Leírás
In this talk, the construct of ‘uncertainty’ in professional mathematics is investigated in relation to mathematical creativity. Specific focus is on ‘Big C’ research mathematicians’ conceptions of what uncertainty means and ways in which it influences their research. The talk will report on a 4-year study involving 18 research mathematicians who were at the forefront of their research domains. The study revealed a dialectic or tension between (1) logic versus heuristics (analytic versus synthetic), (2) learner-researcher and researcher-learner transition, (3) axiom tweaking versus constraints. The findings also indicated that textbooks, unexpected moments, risk taking, and a community of support play a crucial role and characterize the interplay of uncertainty with mathematical creativity. A schema for understanding the dialectics of uncertainty sheds new light on a hitherto unexplored aspect of mathematical creativity, namely, uncertainty, vital for the development of mathematicians as researchers in addition to the growth of their discipline.