Are there limits to what computers can do? How complex is too complex for computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called Computational Complexity. Computational complexity theorists want to know which problems are practically solvable using clever algorithms and which problems are truly difficult, maybe even virtually impossible, for computers to crack. This hardness is central to what’s called the P versus NP problem, one of the most difficult and important questions in all of math and science. This video covers a wide range of topics including: the history of computer science, how transistor-based electronic computers solve problems using Boolean logical operations and algorithms, what is a Turing Machine, the different classes of problems, circuit complexity, and the emerging field of meta-complexity, where researchers study the self-referential nature of complexity questions. Featuring computer scientist Scott Aaronson (full disclosure, he is also member of the Quanta Magazine Board). Check out his blog: https://scottaaronson.blog/ Read the companion article about meta-complexity at Quanta Magazine: https://www.quantamagazine.org/complexity-theorys-50-year-journey-to-the-limits-of-knowledge-20230817/ 00:00 Introduction to the P vs NP problem 02:16 Intro to Computational Complexity 02:30 How do computers solve problems? 03:02 Alan Turing and Turing Machines 04:05 George Boole and Boolean Algebra 05:21 Claude Shannon and the invention of transistors 06:22 John Von Neumann and the invention of the Universal Electronic Computer 07:05 Algorithms and their limits 08:22 Discovery of different classes of computational problems 08:56 Polynomial P problems explained 09:56 Exponential NP Problems explained 11:36 Implications if P = NP 12:48 Discovery of NP Complete problems 13:45 Knapsack Problem and Traveling Salesman problem 14:24 Boolean Satisfiability Problem (SAT) defined 15:32 Circuit Complexity Theory 16:55 Natural Proofs Barrier 17:36 Meta-complexity 18:12 Minimum Circuit Size Problem (MCSP) - VISIT our Website: https://www.quantamagazine.org/ - LIKE us on Facebook: https://www.facebook.com/QuantaNews - FOLLOW us Twitter: https://twitter.com/QuantaMagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/