What is systems biology? What can biologists gain from an attempt to algebraize the questions in systems biology? Starting with plausible biological theses, can one algebraically model them and then manipulate them to suggest meaningful hypotheses? Using these hypotheses, can one measure and mine suitable experimental data to validate or refute these hypotheses? Through these intertwined processes of measuring, mining, modeling and manipulating biological systems, can one generate the set of theses and hypotheses upon which systems biology will be founded? This review provides one algorithmic-algebraist's somewhat idiosyncratic response to these and other related questions, but also aims to persuade young algebraists to examine the possible role they and algebra can play to enrich this subject.