"On Computable Numbers"

"On Computable Numbers" is a foundational mathematical paper by Alan Turing that introduces the concept of what it means for a number to be "computable." Essentially, a computable number is one that can be generated by a well-defined algorithm or step-by-step set of instructions using a computer. Turing's work formalized the idea of mechanical computation, laying the groundwork for modern computer science. The paper shows that some problems are solvable by algorithms, while others are not, highlighting limits of mechanical calculation and influencing the development of theoretical computer science and the understanding of what computers can do.