The motivation for writing this amuses me. The Wikipedia prose "proof" is frustratingly familiar to many math textbooks I had when getting my BS many years ago. Fortunately, I had a couple professors who insisted on properly structuring proofs so that they were, you know, actually readable and understandable.
That Wikipedia prose is like the lazy author's approach, it's a brain dump and not a real attempt to inform or educate. It is nice that there is Python code in the relevant section on the algorithm, that's informative (and why I like Python, it's executable pseudocode). But it would also be nice to have properly structured proofs to go along with the awful prose section (and either remove it or clean it up).
I don't know if it is math but formal scientific writing can make even simple concepts hard to grasp for me, a developer.
During my studies, I had to assist to a conference by a mathematician explaining some image processing algorithm. It took me half an hour to realize that all that was a good old "make each pixel the weighted average of its surroundings" blur, also known as a convolution filter. And I spent the other half hour completely lost trying to understand what was special about his blur. I think no one actually understood anything, in fact, I probably did better than most because I was familiar with convolution filters from personal experience.
Had he explained it in terms of pixels and loops instead of what was probably (for us) a Greek letter soup, I am sure we would have understood.
There is a chronic problem in audio/image processing where domain experts have developed their own notation and terminology and do a really poor job connecting it to the simple concepts they represent.
> Had he explained it in terms of pixels and loops instead of what was probably (for us) a Greek letter soup, I am sure we would have understood.
Unfortunately concretizing the math to realizations leaves you with a cookbook for implementing the least interesting bits of signal processing. Looking at some matrix multiplication as for loops doesn't teach you how a filter works.
Like just to give an example, I don't think it's possible to come up with an explanation of the Remez Exchange Algorithm in any physically meaningful context since it's fundamentally about recognizing the mathematical properties of a higher order abstraction of the system designed with it. But we can be a bit smarter about how we write, since "an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm L∞ sense" is Wikipedia word soup that belies the concepts and connections that make it useful. It's just hard to do it in a sentence and not a semester.
I had the same experience as a math undergrad. Too many professors seem to have forgotten what it was like to be a student. They write books that are great reference material for their colleagues but which are utterly opaque to a student who is still working to build their foundation.
Textbooks often format proofs as a sequence paragraphs, but this really obscures the logical structure of the argument. As a student, I found it very helpful to write down proofs as nested lists [1,2] instead.
Admittedly, now that I have more experience, I do like my proofs to be more terse when I'm communicating them just to myself.
Your examples are, more or less, how I was taught to construct proofs. It's just much clearer and easier to read/follow than the prose-style in that Wikipedia page. And you can always supplement one with the other, just like the code example. Technically unnecessary since there was a prose description of the algorithm, but from a readability/understandability perspective it's immensely useful.
Wikipedia is notoriously useless for learning anything even vaguely mathematical. It's too bad there's not a "Wikimath" for people who aren't mathematicians.
> Wikipedia is notoriously useless for learning anything even vaguely mathematical. It's too bad there's not a "Wikimath" for people who aren't mathematicians.
The nlab and wiki2.org are nice for the subjects they cover.
That Wikipedia prose is like the lazy author's approach, it's a brain dump and not a real attempt to inform or educate. It is nice that there is Python code in the relevant section on the algorithm, that's informative (and why I like Python, it's executable pseudocode). But it would also be nice to have properly structured proofs to go along with the awful prose section (and either remove it or clean it up).
Also, here's the discussion from when this was first posted: https://news.ycombinator.com/item?id=14967697