How Have Pattern Recognition Algorithms Been Used to Identify and Support Conjectures in Number Theory?

Samar Singh

How Have Pattern Recognition Algorithms Been Used to Identify and Support Conjectures in Number Theory?

Author(s)	Mr. Samar Singh
Country	India
Abstract	The discipline of this research paper revolves around recent LLM benchmarks that have mainly pivoted around general mathematical problems. Artificial Intelligence can be used to identify structure in data trends, images, numbers, and signals. Researchers have been using AI modules to discover and prove conjectures in number theory patterns. One of the most celebrated conjectures as an example is the Birch–Swinnerton–Dyer (BSD) conjecture, which detects logical patterns supporting the varying ranks in different elliptic curves, utilizing databases such as the Cremona database within a high-dimensional point cloud. Despite substantial progress over the past few decades, researchers and data scientists are yet to prove this conjecture. In contemporary mathematical research, pattern recognition and machine learning techniques are primarily employed to empirically support conjectures by uncovering statistical correlations and latent structure in large datasets, rather than to generate formal proofs. Therefore, this research will feature key mathematical patterns in prime numbers, such as the Hermitian symmetric matrix and analytic functions such as the Riemann–Zeta function, to systematically examine patterns and behaviours that emerge from the seemingly chaotic distribution of prime numbers. By synthesising insights from analytic number theory and modern data-driven methodologies, this paper explores how computational tools help reveal order within mathematical systems traditionally regarded as stochastic or incompressible. This research demonstrates the scope of AI in pattern recognition, along with the role of number theory as a rigorous and mathematically grounded benchmark for evaluating the capabilities and limitations of artificial intelligence systems. Ultimately, the paper highlights the growing interdisciplinary relationship between mathematics and artificial intelligence, illustrating how empirical pattern detection complements theoretical reasoning in the investigation of long-standing mathematical conjectures.
Keywords	Artificial Intelligence, Large Language Models, Pattern Recognition, Machine Learning in Mathematics, Number Theory, Mathematical Conjectures, Birch–Swinnerton–Dyer Conjecture, Analytic Number Theory, Prime Number Distribution, Riemann–Zeta Function, Elliptic Curves, Data-Driven Mathematical Discovery
Field	Computer > Artificial Intelligence / Simulation / Virtual Reality
Published In	Volume 8, Issue 1, January-February 2026
Published On	2026-02-06

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How Have Pattern Recognition Algorithms Been Used to Identify and Support Conjectures in Number Theory?

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