A Mathematical Analysis of the Impact of Artificial Intelligence on Higher Mathematics Education

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-73
Published: Mar 19, 2026
Cite as:
Ali Ben Ahmed, Jihen Borni, Susan Samein, A Mathematical Analysis of the Impact of Artificial Intelligence on Higher Mathematics Education, Int. J. Anal. Appl., 24 (2026), 73.

Main Article Content

Ali Ben Ahmed, Jihen Borni, Susan Samein

Abstract

In this paper, we analyze the impact of artificial intelligence (AI) on higher mathematics education using a mathematical and quantitative framework. Student knowledge is modeled through three components: conceptual understanding, procedural fluency and reasoning depth. We compare learning outcomes with and without AI assistance using controlled data and structural analysis of solutions. The results show significant improvements in conceptual and procedural performance under AI-assisted learning, while gains in reasoning depth remain limited. Structural metrics indicate that AI-generated solutions are wider and more redundant and that error propagation increases in multi-step tasks. Case studies in calculus, linear algebra, real analysis and differential equations confirm these patterns. The study provides a clear analytical description of how AI modifies mathematical learning and offers guidance for its responsible integration into university-level instruction.

Article Details

References

  1. V. Aleven, B.M. McLaren, J. Sewall, M. van Velsen, O. Popescu, et al., Example-Tracing Tutors: Intelligent Tutor Development for Non-Programmers, Int. J. Artif. Intell. Educ. 26 (2016), 224–269. https://doi.org/10.1007/s40593-015-0088-2.
  2. R. Bommasani, D.A. Hudson, E. Adeli, R. Altman, S. Arora, et al. On the Opportunities and Risks of Foundation Models, arXiv:2108.07258 (2021). https://doi.org/10.48550/ARXIV.2108.07258.
  3. C.K.Y. Chan, W. Hu, Students’ Voices on Generative AI: Perceptions, Benefits, and Challenges in Higher Education, Int. J. Educ. Technol. High. Educ. 20 (2023), 43. https://doi.org/10.1186/s41239-023-00411-8.
  4. M. Chassignol, A. Khoroshavin, A. Klimova, A. Bilyatdinova, Artificial Intelligence Trends in Education: A Narrative Overview, Procedia Comput. Sci. 136 (2018), 16–24. https://doi.org/10.1016/j.procs.2018.08.233.
  5. P. Drijvers, Digital Technology in Mathematics Education: Why It Works (or Doesn’t), in: Selected Regular Lectures from the 12th International Congress on Mathematical Education, Springer International Publishing, Cham, 2015: pp. 135–151. https://doi.org/10.1007/978-3-319-17187-6_8.
  6. Y.K. Dwivedi, N. Kshetri, L. Hughes, E.L. Slade, A. Jeyaraj, et al., Opinion Paper: “So What If ChatGPT Wrote It?” Multidisciplinary Perspectives on Opportunities, Challenges and Implications of Generative Conversational AI for Research, Practice and Policy, Int. J. Inf. Manag. 71 (2023), 102642. https://doi.org/10.1016/j.ijinfomgt.2023.102642.
  7. T. Eloundou, S. Manning, P. Mishkin, D. Rock, GPTs Are GPTs: An Early Look at the Labor Market Impact Potential of Large Language Models, arXiv:2303.10130 (2023). https://doi.org/10.48550/ARXIV.2303.10130.
  8. F. Ferri, P. Grifoni, T. Guzzo, Online Learning and Emergency Remote Teaching: Opportunities and Challenges in Emergency Situations, Societies 10 (2020), 86. https://doi.org/10.3390/soc10040086.
  9. G. Hanna, M. De Villiers, eds., Proof and Proving in Mathematics Education: The 19th ICMI Study, Springer, 2012. https://doi.org/10.1007/978-94-007-2129-6.
  10. N.T. Heffernan, C.L. Heffernan, The ASSISTments Ecosystem: Building a Platform That Brings Scientists and Teachers Together for Minimally Invasive Research on Human Learning and Teaching, Int. J. Artif. Intell. Educ. 24 (2014), 470–497. https://doi.org/10.1007/s40593-014-0024-x.
  11. W. Holmes, M. Bialik, C. Fadel, Artificial Intelligence in Education: Promises and Implications for Teaching and Learning, Center for Curriculum Redesign, Boston, 2019.
  12. A. Thoma, P. Iannone, Learning About Proof with the Theorem Prover LEAN: The Abundant Numbers Task, Int. J. Res. Undergrad. Math. Educ. 8 (2021), 64–93. https://doi.org/10.1007/s40753-021-00140-1.
  13. E. Kasneci, K. Sessler, S. Küchemann, M. Bannert, D. Dementieva, et al., ChatGPT for Good? on Opportunities and Challenges of Large Language Models for Education, Learn. Individ. Differ. 103 (2023), 102274. https://doi.org/10.1016/j.lindif.2023.102274.
  14. R. Luckin, Machine Learning and Human Intelligence: The Future of Education for the 21st Century, UCL Institute of Education Press, 2018.
  15. M. Mitchell, Artificial Intelligence: A Guide for Thinking Humans, Farrar, Straus and Giroux, 2019.
  16. OpenAI, J. Achiam, S. Adler, S. Agarwal, L. Ahmad, et al. GPT-4 Technical Report, arXiv:2303.08774 (2023). https://doi.org/10.48550/ARXIV.2303.08774.
  17. I. Tuomi, The Impact of Artificial Intelligence on Learning, Teaching, and Education: Policies for the Future, JRC Science for Policy Report, European Commission, 2019.
  18. O. Zawacki-Richter, V.I. Marín, M. Bond, F. Gouverneur, Systematic Review of Research on Artificial Intelligence Applications in Higher Education – Where Are the Educators?, Int. J. Educ. Technol. High. Educ. 16 (2019), 39. https://doi.org/10.1186/s41239-019-0171-0.