Hard optimization problems often look impossible through worst-case analysis, but real-world problems can contain structure that helps algorithms work faster. Ellen Vitercik, Ph.D., of Stanford University explains how machine learning can improve algorithm design for NP-hard optimization problems while preserving the formal guarantees that make solvers useful. She discusses beyond worst-case analysis, problem-specific heuristics, and the gap between tools that perform well in practice and methods that prove optimality. Vitercik also describes research on LLM reasoning using data structure tasks, where answers can be checked programmatically and failures reveal when models rely on pattern matching rather than true generalization. Her work helps clarify how AI may support stronger algorithms, more useful benchmarks, and more reliable reasoning systems. Series: "Data Science Channel" [Science] [Show ID: 41179]