Asper Markus
Sudhoffs Arch. 2003;87(1):1-31.
Greek theoretical mathematics emerges among sixth-century Ionians from a background of professional practitioners, concerned chiefly with arithmetical operations. Its characteristical features (impersonalization, standardization, diagrams) develop as part of an elitist play of distinction at fifth- and fourth-century Athens, mainly to ascertain the tradition of that knowledge without adequate institutions. Sophists challenge the mathematicians' practices, philosophers adopt the mathematicians' knowledge as a model of truth, but the mathematicians themselves remain autonomous. Even hellenistic mathematics, semi-institutionalized at royal courts, is little more than a private affair of a narrow circle of intellectuals. All this time the practitioners' traditions persist basically unaltered and constantly present the theoreticians with a social and epistemic background to differentiate "their" mathematics from. Finally, these two branches of Greek mathematics, a practical and a theoretical one, are describable as reciprocally systematized forms of knowledge.
希腊理论数学在公元前6世纪的爱奥尼亚人当中兴起，源于专业从业者的背景，主要涉及算术运算。其特征（非人格化、标准化、图表）在公元前5世纪和4世纪的雅典作为一种精英阶层区分的游戏的一部分而发展起来，主要是在没有适当制度的情况下确定那种知识的传统。智者派挑战数学家的做法，哲学家将数学家的知识作为真理的典范采纳，但数学家本身保持自主。甚至在皇家宫廷半制度化的希腊化数学，也不过是一小群知识分子的私事。在这段时间里，从业者的传统基本保持不变，不断为理论家提供一个社会和认知背景，以便将“他们的”数学与之区分开来。最后，希腊数学的这两个分支，一个是实践的，一个是理论的，可以被描述为相互系统化的知识形式。
