ANN Representation:

Mostly 'ANNs' are taught on "AI" courses since their motivation from brain studies and the fact which they are used in an "AI" task and namely machine learning. Moreover now I would argue such that their real home is in statistics as a representation scheme that they are just fancy mathematical functions. 

Well now imagine being asked to come up through a function to take the following inputs and then produce their associated outputs:

However the function you would learn would be as f(x) = x². But now imagine like you had a set of values before a single instance as input to your function:  

Presumably now it is still possible to learn a function as: for example that there multiply the first and last element and take the middle one as of the product. But remember that the functions we are learning are getting more complicated so then they are still mathematical. Hence ANNs just take this further: as the functions they learn are usually so complicated that it's difficult to understand them on a global level. It means that they are still just functions that play around with numbers.