Changing Pedagogical Paradigms: Integrating Generative AI in Mathematics to Enhance Digital Literacy through 'Mathematical Battles with AI'

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.