Pauli's exclusion principle is one wall of a polytope; we mapped all 799 corners (nutfieldsecurity.com)

A recent project explored the application of AI in quantum mechanics, specifically addressing an area of research related to generalized Pauli constraints. Utilizing AI tools like Claude, a security engineer with a background in math and physics embarked on a week-long journey while on vacation, aiming to uncover the corners of a polytope that arises from the Pauli exclusion principle. Previous studies had identified these corners as critical configurations of quantum states, but two specific corners remained elusive due to the absence of explicit examples. The engineer, using AI-assisted methodologies, successfully discovered new corner states and distinguished between those that could be constructed using classical methods and those that required intrinsic quantum interference. This work is significant for the AI/ML community as it demonstrates how AI can facilitate advanced research in complex, traditionally inaccessible fields. The study not only highlighted the potential of AI to assist in mathematical exploration but also underscored the importance of rigorous verification processes to mitigate errors produced by AI systems. Ultimately, the engineer classified 799 corners of constraint systems and sparked a dialogue with active researchers, revealing the collaborative potential of citizen science enhanced by AI. This venture showcases how AI can lower barriers to entry in sophisticated mathematical domains, while emphasizing the critical necessity for thorough validation to ensure scientific integrity.