Published Paper Details:

Artificial intelligence has advanced through a convergence of mathematical theory, computational power, and data-driven modelling. Although modern systems often appear to rely primarily on engineering scale and empirical performance, their behaviour is best understood through rigorous mathematical frameworks that articulate representation, optimisation, inference, and generalisation. This paper examines the principal mathematical structures underlying contemporary artificial intelligence and analyses how these structures interact with deep networks, generative architectures, and reinforcement learning. It also considers the emerging role of artificial systems in mathematical discovery, where learning models participate in theorem exploration, symbolic manipulation, and proof development. Through this integrated study, the paper demonstrates that mathematics and artificial intelligence form a bidirectional and evolving relationship in which theory clarifies system behaviour and artificial systems generate new mathematical questions.