I remember learning this in my algorithms class many years ago. We used the Comen et al Intro to Algorithms book, which goes a long way to providing a proof for every algorithm discussed: https://mitpress.mit.edu/books/introduction-algorithms-third...

Wikipedia does mention it though:

  In mathematics and computer science, an algorithm is *a finite sequence* of well-defined, computer-implementable instructions, typically to solve a class of specific problems or to perform a computation.

"Finite sequence", meaning it terminates. The wiki citation (The Definitive Glossary of Higher Mathematical Jargon) provides a little more: "A finite series of well-defined, computer-implementable instructions to solve a specific set of computable problems. It takes a finite amount of initial input(s), processes them unambiguously at each operation, before returning its outputs within a finite amount of time." https://mathvault.ca/math-glossary/#algo

So they stipulate finite input and output and finite runtime. This is in contrast to something like a webserver or OS, which has a potentially unbounded number of inputs, and is expected to run effectively forever.

I mean think about it, what does an OS kernel look like in its most distilled form? It's essentially just an entry point to an infinite loop. Same as games, where they're called "event loops" in that domain.

The way I think about it is this: if computers and programming languages and software didn't exist, algorithms still would. I don't think you can say the same about e.q. Quake. Quake isn't a mathematical truth even though it uses them to work, kind of like how engineers use physics to build a bridge, but the bridge itself isn't physics.

Well, I don't consider an OS or a browser to be the implementation of an algorithm. It has to be possible to understand an algorithm, re-implement it, and so on. I'd say you have to be able to hold it in your head - like Eratosthenes' Sieve.

I don't see anything in the WP article about proofs of correctness. "Finite sequence" surely just means that the number of instructions isn't infinite? Come to think of it, that wording seems rather hand-wavey; I wonder if I can find citations to help me improve it.

> I don't see anything in the WP article about proofs of correctness. "Finite sequence" surely just means that the number of instructions isn't infinite?

Well how are you going to show that the algorithm terminates for all inputs without a proof of correctness?