Why do some problems seem impossible to solve? In this episode of The Vancrux Podcast, we explore why certain questions appear to resist every attempt at an answer. Is a problem truly impossible, or are we simply approaching it with the wrong assumptions, tools or way of thinking? We examine the limits of mathematics, logic, science and human reasoning, from Gödel’s incompleteness theorems and the halting problem to paradoxes, undecidability, complexity and the limits of computation. We also explore why some problems are difficult because they are too complex, while others may be impossible in principle—and what happens when we confuse the two. Along the way, we consider whether every well-formed question must have an answer, whether reality itself places limits on what we can know, and whether c ...