One of the earliest-known entries of the word "algorithm" in a dictionary can be found in Samuel Johnson's Dictionary of the English Language from 1785.

The entry on page 130 reads (approximately):
algorithm: Arabic words, which are used to imply the six operations of arithmetic, or the science of numbers.

Today, "algorithm" is defined as:

- A well-defined procedure to solve a problem.

- A clearly specified set of simple instructions to be followed to solve a problem.

- A finite, deterministic, and effective problem-solving method.

- An explicit, precise, unambiguous, mechanically-executable sequence of elementary
instructions.^{1}

- A sequence of computational steps that transform input into output.^{2}

- A set of rules that precisely defines a sequence of operations.^{3}

- A precisely defined set of mathematical or logical operations for the performance of a particular task.^{4}

- A step-by-step process to efficiently reach the desired goal.^{5}

- A systematic method for solving a problem.^{6}

- A well-defined computational procedure that takes a variable input and halts with an output.^{7}

1. Jeff Erickson's algorithms notes

2. Introduction to Algorithms / Cormen, Leiserson, Rivest, Stein / MIT Press link

3. Introduction to Computer Organization and Data Structures (1972 ed.) / Stone / McGraw-Hill, New York.

4. OED Online, Oxford University Press, June 2019, www.oed.com/view/Entry/4959

5. Arizona State University graduate course syllabus "Foundations of Algorithms" CSE 551

6. Universal Book of Mathematics / Darling / Wiley / 2004

7. Handbook of Applied Cryptography / Menezes et al / CRC Press / 2001 / p.57

See also: wikipedia