The Logic and the Ledger: Tracing the DNA of AI
DOI:
https://doi.org/10.46243/jst.2025.v10.i12.pp01-10Keywords:
Artificial Intelligence, Mathematical Backbone of AI, Deep Learning, Machine Learning, Large Language ModelsAbstract
The development of intelligent systems is fundamentally and inseparably linked to a sophisticated
mathematical framework. Modern artificial intelligence (AI), particularly its subfields of machine learning
(ML) and deep learning, is not a new discipline of computer science but rather a highly advanced
application of classical and novel mathematical principles. The models and algorithms that enable systems
to process data, learn intricate patterns, and optimize predictions are built upon a bedrock of abstract
mathematical theories. This paper systematically deconstructs this relationship, demonstrating how core
mathematical disciplines serve as the language, the engine, and the conceptual framework for all
intelligent systems. The analysis will traverse from foundational principles to their application in
cutting-edge architectures and conclude with a discussion of the theoretical and practical challenges that
are currently shaping the future of the field.
References
Jeff Shepard (2025). What is the mathematics behind artificial intelligence?. EEWorld Online, https://www.eeworldonline.com/what-is-themathe matics-behind-artificial-intelligence/
Standford University (2016). One Hundred Year Study on Artificial Intelligence (AI100):
Lawrence Livermore National Security. The birth of Artificial Intelligence (AI) research. Science and Technology. https://st.llnl.gov/news/lookback/birth-artificial-i ntelligence-ai-research
Ashok K. Goel (2021). Looking back, looking ahead: Symbolic versus connectionist AI. AI Magazine. 2021;42:83–85, DOI: 10.1609/ aaai.12026
Jieshu’s Blog. Symbolism vs. Connectionism: A Closing Gap in Artificial Intelligence. http:// wangjieshu.com/2017/12/23/symbol-vsco nnectionism-a-closing-gap-in-artificialintelligence/
Wikipedia. Machine learning. https:// en.wikipedia.org/wiki/Machine_learning
ObjectiveMind.ai. The Math Behind the Machine: AI Fundamentals Explained. June 2025. https:// www.objectivemind.ai/the-math-behind-th e-machine-ai-fundamentals-explained
Relief. The Math Behind Machine Learning Linear Algebra Calculus and Probability. Mar 3, 2025, Medium. https://medium. com/@preetikapuria587/the-math-behindmachine-learning-linear-algebra-calculus-a ndprobability-91f1e0d1350e
Coursera. Mathematics for Machine Learning and Data Science Specialization. https://www. coursera.org/specializations/mathem atics-formachine-learning-and-data-science
{igebra.ai}. A Data & AI Research. The Power of Math and AI: Synergies for the Future. https:// www.igebra.ai/blog/the-power-of-math-an d-aisynergies-for-the-future/
Richmond Alake. A Data Scientist’s Guide to Gradient Descent and Backpropagation Algorithms. NVidia Developers Technical Blog. Feb 09, 2022. https://developer.nvidia.com/ blog/a-data-scientist s-guide-to-gradientdescent-and-backpropagation-a lgorithms/
GeeksforGeeks. Optimization Rule in Deep Neural Networks. https://www.geeksforgeeks. org/deep-learning/opti mization-rule-in-deepneural-networks/
Mbali Kalirane. Gradient Descent vs. Backpropagation: What’s the Difference? Analytics Vidhya. https://www.analyticsvidhya. com/blog/2023/01/g radient-descent-vsbackpropagation-whats-the-diffe rence/
Massimiliano Ferrara. Explainable artificial Rajendran Swamidurai, Uma Kannan: The Logic and the Ledger: Tracing the DNA of AI intelligence and mathematics: What lies behind? Let us focus on this new research field. Eur. Math. Soc. Mag. 135 (2025), pp. 39–44, DOI 10.4171/MAG/235
IBM. What Is Machine Learning (ML)? https:// www.ibm.com/think/topics/machine-learn ing
Oleksii Malyshev. Math at the Heart of CNN: Part
Svitla Systems, June 21, 2024, https://svitla. com/blog/math-at-the-heart-of-cnn/
Lamiae Hana. Classical ML vs. Deep Learning: What is the difference between Classical ML & Deep Learning? Medium. https://lamiae-hana. medium.com/classical-ml-vs-deep-learningf8e28a52132d
Michael Bronstein, Taco Cohen, and Petar Veličković (2023). Towards Geometric Deep Learning. The Gradient. 18 Feb, 2023. https:// thegradient.pub/towards-geometric-deep-le arning/
Siddharth Bhalsod. Geometric Deep Learning: An In-Depth Exploration of Principles, Applications, and Future Directions. DEV Community. Oct 27, 2024. https://dev.to/ siddharthbhalsod/geometric-deep-le arningan-in-depth-exploration-of-principles-applic ations-and-future-directions-kn6
CAIS. Recurrent Neural Networks. https:// caisplusplus.usc.edu/curriculum/neural-n etwork-flavors/recurrent-neural-networks
Wikipedia. Attention (machine learning). https://en.wikipedia.org/wiki/Attention_ (machine_ learning)
IBM. What is an attention mechanism? https:// www.ibm.com/think/topics/attention-mec hanism
Muhammad Raza. LLMs vs. SLMs: The Differences in Large & Small Language Models. Splunk. February 17, 2025. https://www. splunk.com/en_us/blog/learn/langu agemodels-slm-vs-llm.html
Tomasz Jażdżewski (2025). LLMs vs classic Machine Learning. VirtusLab. Apr 7, 2025. https://virtuslab.com/blog/data/llm-vsclassic-ml/
Cloudian. 6 Types of AI Workloads, Challenges & Critical Best Practices. https://cloudian. com/guides/ai-infrastructure/6-t ypes-ofai-workloads-challenges-and-critical-best-p ractices/
Code Upscale. LLMs vs Traditional ML: What’s the Real Difference? Apr 8, 2025. https:// codeupscale.com/articles/llms-vs-tradition alml
Okuno, A., & Yano, K. (2023). A Generalization Gap Estimation for Overparameterized Models via the Langevin Functional Variance. Journal of Computational and Graphical Statistics, 32(4), 1287–1295. https://doi.org/10.1080/1061860 0.2023.2197488
Stephan Wojtowytsch. Generalization. University of Pittsburgh. https://sites.google. com/site/stephanwojtowytsch/ teaching/689deep-learning/generalization
Jingling Li, Yanchao Sun, Jiahao Su, Taiji Suzuki, Furong Huang. Understanding Generalization in Deep Learning via Tensor Methods. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics. PMLR 108:504-515, 2020
Wu, Lei, Zhanxing Zhu and E Weinan. Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes. ArXiv abs/1706.10239 (2017): n. pag
Trisha Pillay. New AI Architectures To Watch Out For. EM360Tech. 06 August 2025. https:// em360tech.com/tech-articles/new-ai-archi tectures-watch-out
Hamon, R., Junklewitz, H., Sanchez, I. Robustness and Explainability of Artificial Intelligence-From technical to policy solutions, EUR 30040, Publications Office of the European Union, Luxembourg, Luxembourg, 2020, ISBN 978-92-79-14660-5 (online), doi:10.2760/57493 (online), JRC119336
MATLAB. Interpretability. MATLAB & Simulink–MathWorks. https://www.mathworks.com/ discovery/interpreta bility.html
Christoph Molnar. Interpretable Machine Learning: A Guide for Making Black Box Models Explainable. Third Edition, Publisher : Christoph Molnar, March 12, 2025, ISBN-10 : 3911578032, ISBN-13: 978-3911578035
Management Solutions. Interpretability techniques: state of the art-Explainable artificial intelligence (XAI). https://www. managementsolutions.com/sites/defa ult/files/ minisite/static/22959b0f-b3da-47c8-9d5c- 80ec3216552b/iax/pdf/explainable-artificialintell igence-en-04.pdf Rajendran Swamidurai, Uma Kannan: The Logic and the Ledger: Tracing the DNA of AI
V Devansh. How Google and Stanford made AI more Interpretable with a 20 year old Technique Why AI Interpretability Has Hit Its First Fundamental Wall. Medium. https://machinelearning-made-simple.medium.co m/breakingdown-db-ksvd-scalable-alternating-opti mization-for-disentangling-high-dimensional- 87d3e 2237de4
Wikipedia. Topological deep learning. https:// en.wikipedia.org/wiki/Topological_deep_lea rning
Venkat Manish. Topological Deep Learning: Advancing AI Beyond Conventional Limits. Medium. Feb 1, 2025. https://medium.com/@ thatikondamanish/topologi cal-deep-learningadvancing-ai-beyond-conventiona l-limitsa6be9799759d
Mintu Debnath, Vijay Kumar Salvia, Alighazi Siddiqui, Khalid Ali Qidwai, P. Durga Devi, S. Bavankumar. Mathematical Foundations of Explainable AI: A Framework based on Topological Data Analysis. Communications on Applied Nonlinear Analysis. Vol. 32, No.9s (2025), DOI: https://doi.org/10.52783/cana. v32.4650
Sethu Iyer. Category Theory in Deep Learning: A New Lens for Abstraction, Composition, and the Nature of Intelligence. Medium. Jan 13, 2025. https://medium.com/@sethuiyer/ category-theory-i n-deep-learning-a-new-lensfor-abstraction-compos ition-and-the-nature-of- 2806963c677f
AWS. Deep Learning vs Machine Learning-Difference Between Data Technologies. Amazon Web Services, Inc. 2025. https://aws. amazon.com/compare/the-difference-betweenmachine-learning-and-deep-learning/
Boles. AI leaps from math dunce to whiz. Harvard Gazette. July 23, 2025. https://news. harvard.edu/gazette/story/2025/07/ ai-leapsfrom-math-dunce-to-whiz/
Whitney Clavin. AI Program Plays the Long Game to Solve Decades-Old Math Problems. www.caltech.edu. Feb 13, 2025. https://www. caltech.edu/about/news/ai-program-playsthe-long-game-to-solve-decades-old-math-pro blems
AI for Mathematics and Theoretical Computer Science. Simons Institute for the Theory of Computing and SLMath Joint Workshop. 2025. https://simons.berkeley.edu/workshops/ simons-in stitute-theory-computing-slmathjoint-workshop-ai-mathematics-theoretical
