AI Applications in Number Theory: LLMs for Algorithms and Ensemble Methods for Conjecture Verification
A new research paper published on arXiv explores two specific applications of Artificial Intelligence within algorithmic and analytic number theory. The study first evaluates the performance of the open-source large language model Qwen2.5-Math-7B-Instruct on specialized tasks. When provided with optimal non-spoiling hints, the model achieved at least 95% accuracy on a benchmark of sixty algorithmic and computational problems derived from classical textbooks and Math StackExchange. The second part of the research empirically verifies a folklore conjecture in analytic number theory, which posits that the modulus of a Dirichlet character is uniquely determined by the initial nontrivial zeros of its corresponding L-function. By training a LightGBM multiclass classifier on statistical features of these zeros for 214 randomly chosen functions, the model predicted the conductor with at least 93.9% test accuracy for small values. This work demonstrates the potential of AI models to assist in solving complex mathematical problems and verifying theoretical conjectures, moving beyond general mathematics benchmarks to specialized domain applications. The code and dataset for the conjecture verification portion are made available to the scientific community.
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AI Applications in Number Theory: LLMs for Algorithms and Ensemble Methods for Conjecture Verification
A new research paper published on arXiv explores two specific applications of Artificial Intelligence within algorithmic and analytic number theory. The study first evaluates the performance of the open-source large language model Qwen2.5-Math-7B-Instruct on specialized tasks. When provided with optimal non-spoiling hints, the model achieved at least 95% accuracy on a benchmark of sixty algorithmic and computational problems derived from classical textbooks and Math StackExchange. The second part of the research empirically verifies a folklore conjecture in analytic number theory, which posits that the modulus of a Dirichlet character is uniquely determined by the initial nontrivial zeros of its corresponding L-function. By training a LightGBM multiclass classifier on statistical features of these zeros for 214 randomly chosen functions, the model predicted the conductor with at least 93.9% test accuracy for small values. This work demonstrates the potential of AI models to assist in solving complex mathematical problems and verifying theoretical conjectures, moving beyond general mathematics benchmarks to specialized domain applications. The code and dataset for the conjecture verification portion are made available to the scientific community.
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