The term is derived from a Persian scholar in the 9th century (Muhammad ibn Musa al-Khwarizmi). The term has been adulterated and was called algorism in middle age English. The term algorithm held from the 17th century.
So an algorithm is basically a rule.
The simpler form is the table of multiplication stating that a number multiplied by another equals another number. It’s correct but basically to multiply 5 by 7, you need to learn the result 35 by heart…we can’t easily imagine children not spending time on this and how important it is.
There is also the option of using a calculator and entering “5” x “7” = “35”. Again the result is correct, the rules in the calculator chip or in the child’s brain are not explaianble, however, the results are correct.
An algorithm in artificial neural networks is again a rule connecting an input layer to the computed. It is a mathematical equation which reflects what goes on in the hidden layers of an artificial neural network for example. We want the equation to be as simple as possible to help mathematical understanding. However reaching explainability is a different story, particularly in health where results are more complicated that a multiplication of two numbers.
Ideally algorithms reach explainability, and this is an essential feature in health where problems can become more complex than upstream administrative identifiers such as structures patient data (name, date of birth, insurance type etc…)