Why Historical Research Needs Mathematicians Now More Than Ever

Abstract

Using the history of the calculus as an example, I identify some trends in recent scholarship and argue that the time is ripe for a “new internalism” in the historiography of mathematics. The field has made steady progress in the past century: mathematicians have provided clear expositions of the technical content of past mathematics, and historians have produced meticulous editions of textual sources. These contributions have been invaluable, but we are reaching a point where the marginal utility of further works of these types is diminishing. It is time to shape a paradigm of historical scholarship that goes beyond the factual-descriptive phase of the past century. Comparative interpretative work is now feasible thanks to the gains of the past century. Cognitive questions about mathematical practice provide a fascinating and underexplored avenue of research that we now have the tools to tackle. Mathematically trained researchers are needed for this enterprise.