Hard vs Undecidable Problems Explained | Why Some Problems Can’t Be Solved

Not all problems in computer science are solvable, no matter how powerful the computer. In this video, we break down the difference between hard problems and undecidable problems in a simple, intuitive way. You’ll learn why challenges like the Traveling Salesperson Problem take an impractical amount of time to solve exactly, and how developers use heuristics and approximations to get useful answers. We’ll also explore undecidable problems, including the famous Halting Problem, and see why no algorithm can ever predict whether every program will stop or run forever. Understanding these limits helps programmers design smarter systems, use shortcuts safely, and build reliable software in a complex world. 🔍 Topics covered: 00:23 Can Computers Solve Everything? 01:09 Impractical Problems: The Wall of Time Explained 03:11 Heuristics : The smart shortcut 04:37 Impossible Problems: The Wall of Logic 05:53 Proving the Impossible 08:34 Why These Limits Matter : Real-world Implications