Thanks to the four color problem, a rift rose between orthodox mathematicians and the budding computer science community over what comprises a proof. Recently when I was refreshing my memory on the four color problem, I became distracted by this disagreement and the question What is a proof?. So, I looked into some info surrounding these topics such as the history of proofs and proof assistants, problems mathematicians raise with proof assistants, and the validity of proof assistants.
With an amusing history spanning over 150 years, the four color problem is one of the most famous problems in mathematics and computer science. The four color theorem states that the regions of a map (a plane separated into contiguous regions) can be marked with four colors in such a way that regions sharing a border are different colors.
If it is easy to verify whether a solution to a problem is correct, is the problem easy to solve? This question is posed as the P vs NP problem and is considered one of the most important unsolved problems in Mathematics. This post will be brief and forgo many technical details surrounding the question for the sake of accessibility.
Games are the perfect mix of chaos and strategy: they are dynamic, since players’ decisions affect them, but there often exists an optimal way to play. This post discusses
- why we can solve some games but not others.
- how we solve these games.
- different processes developed along the way.
The solvability of tic-tac-toe, set take-away, Connect 4, checkers, and chess will be examined in further detail.