A Review Paper on The Mathematical Foundations of Artificial Intelligence

Year : 2025 | Volume : 12 | Issue : 03 | Page : 7 14
    By

    Bhadrayu Srivastava,

  • Dr. Mrinalini Srivastava,

  1. Student, Department of Computer Science and Engineering, School of Engineering, Babu Banarasi Das University, Lucknow, Lucknow, India
  2. Associate Professor, Department of Electronics and Communication Engineering, School of Engineering, Babu Banarasi Das University, Lucknow, India

Abstract

Artificial Intelligence (AI) is deeply rooted in various branches of mathematics, which provide the theoretical foundation and practical tools for developing intelligent systems. This paper explores the crucial role of mathematics in AI, focusing on key areas such as Linear Algebra, Probability and Statistics, Optimization Techniques, Calculus, Graph Theory, and Fourier and Wavelet Transforms. Linear Algebra is fundamental for representing and manipulating data, with applications in dimensionality reduction and neural networks. Probability and Statistics enable AI systems to handle uncertainty, make informed decisions, and learn from data. Optimization Techniques, particularly gradient descent and backpropagation, are essential for training AI models and minimizing error functions. Calculus provides the tools to analyze continuous change and is crucial for understanding learning dynamics in AI algorithms. Graph Theory offers a framework for modeling complex relationships and networks, with applications in Graph Neural Networks and knowledge representation. Fourier and Wavelet Transforms are vital for signal processing and feature extraction, enabling AI to analyze and interpret data in various domains, such as vision and speech processing. This paper highlights the indispensable role of mathematics in advancing the field of Artificial Intelligence and developing increasingly sophisticated intelligent systems.

Keywords: Calculus, graph theory, linear algebra, probability, optimization, statistics, wavelet transforms

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article:
Bhadrayu Srivastava, Dr. Mrinalini Srivastava. A Review Paper on The Mathematical Foundations of Artificial Intelligence. Research & Reviews: Discrete Mathematical Structures. 2025; 12(03):7-14.
How to cite this URL:
Bhadrayu Srivastava, Dr. Mrinalini Srivastava. A Review Paper on The Mathematical Foundations of Artificial Intelligence. Research & Reviews: Discrete Mathematical Structures. 2025; 12(03):7-14. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=230512


References

  1. Aggarwal CC. Neural Networks and Deep Learning: A Textbook. Cham: Springer; 2018.
  2. Sharma R, Sharma A. Deep Learning Algorithms: A Comprehensive Study. Int J Adv Res Comput Sci. 2021;12(1):1–8.
  3. Murphy KP. Probabilistic Machine Learning: An Introduction. Cambridge, MA: MIT Press; 2022.
  4. Ray S, Bhattacharya S. Statistical Modeling for Robust AI in Diverse Indian Datasets. In: 2021 International Conference on Computational Intelligence, Data Science and Cloud Computing (ICloudCom); 2021 Dec 18–19; India. Piscataway, NJ: IEEE; 2021. p. 1–6.
  5. Boyd S, Vandenberghe L. Convex Optimization. Cambridge: Cambridge University Press; 2018.
  6. Mishra A, Jain S. Optimized Backpropagation for Efficient Neural Network Training in Indian Datasets. In: 2019 International Conference on Intelligent Computing and Control Systems (ICICCS); 2019 Jun 20–21; Madurai, India. Piscataway, NJ: IEEE; 2019. p. 1290–4. 7. Rudin W. Principles of Mathematical Analysis. 3rd ed. New York: McGraw-Hill Education; 2021.
  7. Sharma V, Rao P. Advanced Calculus for Optimization in Indian AI Datasets. In: 2020 International Conference on Smart Electronics and Communication (ICOSEC); 2020 Sep 10– 12; Tamil Nadu, India. Piscataway, NJ: IEEE; 2020. p. 1–6.
  8. Hogan A, Blomqvist E, Corcoglioniti F, Davies E, Fionda V, Gutierrez-Basulto V, et al. Knowledge Graphs. ACM Comput Surv. 2021;54(4):1–37.
  9. Sarkar A, Chakraborty D. Graph-Based Analysis of Social Networks for AI Applications in Indian Contexts. In: 2019 IEEE 9th International Conference on Cloud Computing, Data Science & Engineering (Confluence); 2019 Jan 10–11; Noida, India. Piscataway, NJ: IEEE; 2019. p. 642–7.
  10. Mallat S. A Wavelet Tour of Signal Processing. 3rd ed. San Diego: Academic Press; 2018.
  11. Kumar A, Singh R. Fourier and Wavelet Transform Based Feature Extraction for Speech Recognition in Diverse Indian Dialects. In: 2022 IEEE International Conference on Signal Processing, Information, Communication & Systems (SPICSCON); 2022 Nov 17–18; India. Piscataway, NJ: IEEE; 2022. p. 1–6.
  12. Jolliffe IT, Cadima J. Principal Component Analysis: A Review and Recent Developments. Philos Trans R Soc A. 2016;374(2065):20150202.
  13. Wasserman L. All of Statistics: A Concise Course in Statistical Inference. New York: Springer; 2004.
  14. Nielsen MA. Neural Networks and Deep Learning. San Francisco: Determination Press; 2015.
  15. Stewart J. Calculus. 8th ed. Boston: Cengage Learning; 2015.
  16. Barabási AL. Network Science. Cambridge: Cambridge University Press; 2016.
  17. Oppenheim AV, Schafer RW. Discrete Time Signal Processing. Upper Saddle River, NJ: Pearson Education; 2010.
Regular Issue Subscription Review Article
Volume 12
Issue 03
Received 17/09/2025
Accepted 25/09/2025
Published 30/09/2025
Publication Time 13 Days
174

Login


My IP

PlumX Metrics