A Theory of Reception for the History of Mathematics

Abstract

This chapter discusses the adaptation of the theory of reception to mathematics. It highlights a theory of reception that can provide the historian with a different point of view, that is, a new tool for the solution of historical problems. Some features peculiar to mathematics are discussed in the chapter. The shifting horizon of expectations of a mathematical work to include more rigors is the product of social forces and the result of scientific efforts. Subsequent generations incorporated this rigorous focus to varying degrees in their horizons of expectations, and the degree of its dominance determines the approach to mathematical problems in the different communities of analysts. This sort of analysis is applicable to other notions than rigor. The reorienting ideas of set theory, analytic number theory, and abstract algebra offer key moments in the history of mathematics where the reception of these ideas can be studied and the historical narrative enriched by the broader picture revealed. The chapter focuses on the reception of topology at the turn of the century as an instance of the method.