This paper presents a proof of Beal's conjecture, a long-standing open problem in number theory, guided by insights from machine learning. The proof leverages a novel combination of techniques from modular arithmetic, prime factorization, and the theory of Diophantine equations. Key lemmas, including an expanded version of a modular constraint and a pairwise coprimality condition, are derived with the help of patterns discovered through computational experiments. These lemmas, together with a refined conjecture based on the distribution of prime factors in the dataset, are used to derive a contradiction, proving that any solution to Beal's equation must have a common prime factor among its bases. The proof demonstrates the potential of machine learning in guiding the discovery of mathematical proofs and opens up new avenues for research at the intersection of artificial intelligence and number theory.