Who developed the first algorithm for the analytical machine?

The first algorithm for the analytical engine, which is considered one of the first concepts for a general-purpose computer, was developed by Ada Lovelace. Lovelace worked alongside Charles Babbage, who designed the analytical engine, but her contribution was significant in that she translated and expanded upon Babbage's ideas. She created what is now recognized as the first published computer program, specifically designed to be executed by the machine once it was built. Lovelace's notes included a detailed description of an algorithm for calculating Bernoulli numbers, demonstrating her understanding of the machine's potential to manipulate symbols and perform complex calculations, which laid the groundwork for future programming.

Charles Babbage was instrumental in the design of computing machinery but did not write an algorithm himself. Alan Turing is well-known for his foundational work in computer science and artificial intelligence but came much later, while Grace Hopper was pivotal in the development of programming languages.