The Collatz Conjecture

Mr. Daniel Gulbrandsen
Graduate Teaching Assistant
University of Wisconsin – Milwaukee

“The Collatz Conjecture (Lothar Collatz, 1937) is simple to state:

Begin with any positive integer. If the integer is even, divide by it 2. If the integer is odd, multiply it by 3 then add 1. Reiterate this process. The conjecture is that no matter what positive integer we begin with, we will eventually iterate to 1.

With such a simply stated conjecture, one might expect a simple resolution. Appearances, however, can be deceiving. In fact, shortly after its conception, the Collatz Conjecture’s simple appearance notoriously beguiled math departments across the globe into devoting entire semesters searching for a simple resolution, but only to end up empty-handed. But what are mathematicians if not persistent?
In this talk we will investigate this conjecture, and we will describe some progress that mathematicians have been able to make towards a resolution to this open problem.”