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In reading a description on Usenet of a NIST competition for selecting a standard cipher, I read:

Consider that the best currently known methods for factoring use randomization: Construct enough cases at random, and eventually you can paste them together into a set of factors. This notion of an algorithm is very new - at best, 40-50 years old, though in terms of actual practice, perhaps no more than 25 years old. Mathematics in the past has dealt with proofs, which may be constructive or non-constructive. Constructive proofs have historically been given as deterministic algorithms.

Emphasis mine. I know for a fact that the concept is much older than that, as there are numerous algorithms named after people from classical antiquity. This makes me wonder how old the concept of the algorithm really is. Wikipedia merely says that it has existed for centuries, and cites the Sieve of Eratosthenes as an early example. Here I define algorithm as an unambiguous series of steps and procedures to solve a specific problem, particularly a mathematical problem. Note that I am not asking about the terminology, but about the earliest known instance of a well-defined algorithm.

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    $\begingroup$ The Babylonian method of computing square roots dates back to 60 AD, but I'd expect some stuff to be older still $\endgroup$
    – John Dvorak
    Commented Feb 23, 2019 at 8:08
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    $\begingroup$ @JohnDvorak The Euclidean algorithm was described in 300 BCE. $\endgroup$
    – forest
    Commented Feb 23, 2019 at 8:09
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    $\begingroup$ Egyptians seem to have figured out the multiplication algorithm c 1700-2000 BCE ago. en.wikipedia.org/wiki/Timeline_of_algorithms $\endgroup$
    – Denis de Bernardy
    Commented Feb 23, 2019 at 9:04
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    $\begingroup$ If you don't limit it to mathematics, algorithms are as old as life. The algorithm for drinking water (approach pool, open mouth, apply suction, swallow) for example. You might want to use a stricter definition of algorithm. $\endgroup$
    – terdon
    Commented Feb 23, 2019 at 14:52
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    $\begingroup$ @terdon If someone has written explicit and deterministic step-by-step instructions for solving the problem of drinking water such that a person who does not know how to drink water could follow it and succeed in drinking, I would consider that a legitimate (if silly) instance of an algorithm. $\endgroup$
    – forest
    Commented Feb 24, 2019 at 3:35

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Surely the Rhind Papyrus (around 1500 BC) contains many algorithms. At that time, such things were presented this way: State a specific problem, then show how to solve it. After several such problems/solutions, the algorithm is supposed to be clear, and the student can solve similar problems in the same way.

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  • $\begingroup$ That seems to contain just examples of mathematical problems and their solutions. It may have allowed people to come up with algorithms, but I don't see any explicitly mentioned in it. $\endgroup$
    – forest
    Commented Feb 24, 2019 at 3:40

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