Semester Project

Foundations of Graph Theory

There have been few advancements in Mathematics as influential as set theory, and there have been even fewer that seem so simple. The idea of a set or a collection of objects has been around for as long as humans have been collecting things. Arranging rocks, people, money, food, or any other object based, on common characteristics is intuitive for just about anyone. Even in Math mathematicians have been differentiating between different groups of numbers--such as the integers or the rational numbers--and geometric shapes since the days of the Euclid. However, idea of creating a more rigorous mathematical definition of a set did not emerge until the mid 19th. Today, set theory is often seen as the foundation of modern math as it creates a formalized construction and notation for any mathematical object.

In this paper, I will explore the beginnings of the ideas of set theory and specifically the problems that mathematicians faced as they endeavoured to create a set of axioms that could truly lay a rigorous foundation for all math. The stories of how those problems were solved, and the new ones that emerged from their solutions, serve as a reminder that while math is incredibly powerful, it is an ultimately imperfect and incomplete method of viewing the world.