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We introduce IRIS, a geometric and heuristic-based scoring system for evaluating mathematical conjectures and theorems expressed as linear inequalities over numerical invariants. The IRIS score reflects multiple dimensions of significance—including sharpness, diversity, difficulty, and novelty—and enables the principled ranking of conjectures by their structural importance. As a tool for fully automated discovery, IRIS supports the generation and prioritization of high-value conjectures. We demonstrate its utility through case studies in convex geometry and graph theory, showing that IRIS can assist in both rediscovery of known results and proposal of novel, nontrivial conjectures.more » « lessFree, publicly-accessible full text available August 15, 2026
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