From the beginning of my educational career I have known of evolution and the ways natural selection acts on advantageous traits to push evolution forward. It was not until I reached college, however, that I started to understand the connections we as humans have to all of the life that surrounds us. I recall learning in my high school science classes that we have large portions of DNA in common with other species, but the notion of all life stemming from a common ancestor was brushed over when learning about evolution. Additionally, coming from a scientifically illiterate family who denies theories such as evolution and climate change, my thoughts on evolution were never stimulated through interactions at home. It was not until I took an ISS course at MSU that touched on various aspects of anthropology that evolution became a much clearer concept to me. Learning that humans did not evolve from other primates that exist today, but that we all evolved together helped me to better understand our place in the natural world as a part of it instead of apart from it. 

As a mathematics major the majority of my courses do not concern much of the physical world and notions of evolutionary biology are not explicitly discussed in any of my courses. When mathematics does discuss the physical world it is almost exclusively in the realm of applications to the physical world that help us to quantify concepts discovered empirically. The Hardy-Weinberg principle is just one of the many applications of mathematics to natural phenomena, specifically it is an application of mathematics to evolution. The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. Hardy’s equation defined a recurrence relation for the allele frequencies which was derived from fundamental principles in probability. While there are several assumptions that must be made to apply this equation in its simplest form and it cannot be used to fully understand how allele frequencies work, it can still be used to better understand evolution. 

Aside from applications of mathematics, when I think about mathematics in the context of evolution I see many parallels between the evolution of mathematics and biological evolution. In evolutionary biology, we all derive from a distant common ancestor and through mutations, the existence of different ecological niches, and selective pressures we see the vast variations of life on earth. Fields of mathematics begin with the declaration of axioms and from these axioms we deduce results such as theorems that are then used in conjunction with the axioms and other theorems to prove more powerful results. Mathematics is always going through mutations, each subsequently making the body of work much stronger and more useful. As different fields of interest come about, different fields of mathematics arise to study those interests, such as geometry, differential equations, or number theory. These fields of mathematics all vary in the mathematics produced and used to further their body of work, but all are connected at a very basic level and share many common themes.