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Explore one of computer science's most famous unsolved problems in this Members' Colloquium lecture delivered at the Institute for Advanced Study. Delve into the P vs. NP problem, which was formulated approximately 50 years ago and selected as one of the seven Clay Millennium Problems 25 years ago. Understand how our comprehension of this problem's depth, breadth, and impact has evolved dramatically over the decades. Learn about the fundamental question of whether every problem whose solution can be quickly verified can also be quickly solved. Discover the numerous research directions and scientific connections that have emerged from this central question in computational complexity theory. Gain insights into why this problem remains one of the most significant challenges in mathematics and computer science, with implications spanning cryptography, optimization, artificial intelligence, and beyond.
