Short answers, pulled from the story.
An algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. As an effective method, it can be expressed in a finite amount of space and time within a well-defined formal language. A program is an algorithm only if it eventually stops.
The word algorithm comes from the Latinized name of the Persian scholar Muḥammad ibn Mūsā al-Khwārizmī, who wrote around 825 AD. Latin translations such as the Liber Algoritmi de numero Indorum opened with Dixit Algoritmi, meaning "Thus spoke Al-Khwarizmi". Influenced by the Greek word arithmos, the form algorithm was used in English by Thomas Hood in 1596.
The earliest known algorithm is a division procedure described on a Sumerian clay tablet found in Shuruppak near Baghdad, dated to around 2500 BC. Step-by-step mathematical procedures also appear in Babylonian, Egyptian, Indian, Greek, Chinese, and Arabic mathematics.
Ada Lovelace designed the first algorithm intended for a computer, written for Charles Babbage's analytical engine. Although the full second device was built only decades after her death, Lovelace has been called "history's first programmer".
Algorithms are classified by design paradigms including brute-force search, divide-and-conquer, search and enumeration, randomized algorithms, and reduction of complexity. For optimization problems they also fall into linear programming, dynamic programming, the greedy method, and heuristic methods.
In 2023, Google DeepMind introduced AlphaDev, a reinforcement learning system based on AlphaZero that discovered improved sorting and hashing algorithms later integrated into the LLVM standard C++ sorting library. In 2025, DeepMind introduced AlphaEvolve, an evolutionary coding agent powered by large language models that proposes, tests, and refines algorithms over multiple iterations.