An Exploration-Driven Hybrid Machine Learning Framework for Advanced Mathematical Problem Solving
Abstract
Solving advanced mathematical problems requires a combination of logical reasoning, pattern recognition, and efficient exploration of complex solution spaces. Traditional rule-based systems often struggle with high-dimensional and non-linear problems, while standalone machine learning (ML) approaches are limited by their dependence on existing data and lack of systematic exploration capabilities. This paper proposes a novel hybrid framework that integrates the Theory of Exploration with machine learning to enhance mathematical problem-solving efficiency and accuracy.
The proposed model incorporates three key components: an exploration engine for generating diverse hypotheses, a machine learning module for evaluating and optimizing candidate solutions, and a reasoning layer to ensure mathematical correctness and validation. A feedback-driven iterative mechanism enables continuous refinement by dynamically balancing exploration and exploitation.
Experimental evaluation demonstrates that the integrated approach significantly outperforms conventional and ML-only methods in terms of accuracy, convergence speed, and error reduction across various problem types, including algebraic, optimization, and pattern recognition tasks. The framework not only improves computational efficiency but also promotes adaptive learning and discovery of novel solution pathways.
This research highlights the importance of combining exploratory intelligence with data-driven learning and presents a scalable approach applicable to optimization, theorem discovery, and intelligent educational systems. The proposed methodology paves the way for more adaptive, interpretable, and cognitively inspired mathematical problem-solving systems
How to Cite
Swati, Dr Jogender, "An Exploration-Driven Hybrid Machine Learning Framework for Advanced Mathematical Problem Solving", Vol. 4, Issue 4, 23-07-2026, pp. 38-49. DOI: 10.5281/zenodo.22040631
