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

**Abstract**

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.*

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Technical Report:** Pdf (95 KB)