 Like Felsenstein, Sterner and Lidgard (2018) encourage historians and philosophers of biology to “move past the systematics wars”. Their point is not that this was unimportant, but that a singular focus on it tends to overshadow the impact of other important historical advances during this period. We agree. To remedy this, Sterner and Lidgard suggest paying attention to the practice of systematists in this period, rather than more narrowly focusing on definitional disputes (embodying the so-called philosophy of science in practice approach (Ankeny, Chang, Boumans, &amp; Boon 2011)). Doing so reveals that alongside the Systematics Wars were the dual methodological revolutions of the mathematization of systematics and the incorporation of molecular data. These trends cut across the separate schools of systematics, generating their own set of controversies. This is particularly acute in phylogenetics, where the rise of the use of mathematical and computational tools was both enthusiastically embraced and deeply resisted. We start with a short description of the impact of molecular data on phylogenetics, before moving to how mathematical and statistical tools were incorporated into phylogenetic methods in  section 1.2.3  (for other histories on these topics see Dietrich 1994, 1998; Hagen 2001; Sterner &amp; Lidgard 2018).