Undecidability: The Programmer's Pandora's Box

This article provides a clear explanation of the concept of "undecidability" in computer science. Using accessible language and concrete examples (like determining if a number is the sum of two primes), the author explains decision problems and the role of Turing machines. The key takeaway is that undecidability doesn't mean it's impossible to tell if a program will halt, but rather that there's no universal algorithm to determine the halting behavior of all programs. This makes many problems (such as verifying program properties) require significant effort and may be unsolvable, highlighting the necessity of fields like formal verification and program analysis.