Authors : Shriya Raghuraj Kundargi; Dr. Prakasha H T

Volume/Issue : Volume 9 - 2024, Issue 6 - June

Google Scholar : https://tinyurl.com/mrybebdk

Scribd : https://tinyurl.com/bdddwez4

DOI : https://doi.org/10.38124/ijisrt/IJISRT24JUN1204

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Abstract : This paper presents a comprehensive case study on the application of Artificial Intelligence (AI) in mathematics, focusing on the Ramanujan series and the intricate relationship between the mathematical constants e and π. The study explores how AI, particularly machine learning and pattern recognition techniques, can be harnessed to discover new mathematical series and patterns, thereby extending the pioneering work of the legendary mathematician Srinivasa Ramanujan. The paper begins with an overview of the Ramanujan series, illustrating their significance and applications in mathematical computations. It then delves into the specifics of AI methodologies employed to unearth new series for e and π, highlighting the algorithms and models used. Through detailed analysis and experimentation, the study demonstrates how AI can generate new series expansions for e and π, offering enhanced convergence rates and computational efficiencies. Furthermore, the paper examines the relationship between these two constants, providing insights into their interconnected nature through AI-discovered series and patterns. Practical applications of these new series in fields such as numerical methods, cryptography, and theoretical physics are also discussed. By showcasing the successful integration of AI in the realm of mathematical research, this case study underscores the potential of AI to revolutionize traditional mathematical approaches, fostering the discovery of new knowledge and the refinement of existing theories. The findings contribute to a deeper understanding of the interplay between e and π, reinforcing the profound impact of Ramanujan's work in modern mathematics and the transformative power of AI in advancing this legacy.

Keywords : Artificial Intelligence, Ramanujan Series, Mathematical Constants, e, π, Machine Learning, Pattern Recognition, Numerical Methods, Cryptography, Theoretical Physics, Convergence Rates, Computational Efficiency.

References :

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8. New AI 'Ramanujan Machine' uncovers hidden patterns in numbers By Stephanie Pappas