A University of Florida team applied the recently proven three-dimensional Kakeya conjecture to large model training, developing the GeoLAN method to address AI’s “black box” problem. This approach leverages the concept of “sticky Kakeya sets” derived from the proof of the Kakeya conjecture to impose geometric constraints on the semantic space of large models, clarifying concepts from the training stage and making AI reasoning paths traceable. Experiments on models such as Llama-3-8B and Gemma-3-4B demonstrated significant performance improvements. The underlying issue addressed is representation collapse, where Transformers cram all semantic information into a narrow area, causing concept entanglement. Meanwhile, Fields Medalist Jacob Tsimerman announced on the day of his award that he is joining OpenAI to work on AI safety, highlighting the unprecedented convergence of mathematics and AI.