Detailed Explanation: An algorithm is a finite sequence of well-defined instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are essential in both computer science and mathematics, enabling machines to process data, perform calculations, and automate reasoning. They can be expressed in various forms, such as natural language, pseudocode, flowcharts, or programming languages, and can vary in complexity from simple operations to intricate processes involving multiple steps and conditional logic. In AI, algorithms are fundamental in creating models for machine learning, optimizing neural networks, and enabling intelligent behavior in systems.

Historical Overview: The concept of algorithms dates back to ancient times, with its origins often attributed to Persian mathematician Al-Khwarizmi around 825 AD. The term "algorithm" itself is derived from the Latinized name of Al-Khwarizmi. The formalization and study of algorithms gained significant momentum with the development of computer science in the mid-20th century, particularly after Alan Turing's work on the theoretical foundations of computation in the 1930s and 1940s.

Key Contributors:

- Al-Khwarizmi: Often called the "father of algebra," his works introduced systematic methods for solving linear and quadratic equations.
- Alan Turing: Laid the groundwork for theoretical computer science, particularly with the Turing machine, which formalized the concept of computation and algorithms.
- Donald Knuth: Author of "The Art of Computer Programming," he significantly advanced the study and understanding of algorithms and data structures.