Abstract
Recent developments in algorithmic problem-solving techniques have significantly influenced diverse domains, from mathematical computations to real-world problem-solving. This paper explores the advancements in algorithm development, emphasizing the application of mathematical reasoning and rigorous design in functions and recursive functions. Additionally, the review spans the landscape of solving mathematical word problems (MWPs), analysing methodologies, and providing insights into the challenges and complexities inherent in natural language processing, machine learning, and artificial intelligence. In a comparative study, computational and algorithmic advances for solving Richards’ equation are evaluated, revealing their joint contributions to a substantial improvement in efficiency. The collective insights from these perspectives underscore the transformative impact of algorithmic advancements across interdisciplinary domains.
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