The University of Montana
Department of Mathematical Sciences

Technical report #12/2005

Mathematical Objects and the Evolution of Rigor

Luis Moreno-Armella
Cinvestav, Mexico

Bharath Sriraman
The University of Montana, USA

Guillermina Waldegg (Posthumously)
Cinvestav, Mexico


In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is co-substantia1 with the operational inventions that accompany them and that determine the normativity to which they are subjected.

Keywords: Arithmetic; Calculus; Geometry; History of mathematics; Mathematics foundations; Normativity; Non-Euclidean Geometry; Operationality; Proof

AMS Subject Classification: 01, 03, 97

Pre-print of: Moreno-Armella, L., Sriraman, B.,& Waldegg, G . Mathematical Objects and the evolution of rigor. In press in the Mediterranean Journal for Research in Mathematics in Mathematics Education.

Download Technical Report: Pdf (95 KB)