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I am a masters student in the process of writing a thesis in computer science.

In particular, there is someone who works in industry who is probably one of, if not the world leading experts in a particular kind of mathematical set of functions. However this person is very much not an academic, he is an industry researcher whose primary objective is practical applications rather than publishing papers.

He maintains a personal blog where he explains a lot of concepts related to this topic in depth. I have used and referenced his blog religiously all through my masters. For example he has a list of functions in this class that can be used to construct very interesting things as well as which operations can be used to combine them.

I know some of these functions he didn't make, they have been known if not since antiquity, at least since the middle ages, others he may have come up with or may have heard about them from someone else and just wrote them in his blog.

What do I do here? It seems like I should cite him since this resource is probably the thing I referenced the most through my masters, but he is probably not the first author of most of the concepts in there, but for many, the first author is likely lost to history.

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I think there are two questions here - should you cite this blog and how do you cite "common knowledge".

  1. You should definitely cite his blog if you used it. I think that almost goes without saying. You obviously relied on his work as a source of information and practical guidance. The possible problem I see here is if he does not provide references himself. You likely want to verify and cite peer-reviewed work as well - even if you originally found a particular method or piece of information in his blog. This is not to say that you need to double check his work (since it sounds like he is a reliable and well known expert in your field). Just that it usually isn't good form to only cite a secondary, non-peer reviewed source like a blog.
  2. As for citing common knowledge, this is just my opinion so take it with a grain of salt... I tend to err on the side of caution. "Common knowledge" is a bit subjective and may not actually common knowledge for everyone who is interested in reading a paper. It's nice to provide references for critical pieces of your argument, even if you think they fall into the category of "common knowledge". In your case, since you are writing a master's level thesis, you should probably over-cite a bit (when in doubt, add a citation) anyway. You can always trim irrelevant citations during editing.

To sum up, in your case, I would cite the blog. Acknowledge that you initially found information there. But you should also provide peer-reviewed sources for any methods you use and any claims you make. For a function that is so old that you cannot reliably trace the source, you can cite any number of reviews, textbooks (in a pinch), or other academic sources that explain the method. I'm sure they exist. Pick one and include it as a reference along with the blog. This probably isn't always necessary but in this case I think it's good practice. The point of a master's thesis is to show that you understand the field and that you can do basic research, not that you can copy a series of blog posts. Keep that in mind.

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    I would say question with common knowledge is more about primary versus secondary sources. If you think a certain fact is common knowledge that it is sufficient to cite a secondary source (something like: this common fact can for example be found in the standard textbook xxx by yyy). You don't need to figure out where this appeared first but you can still give a good source.
    – quarague
    Jun 1, 2023 at 7:31
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    +1 for the point of a master's thesis ... Jun 1, 2023 at 8:38
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    The one thing to add is that you should cite sources for specific statements. So you can't just say, I used this source (i.e. the blog) and then not cite the individual results discussed there. For any result that isn't yours you should cite the original source if possible. One can also cite something as a useful pedagogical tool (usually done in the introduction). But that doesn’t relieve you from your duty to cite the original works. The exception being things that are considered "common knowledge".
    – Kvothe
    Jun 1, 2023 at 15:38
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Short answer: you probably should, but you probably don't have to.

Longer answer: there are a few levels on which to consider this:

  • Research content: this is the one you allude to. If you are taking original ideas from the blog, then obviously you need to cite it. Otherwise you are claiming original work when in fact it is not original. If these concepts have been known "since antiquity," then the blog probably does not contain original ideas, so there's no need to cite on this account. And it's not necessary to track down the original citation for common knowledge (though a statement like "This formula has been known since antiquity and is sometimes attributed to Euler" may be a good idea, if only to avoid questions like "where did that come from?").
  • Pedagogical content: the writing is also an "idea." The examples used, the organization, certain memorable turns of phrase, etc. So, the question becomes, how much of your paper uses pedagogical ideas from the blog?
    • If you essentially rewrote the blog in your own words, then you have to cite. It is plagiarism to copy-and-paste content and then change some of the words.
    • Even if you wrote something from scratch without looking at the blog, it's possible you remembered some of the author's insights and those influenced your writing. This is particularly likely if all of your knowledge on this topic is from the one source.
    • On the other hand, if you reviewed dozens of sources on this topic and you don't see any obvious similarities between what you wrote and the blog, then it might not be necessary to cite.
  • Providing a useful reference. Remember that citations are not only a means of avoiding plagiarism; they also allow others to dig deeper into related topics. If this blog was so helpful to you, it will likely be helpful to others, and so it's good practice to cite it. Perhaps even with a comment: "For an accessible and thorough description of this topic, see [4].").
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    +1 for the comments ... For an accessible and thorough description of this topic, see [...], ...and for ... This formula has been known since antiquity and is sometimes attributed to XYZ Jun 1, 2023 at 8:34
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I'll add in to @sErISaNo and @cag51 excellent suggestions by narrowing down to

I know some of these functions he didn't make, they have been known if not since antiquity, at least since the middle ages, others he may have come up with or may have heard about them from someone else and just wrote them in his blog

You may consider a snowball tactic (as normally done in lit review).

For where it might be necessary, apart from citing his blog and following cag51 phrasing approach, you can identify 'peer-reviewed sources' (as sErISaNo indicated), through forward/reverse chaining (literature search).
In your case, where the scientific blog did not provide references, you use phrases from the blog and the mathematical functions/concepts for your search.

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Just provide a blanket opening disclaimer, similar to the one found in this arXiv publication presenting the Pythagora's theorem.

We follow [1], [2] and [3] for the historical comments and sources.

Where [1] [2] [3] are the blog you mention, some wikipedia page you accessed while reading the blog and possibly some other blog.

This is not the most elegant way, but it provides you a quick opening, then you can refer to the blog whenever is needed simply by providing again the reference, for example

the derivative of sin is cos, although the derivative of cos is -sin, which leads to important and trivial fact (see [3] for the historical context)

Quite boring, quite lazy, but at least what is not your own product is clearly referenced. In my view, you may get less points because you do not demonstrate independency in presenting the historical context or knowing why a common fact is common, but at least you do not loose points or invalidate your thesis because you plagiarized some content from somewhere else...

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Simply put, decide whether you cite a work by asking yourself the following question: If you are writing a history of your field, would you give credit to the author for the contribution? If not, don't cite his work. You can thank him for his nice blog in the acknowledgments section instead.

Long answer: I don't think you should cite his blog if it only contains pedagogical explanation at the common-knowledge level. In that case you should cite the original sources instead. There are just too many secondary sources, and citing only one of them based on your preference is unfair to the others.

However, if the blog contains original results and/or nontrivial efforts towards explaining very complex concepts (to me the criterion should be beyond the understanding of an average expert in your field), I would consider citing it as justified as citing any original work published on a preprint server.

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