Transformative impact of artificial intelligence on mathematical reasoning

Implications, advances, and challenges

Abstract

This article explores the growing impact of Artificial Intelligence (AI) on mathematical reasoning, with emphasis on its progress, limitations and epistemological projections. It examines how AI, through computational models and techniques such as machine learning, automatic theorem proving and optimization using evolutionary algorithms, has achieved significant levels of autonomy in solving complex mathematical problems. Historically, from the Turing Machine to today's neural networks, AI has contributed to remarkable advances, including solving problems in representation theory and diophantine equations. However, fundamental challenges remain: AI lacks deep conceptual understanding, has difficulties in generalization, and relies heavily on data, which compromises transparency and rigor in deductive processes. The article highlights the need to develop symbolic and intuitive capabilities in intelligent systems, and further reasoning. Finally, it proposes a collaborative vision between human intelligence and AI, where the latter acts as a catalyst for mathematical thinking, without replacing its creative dimension. The research emphasizes that the ethical and critical development of AI is essential, recognizing mathematics not only as a beneficiary, but also as the structural foundation of AI.