MathGEMs Archive

Abstract: While the real numbers are great, they can't do it all. Where the real numbers fail, the complex numbers save us! By doubling the dimension, we gain more structure and numbers to work with. In classic mathematician fashion, we must ask what happens if we do it again? Do we get 3-dimensional complex numbers? Or 4? And why stop there! We will discuss how to "climb the ladder" of the sets of complex numbers, constructing higher dimensional algebras. We will see the limits of this process and some properties of these new algebras.

Abstract: Factoring numbers is known to be a hard problem. By merely playing a literal game with tennis balls, randomized in much the same was as any board game, we will be able to collectively factor a certain family of numbers. No prerequisite knowledge of number theory or algebra will be necessary, but we will cover the basics of modular arithmetic and divisibility. Hand-Eye coordination is also not necessary, but will help.

Associated paper: https://arxiv.org/abs/2110.13313