tl;dr: (1) Author does not understand the role of research papers (2) Claims mathematical notation is more complicated than code and (3) Thinks ML is easy because you can code the wrong algorithm in 40 lines of code.

I will reply to each of these points:

1. Research papers are meant to be read by researchers who are interested in advancing the state of the art. They are usually pretty bad introductory texts.

In particular, mathematical details regarding whether or not the space is closed, complete, convex, etc. are usually both irrelevant and incomprehensible to a practitioner but are essential to the inner workings of the mathematical proofs.

Practitioners who want to apply the classic algorithms should seek a good book, a wikipedia article, blog post or survey paper. Just about anything OTHER than a research paper would be more helpful.

2. Mathematical notation is difficult if you cannot read it, just like any programming language. Try learning to parse it! It's not that hard, really.

In cases where there is an equivalent piece of code implementing some computation, the mathematical notation is usually much shorter.

3. k-means is very simple, but its the wrong approach to this type of problem. There's an entire field called "recommender systems" with algorithms that would do a much better job here. Some of them are pretty simple too!