# What is the earliest instance of the use of an algorithm to solve problems?

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.

• The Babylonian method of computing square roots dates back to 60 AD, but I'd expect some stuff to be older still Feb 23, 2019 at 8:08
• @JohnDvorak The Euclidean algorithm was described in 300 BCE.
– forest
Feb 23, 2019 at 8:09
• Egyptians seem to have figured out the multiplication algorithm c 1700-2000 BCE ago. en.wikipedia.org/wiki/Timeline_of_algorithms Feb 23, 2019 at 9:04
• 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.
– terdon
Feb 23, 2019 at 14:52
• @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. Feb 24, 2019 at 3:35