Integrating artificial intelligence tools into the teaching of advanced mathematics: Didactic opportunities

Abstract

The rapid proliferation of artificial intelligence tools in the educational sphere calls for a rethinking of established approaches to teaching disciplines in higher education institutions. Advanced mathematics presents a particularly illustrative context because its internal logic, grounded in formal rigor and deductive reasoning, creates specific conditions under which the didactic potential of artificial intelligence is uneven and requires separate consideration. This article aims to study and implement the didactic potential of artificial intelligence tools in the teaching of higher mathematics, taking into account the content and methodological dimensions of this process. Methods: systematization and comparative analysis of scientific publications from 2021–2026, generalization of empirical data from foreign and Ukrainian studies, and classificatory modeling. Results. An original classification of artificial intelligence tools based on 12 didactic functions has been developed. It has been found that their effectiveness varies significantly across subject areas. In procedural computational tasks, it is sufficiently well-founded, whereas in working with mathematical proofs, it is limited and sometimes controversial. The feasibility of a three-pronged strategy that combines generative models, specialized mathematical systems, and adaptive platforms to meet the students' basic educational needs has been substantiated. Conclusions. The effective integration of artificial intelligence into the teaching of higher mathematics is achievable, but it is not limited to simply introducing technologies into the educational process. It requires the teacher's methodological awareness, a clear understanding of each tool's limitations, and the preservation of cognitive load as a necessary condition for the development of mathematical thinking. Artificial intelligence must fit most naturally into the role of a supplement to pedagogical action, rather than a substitute for it. Where the tool automates routine feedback, the instructor gains space to work on the student's conceptual understanding and the quality of their reasoning. It is precisely this division of labor that is methodologically productive.