Surprisingly, the answer to this apparently simple question depends on the year you asked the question!
The term algorithm comes from the name of the Persian mathematical genius, Muhammad ibn Musa al-Khwarizmi (c. 780 – c. 850). Algoritmi is the Latinized version of his name ‘Al-Khwarizmi’. In his lifetime he produced influential works in mathematics, astronomy, and geography.
From the perspective of numbers, Al-Khwarizmi formalised the concepts of the Hindu-Arabic number system we use today, and the decimal point. 12th century Latin translations of his textbook Algorithmo de Numero Indorum codified the Hindu-Arabic numerals, and introduced the decimal positional number system to the Western world. In medieval Latin, algorismus simply meant the decimal number system which became an English word by the 13th Century (source: https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi).
Another of his books, The Compendious Book on Calculation by Completion and Balancing was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. It was first text to describe the use of algebra, in an elementary form, for processes such as solving quadratic equations. The book was translated into Latin by Robert of Chester in 1145, and was used until the sixteenth century as the principal mathematical textbook of European universities. The term algebra comes from the title of this book (the word al-jabr meaning completion).
Then some 200 years ago Charles Babbage, known as the father of computing submitted a one-page paper about an invention, The differential machine. With 25,000 different parts, this machine is to all intents the world’s first mechanical computer. Babbage went on to invent the analyzing machine, a general-purpose computer for which mathematician Ada Lovelace wrote what many consider the first algorithm.
However, it wasn’t until the late 19th century that the term algorithm came to mean a set of step-by-step rules for solving a problem. Then in the early part of the 20th Century, Alan Turing, the father of modern computer science, worked out how in theory, a machine could follow algorithmic instructions and solve complex mathematics. And the rest is ‘history’.
For more on the history of numbers, calendars and calculations see: https://mosaicprojects.com.au/PMKI-ZSY-010.php#Overview