AI in Computational Number Theory

Computational number theory, a branch of mathematics focused on the computational aspects of number theory, has witnessed rapid advancements with the integration of artificial intelligence (AI). AI techniques, particularly machine learning (ML) and deep learning, offer unprecedented opportunities to solve long-standing problems, identify patterns, and accelerate computations. This paper explores the applications, challenges, and future directions of AI in computational number theory, highlighting key achievements and areas of ongoing research. Computational number theory’s incorporation of artificial intelligence (AI) marks a revolutionary development in the investigation and solution of challenging mathematical issues. The computational complexity of issues like factorization, primality testing, and the creation of cryptographic algorithms has long presented a challenge to number theory, the area of mathematics dedicated to the study of integers and their properties. AI has the potential to revolutionize several fields with its strengths in automated reasoning, neural networks, and machine learning. AI’s ability to optimize algorithms, find new patterns, and resolve previously unsolvable issues has been shown in recent number theory applications. Large datasets of integers and their characteristics have been used to train machine learning models, which have led to notable advancements in prime number prediction and integer factorization methods. Additionally, modular forms and L- functions have been analyzed using deep learning, providing insight into intricate structures such as the Riemann Hypothesis. Reinforcement learning methods have also been used to automate the proof of theorems in fields like diophantine equations and elliptic curves and to find counterexamples to long- standing conjectures. Keywords: Artificial Intelligence, computational number, machine learning.