Rigorous means extremely thorough, careful, and demanding. When your teacher assigns a rigorous science experiment, she expects you to measure precisely, record every detail, and check your work multiple times. A rigorous training program for athletes pushes them hard with intense practice and discipline.

The word suggests difficulty combined with high standards and careful attention to getting things exactly right. A math proof needs rigorous logic, where every step follows clearly from the one before. A rigorous investigation leaves no stone unturned, examining every possible clue and testing every theory.

You'll often hear about rigorous academic programs, which means they challenge students seriously and expect excellent work. Scientists use rigorous methods when testing their theories, making sure their experiments are carefully controlled and their conclusions are strongly supported by evidence. When someone conducts a rigorous analysis of a problem, they're thinking deeply and systematically, not just glancing at the surface.

The noun form is rigor, which describes the quality of being thorough and exacting. When you approach a challenging project with rigor, you're committing to doing it right, not just doing it quickly or easily.