A monoid is a mathematical structure which captures associativity (a+(b+c) = (a+b)+c) and has an identity notion (a + 0 = 0 + a = a). They're useful because kn

A monoid is a mathematical structure which captures associativity (a+(b+c) = (a+b)+c) and has an identity notion (a + 0 = 0 + a = a). They're useful because knowing them allows for identifying and mechanically applying transformations to better leverage parallelism and easily implement incremental computations†. I highly recommend this article and the section on monoid homomorphisms in particular, which covers why you should care about monoids and gives a practical example: https://fsharpforfunandprofit.com/posts/monoids-part2/#monoid-homomorphisms https://fsharpforfunandprofit.com/posts/monoids-part2/#monoi... If you've been programming for a while, I can guarantee you already intuitively understand the concept. Giving it a name allows you to automatically recognize and notice that you've already solved this problem before in another guise. Alternatively, having named the concept, it's now chunked into your toolkit for use whenever applicable. Structuring your solution so you know it's a monoid allows leveraging all those benefits almost for free. †With divide and conquer, add memoization and pay attention to the order of subproblems such that you can reuse earlier work, and if you can, we're nearly at dynamic programming. We can specify a bit more structure, to get semirings and collapse a whole heap of disparate seeming machine learning algorithms. But now I have gone too far afield.