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Explore the evolution and cutting-edge advances in automated mathematical conjecturing through this conference talk from Harvard CMSA's Math and Machine Learning Reunion Workshop. Trace the journey from early systems like Fajtlowicz's Graffiti program to modern neural breakthroughs, while discovering how machines can generate deep mathematical insights across diverse fields. Learn about a revolutionary new framework that combines optimization, enumeration, and convex geometric methods with creative heuristics and symbolic translation to produce conjectured inequalities and necessary-sufficient condition statements. Understand how the IRIS (Inequality Ranking and Inference System) model automatically ranks these conjectures and translates them into Lean 4 for formal verification, creating a flexible architecture that generates precise, human-readable, and logically rigorous mathematical statements with minimal manual intervention. Examine concrete results spanning graph theory, polyhedral theory, number theory, and groundbreaking applications to string theory using complete intersection Calabi-Yau threefolds datasets. Discover how the integration of structure, strategy, and aesthetic principles enables machines to generate conjectures that invite mathematical scrutiny and contribute meaningfully to the creative mathematical process.
