The University of Montana

Department of Mathematical Sciences

Technical report #7/2009
The characteristics of mathematical creativity

**Bharath Sriraman**

The University of Montana

**Abstract**

Mathematical creativity ensures the growth of mathematics as a whole. However the source of this growth, the creativity of the mathematician is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics; a qualitative study involving five creative mathematicians was conducted. The mathematicians in this study verbally reflected on the thought processes involved in creating mathematics. Analytic induction was used to analyze the qualitative data in the interview transcripts and to verify the theory driven hypotheses. The results indicate that in general, the mathematicians’ creative process followed the four-stage Gestalt model of preparation– incubation–illumination–verification. It was found that social interaction, imagery, heuristics, intuition, and proof were the common characteristics of mathematical creativity. In addition contemporary models of creativity from psychology were reviewed and used to interpret the characteristics of mathematical creativity.

**Keywords:** Domain specific creativity ; Gestalt psychology ; Jacques Hadamard; Systems views of creativity; Theories of creativity; Mathematical creativity

**AMS Subject Classification:** 97

** Download Technical Report:** pdf (226 KB)

Pre-print of Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM- The International Journal on Mathematics education, vol41, nos 1&2, pp. 13-27.