User:Autumn-Pan/Busy-Beaver-Resource-Guide

This page collects reading materials and learning resources, ranging from beginner-friendly texts to more cutting-edge research. It is highly recommended to look through this page as a beginner, since introductory texts are curated here. Commentary and original documentation will also be provided. Every outside link, including citations, is chosen carefully to not only cite sources, but serve as links to outside resources. The primary purpose for this article is to summarize parts of Busy Beaver research, and to generously append links to outside resources and readings to act as a starting point for learners.

Getting Oriented

This is a collection of general background knowledge on the Busy Beaver challenge and essential information for all niches.

To begin our work with the Busy Beaver function, we must first understand what it is about.

What is the Busy Beaver problem? [1]

• The first link is to the official story, which is outdated and deals with the fifth busy beaver value. However, it is still relevant for understanding the problem as a whole.

In addition to the official story, a number of YouTube videos have also been published on the Busy Beaver problem.[2][3]

We study the Busy Beaver function because it is uncomputable [4]. That is, no algorithm can determine any given value of BB(n) in a finite number of steps. In fact, many formal systems that we use to study mathematics, like Peano arithmetic and Zermelo-Fraenkel set theory[5], fall short of being able to decide all values of BB(n).

• We're actually having ongoing discussions about its independence from Peano arithmetic, which is open to new contributors. [6]

First Steps

The majority of our discussions happen on our discord server [7]. Furthermore, we now have a subreddit which is also open to everyone [8]. If you have any specific questions, feel free to ask them in our "beginners" channel [9]