  Though it goes without saying that linear algebra is fundamental to
mathematical biology, polynomial algebra is less visible. In this article, we
will give a brief tour of four diverse biological problems where multivariate
polynomials play a central role -- a subfield that is sometimes called
"algebraic biology." Namely, these topics include biochemical reaction
networks, Boolean models of gene regulatory networks, algebraic statistics and
genomics, and place fields in neuroscience. After that, we will summarize the
history of discrete and algebraic structures in mathematical biology, from
their early appearances in the late 1960s to the current day. Finally, we will
discuss the role of algebraic biology in the modern classroom and curriculum,
including resources in the literature and relevant software. Our goal is to
make this article widely accessible, reaching the mathematical biologist who
knows no algebra, the algebraist who knows no biology, and especially the
interested student who is curious about the synergy between these two seemingly
unrelated fields.
