In this paper, 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. Based on the hypothesis that uncertainty is both a catalyst and a necessary condition for creativity, a qualitative research design was used to obtain and analyze data from a 4-year study involving 18 research mathematicians who were at the forefront of their research domains. Data analysis using analytic induction confirmed the hypothesis that uncertainty plays an important role as a catalyst of mathematical creativity. The emergent categories from qualitative analysis revealed a dialectic or tension between (1) logic versus heuristics (synthetic versus analytic), (2) learner-researcher and researcher-learner transition, (3) axiom tweaking versus constraints. The findings of the study indicate that textbooks, unexpected moments, risk taking, and a community of support play a crucial role and characterize the interplay of uncertainty with mathematical creativity. The schema for understanding the dialectics of uncertainty sheds new light on an hitherto unexplored aspect of mathematical creativity, namely, uncertainty, vital for the development of mathematicians as researchers in addition to the growth of their discipline.

在本文中，专业数学中“不确定性”的构建与数学创造力的关系进行了研究。特别关注“Big C”研究数学家对不确定性意味着什么以及它影响他们研究的方式的概念。基于不确定性既是创造力的催化剂又是必要条件的假设，定性研究设计用于获取和分析一项为期 4 年的研究数据，该研究涉及 18 位处于其研究领域前沿的研究数学家。使用分析归纳法的数据分析证实了不确定性作为数学创造力的催化剂起着重要作用的假设。定性分析的新兴类别揭示了（1）逻辑与启发式（综合与分析）之间的辩证或张力，(2) 学习者-研究者和研究者-学习者的转变，(3) 公理调整与约束。研究结果表明，教科书、意想不到的时刻、冒险和支持社区起着至关重要的作用，并表征了不确定性与数学创造力的相互作用。理解不确定性辩证法的模式为迄今为止尚未探索的数学创造力的一个方面提供了新的思路，即不确定性，对于数学家作为研究人员的发展以及他们学科的发展至关重要。