Researchers at Pacific Northwest National Laboratory are advancing the intersection of mathematics and artificial intelligence by developing interpretable tools and datasets that accelerate discovery across both disciplines. Led by AI researcher Henry Kvinge, the team focuses on combinatorics as an ideal framework for integrating AI into rigorous mathematical inquiry. Their work includes a comprehensive visual mapping of mathematical statements from Lean’s Mathlib library and the creation of OpenConjecture, a living database housing thousands of unproven theorems designed for collaborative human-AI resolution. A central component of the initiative examines how large language models process mathematical reasoning. Presented at a 2025 International Conference on Machine Learning workshop, the research investigates whether LLMs rely on human-like general rules and mathematical context, a concept the team terms mathematical world models. By analyzing internal model computations, the researchers use mathematics as a precise, digital proxy for complex system behavior. Findings indicate that while LLMs frequently replicate human conceptual frameworks, they also employ unconventional problem-solving strategies that sometimes diverge from intended mathematical principles, underscoring the continued necessity of expert human oversight. To institutionalize cross-disciplinary collaboration, Kvinge and senior data scientists Tim Doster and Tegan Emerson established the Topology, Algebra, and Geometry in Data Science community in 2022. The group hosted its first independent conference December 1–2, 2025, at the University of California, San Diego, strategically co-located with NeurIPS 2025 to maximize academic networking. The next gathering is scheduled for August 2026 at Northeastern University. Parallel to this outreach, the team is developing TAGTorch under the Department of Energy’s Scientific Discovery through Advanced Computing program. Built on PyTorch, the library enables researchers to integrate topology, algebra, and geometry methodologies directly into deep learning architectures. This research aligns with Pacific Northwest National Laboratory’s broader contributions to the DOE’s Genesis Mission, which seeks to construct next-generation computational platforms for scientific advancement and national security. The lab’s guiding philosophy prioritizes interpretability, ensuring that AI systems generate novel theoretical insights rather than functioning as opaque solution generators. By establishing a bidirectional feedback loop where mathematics validates AI reasoning and AI accelerates mathematical exploration, the initiative lays the groundwork for more transparent, efficient, and collaborative research ecosystems across computational sciences.