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 processes 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. Additionally, contemporary models of creativity from psychology were reviewed and used to interpret the characteristics of mathematical creativity Mathematical creativity ensures the growth of the field of mathematics as a whole. The constant increase in the number of journals devoted to mathematics research bears evidence to the growth of mathematics. Yet what lies at the essence of this growth, the creativity of the mathematician, has not been the subject of much research. It is usually the case that most mathematicians are uninterested in analyzing the thought processes that result in mathematical creation (Ervynck, 1991). The earliest known attempt to study mathematical creativity was an extensive questionnaire published in the French periodical L'Enseigement Mathematique (1902). This questionnaire and a lecture on creativity given by the renowned 20th century mathematician Henri Poincaré to the Societé de Psychologie inspired his colleague Jacques Hadamard, another prominent 20th century mathematician, to investigate the psychology of mathematical creativity

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