Bridging the gap: Connecting math and AI for discovery

Henry Kvinge, an AI researcher at the Pacific Northwest National Laboratory (PNNL), has led a groundbreaking effort to bridge the gap between mathematics and artificial intelligence. His team has created a comprehensive "map of mathematics" based on text embeddings derived from the Lean Mathematical Library (Mathlib), a repository of formalized mathematical proofs. The map visualizes mathematical statements as points, with distances indicating similarities between them and colors representing different branches of mathematics, such as algebra or probability theory. This tool provides a novel way to explore the structure and relationships within mathematical knowledge, offering insights that could benefit both AI developers and mathematicians. Kvinge, who originally trained as a mathematician, has long been interested in the intersection of AI and mathematics. He believes that the two fields can mutually enhance each other. For instance, AI can assist in analyzing and generating mathematical content, while mathematics offers a rigorous framework for understanding AI behavior. His work focuses on combinatorics, a branch of mathematics dealing with discrete structures like graphs and permutations. This field is particularly well-suited for AI applications due to its structured nature and abundance of data. To support this interdisciplinary approach, Kvinge and his team have developed datasets representing real, research-level mathematics and tools to accelerate mathematical discovery using AI. These resources aim to improve the efficiency and depth of mathematical research, enabling scientists to explore complex problems with greater precision. Additionally, they have identified mathematical symmetries within AI models, which offer new ways to interpret and explain how these models function internally. Kvinge's efforts align with PNNL's broader commitment to advancing AI technologies. As a key partner in the Genesis Mission, a Department of Energy initiative aimed at creating the world's most powerful scientific platform, he contributes to initiatives that seek to accelerate discovery, strengthen national security, and drive energy innovation. His team's philosophy emphasizes not just solving problems but doing so in a way that sparks new ideas and perspectives among researchers. A central aspect of Kvinge's current research involves examining whether large language models (LLMs), the type of AI behind chatbots and coding assistants, use the same general principles that humans apply when performing mathematical tasks. At the 2025 International Conference on Machine Learning, he presented findings from an analysis of LLMs' internal computations. The study explored how much these models rely on mathematical world models, which are conceptual frameworks used by humans, animals, and AI to simulate and understand the world. Kvinge explained that humans develop world models based on physical experiences, allowing us to make predictions about future events. For example, we know a ball placed at the top of a hill will roll downhill without having witnessed it happen. Since LLMs operate in a purely digital environment, mathematics serves as a useful proxy for studying how these models process and solve problems. By comparing the mathematical world models of LLMs to those of humans, Kvinge hopes to uncover fundamental mechanisms underlying AI cognition. This research has implications beyond AI itself. It could lead to deeper insights into how machines learn and reason, potentially influencing fields ranging from education to cognitive science. Kvinge's ongoing work continues to push the boundaries of what is possible when mathematics and AI collaborate, offering a glimpse into the future of computational discovery.