What is sometimes casually described as the "mathematics community" in the United States already by the late 19th century was displaying divisions, which became more distinct and variegated through the course of the 20th century. The aim of this talk is to use the arena of mathematics education during the 1950s and 1960s, which encompassed most of the so-called "new math" educational reforms, to illuminate fine distinctions between and within professional groups involved with mathematics, notably the American Mathematics Society, the Mathematical Association of America, and the National Council of Teachers of Mathematics. Simple dichotomies such as researchers versus teachers, pure mathematicians versus applied mathematicians, mathematicians versus mathematics educators, or progressive versus traditional educators offer only limited utility in understanding the complex jurisdictional struggle that in fact occurred. By close analysis of the career trajectories of several representative figures from the period, a more nuanced categorization will be proposed, yielding a better understanding of the outcome of the reforms. Special attention will be given to individuals associated with two of the most prominent curriculum reform projects: the University of Illinois Committee on School Mathematics (UICSM), and the School Mathematics Study Group (SMSG), originally headquartered at Yale and later at Stanford.