found many fascinating results not all of which we will not have time to cover — if you are interested, please refer to my website-in-progress CollatzResearch.org for a full discussion. For this talk, we will be examining under a microscope the most critical fact that I have discovered in my Collatz Research, something that totally changes the problem. While at a small local scale the movements of the Collatz dynamical system are wild, unpredictable, and chaotic. They are very hard to work with. In my research, however, I’ve discovered that if you zoom out your considerations to a global scale, studying the sizes of the Collatz branches, you find a shocking kind of stability and uniformity. This talk will be a detailed discussion of this global stability. We will examine extensive experimental evidence suggesting it looks to be true, and we will cover why, if I can prove it true, the divergence half of the Collatz Conjecture follows from it as a corollary.

Event contact: vmatusde at ur dot rochester dot edu