Keywords
qualification paper
mathematics
generative language model
automated theorem proving
academic integrity
How to Cite
Abstract
This article presents a comprehensive analytical review of the current possibilities and challenges of using artificial intelligence (AI) by students in preparing qualification papers in the field of mathematics. The study systematizes the main areas of AI application in mathematical research, including: automated theorem proving using systems such as Lean, Coq, and Isabelle; text, explanation, and code generation with language models such as ChatGPT and Copilot; data analysis and modelling with Wolfram Alpha and Python; symbolic computations using Maple, Maxima, and Mathematica; and the creation of graphs, geometric constructions, and illustrations with GeoGebra AI extensions and generative image models.
The advantages of AI implementation in qualification papers are highlighted, namely: increasing student productivity; saving time by automating routine calculations; providing access to expert knowledge and personalized learning support; improving the quality, clarity, and presentation of scientific texts and results; and expanding the scope of research activities to enable students to undertake projects approaching the level of academic publications.
At the same time, the study identifies significant risks and ethical challenges, such as: threats to academic integrity due to the potential use of AI-generated texts without proper citation; decreased development of students’ critical and logical thinking skills due to overreliance on AI; possible errors and “hallucinations” produced by AI models, leading to incorrect scientific results; dependence on technology; and concerns regarding data confidentiality when using cloud-based AI services. The conclusions outline the prospects for further research, including the development of methodological guidelines for ethical and effective AI use in mathematics education, the study of AI’s impact on the formation of students’ professional competencies, and the optimization of AI-assisted learning in combination with traditional pedagogical methods.
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