This paper introduces `Math Battles with AI', an innovative competitive format designed at ITMO University to redefine the role of generative AI in mathematics education. Moving away from a purely defensive stance, the authors propose an AI agent with intentionally increased hallucination likelihood in specific modes to train verification skills. We describe the three-stage tournament structure and a specialized assessment system that rewards critical verification over blind reliance. Initial results indicate a significant shift in student mindsets, fostering essential skills in digital hygiene and prompt engineering. This work serves as a practical guide for academic institutions aiming to leverage AI for enhancing, rather than undermining, intellectual development.

翻译：本文介绍了一种创新的竞赛形式——“与AI的数学对决”，该形式由ITMO大学设计，旨在重新定义生成式人工智能在数学教育中的角色。作者摒弃了纯粹的防御姿态，提出了一种在特定模式下故意增加幻觉发生概率的AI智能体，以训练学生的验证技能。我们描述了该赛事的三阶段结构以及一个专门的评估系统，该系统奖励批判性验证而非盲目依赖。初步结果表明，学生心态发生了显著转变，培养了数字素养与提示工程方面的关键技能。本工作为学术机构提供了一份实用指南，旨在利用人工智能促进而非削弱智力发展。