This paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes how argumentation can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments.

本文探讨了非正式推理、数学创造力和问题解决之间的关系。它强调了促进互动、假设生成、检验、反驳、推导新解决方案、得出结论和与他人推理的环境的重要性，作为增强数学创造力的关键因素。借鉴论证逻辑，本文提出了一种新颖的方法来揭示使用“证明事件”的形式化证明发展中的具体特征。论证逻辑可以提供促进这些环境的推理机制。本文提出了如何通过论证来发现“证明事件”形式化证明发展中的某些特征。证明事件的概念是由 Goguen 提出的，他将数学证明描述为一种多主体社会事件，不仅涉及“经典”形式证明，还涉及其他非正式证明行为，例如缺陷证明或所谓证明。论证是数学证明发现过程中不可或缺的组成部分，因为证明需要证明者和解释者之间进行对话，以澄清和解决差距或假设。通过论证将证明事件形式化，本文展示了如何有效地模拟证明过程中出现的非正式推理和冲突。该论文提出了植根于论证理论的证明事件演算的扩展版本，并强调了证明、人类推理、认知过程、创造力和数学论证之间的复杂关系。