Modular Hashing and the Collatz conjecture

Choose a positive integer. If it is odd, multiply it by three and add one. If it is even, divide it by two. The Collatz conjecture is a decades old conjecture that states that for all positive integers, if you repeat this process, you will eventually reach one. In computer science, a hash function is a function that is used to map data values into organized ``buckets'', so that the information in the buckets can be easily retrieved later. These two concepts are seemingly unrelated. In this talk, we will discuss a proof that shows that if a certain set of hash functions distribute given values over a certain number of buckets evenly, then the Collatz conjecture is false.