Explore a detailed mathematics lecture examining Roy Kerr's groundbreaking 1963 discovery of rotating black hole solutions in Einstein's field equations and their significance in modern physics. Delve into mathematician Sergiu Klainerman's recent breakthrough work on proving the stability conjecture for slowly rotating Kerr black holes, which hypothesizes that perturbed black holes eventually return to a stable state. Learn how Kerr's two-parameter family of explicit, stationary, rotating asymptotically flat solutions ranks among science's most impactful mathematical discoveries, leading to the first observational confirmation of black holes and generating profound physical and mathematical questions that continue to drive research today.