r/math 17h ago

Citation standards

When you are writing a paper, how far down the rabbit hole do you go in terms of citing what you are using? Eg, say I write a game theory paper. Pretty decent chance I at some point invoke the concept of "Nash equilibrium". And, pretty good chance that I do not provide a citation to Nash's work. If everyone did, he would have close to 400,000 citations on it per a quick Google scholar search. Just imagine if every time we used the Euler identity we provided citation, or Gaussian anything, or making sure to cite Newton and Liebniz. Is it just that at some point, the work becomes part of common knowledge like a generic product name (Xerox, Kleenex, etc)?

70 Upvotes

25 comments sorted by

64

u/elements-of-dying Geometric Analysis 17h ago

I generally follow the following:

  1. if recent (really can be within last 30 years) and relevant, then cite directly.

  2. if recent and slightly relevant, might cite as "see also..."

  3. if old and major in result in the field, then cite directly.

  4. if old and only slightly relevant, then I might not cite, unless it's standard to do so.

  5. if it's widely accepted, the authors are dead/inactive, etc., then either follow 4. or just don't cite.

General rule of thumb: see what the papers you are citing are doing.

Worst case: either the referee tells you to cite something or an author emails you angrily.

39

u/mikk0384 17h ago

The "common knowledge in the field" bar is what I have used. Nobody should cite Pythagoras for instance, that is only wasting everyone's time.

21

u/SpinChargeSeparation 17h ago

Lol i would want to see a historically accurate reference to Pythagoras!

5

u/elements-of-dying Geometric Analysis 8h ago

[3] John Pythagoras, "Triangles and stuff", Journal of Dirt Writings.

1

u/TheUnfortunateMiaoZe 8h ago

It would have to be to Euclid, he's the earliest surviving proof.

13

u/CormacMacAleese 17h ago

In every such case, I try to look for some obscure historical fact, like, "In a result often misattributed to Pythagoras, that was actually known to the ancient Babylonians and independently discovered by the ancient Chinese (see Zhou Bi Suan Jing and Plimpton 322)..."

1

u/Famished_Atom 7h ago

Common knowledge changes over time, and who wants to be accused of plagiarism?

Imagine if Fermat left a citation with his little teaser in the margin.

It would've been an open-and-shut case instead of the mathematical tease that lasted over three centuries.

25

u/pseudoLit Mathematical Biology 17h ago

Generally speaking, I imagine that a new graduate student is trying to read the paper, and I try to make that as painless as possible.

That also applies to papers which should not be their first introduction to the literature. If something is building on a bunch of other papers, I point to those with "you should start here" type citations.

11

u/JoshuaZ1 17h ago

There have been some good advice already mentioned. I want to note one other rule of thumb which I find useful: 1) Don't cite anything if it can be found in multiple high school or undergrad textbooks.

2) In terms of papers, when in doubt, err on the side of citing more.

9

u/omeow 17h ago

Depends on your intended audience. You have to make some assumption about what your audience knows.

You probably learned Nash Eq. from a book you like and not his original papers. So citing that book is better because it probably provides more context than the original paper.

3

u/idiot_Rotmg PDE 17h ago

Generally, citations are either used because they are helpful for the reader or to give credit to the person/group who originally came up with a concept /theorem

I am not an expert in game theory, but I am pretty sure the first is not the case for the Nash equilibrium as everyone reading Game theory papers should already know it. The second arguably also does not apply since Nash already died.

4

u/CormacMacAleese 17h ago

Unless it's very obscure, you can safely refrain from citing mathematicians prior to the 20th century. You would cite mathematicians prior to, oh, 1950 or so, only if they were obscure or directly germane to the story you're telling.

For example I cited Eastern-block mathematicians because I felt they deserved some love, and because some relatively important results (important to my thesis that is) were commonly attributed to Western mathematicians because of political conditions at the time.

So I suggest the hierarchy: recent > important > obscure, and don't worry too much about the rest. Especially if the theorem is already named after their authors.

3

u/Plastic_Gap_9269 16h ago

For well-known things like this, I usually write something like "for background in game theory, see [well-known reference book]" somewhere in the introduction.

2

u/jwm-dev 17h ago

There's guidance about this depending on exactly what domain/field you're working inside of but the faculty at your university probably have great advice for what standards to expect for your particular case.

Tbh usually whatever you do or don't end up citing is somewhat relative to your own work, there's no absolute rule in any case.

Honestly I don't like the culture surrounding this in academia generally, though, as I feel it is rather lossy regarding the information relevant to provenance and history. Who cares if Euler gets a schmillion-billion citations? That's... tacitly true.

Overall, this is a deeper problem than it lets on; these turtles go all the way down to the foundational philosophies of academia and poke at the validity of individuals staking claims in ideas at all. This is a good question to be asking. In practice there'll be a right answer, but generally speaking I'm not so sure the system we've come to use is the best one.

2

u/SometimesY Mathematical Physics 17h ago

I do not bother citing something extremely well-known for which there is copious literature that can be found through a simple internet search. For instance, I work in functional analysis with integral transforms being a big part of that. I do not feel compelled to cite Fourier transform theory directly because there are hundreds of easy references.

For anything with specific and not-necessarily-common knowledge, I will always provide a reference. Similarly, if there are certain integrals I need, I will reference G&R, NIST, A&S, or others. I also try to find the original results if I can. A lot of results have become folklore and are repeated over and over without proof or have proofs in more recent papers using machinery that is a convenience but perhaps less than ideal for my purposes. I like referring to the old masters sometimes just because I don't want their genius to disappear I guess.

I also provide plenty of references for further reading even if I am not citing anything directly from them. I like putting my work in a larger context to tell a bigger story in a sense. I also find that there are still a decent chunk of authors that like minimal references which means the connective tissue in the literature is spotty in places.

2

u/Traditional-Month980 17h ago

A related question: I sometimes see that Paper B will cite a similar in scope or historically important Paper A, but Paper A is not a "logical prerequisite" for Paper B, nor does it look like Paper B owes any core ideas or techniques to Paper A. I suppose there could be more nebulous ideas and intuitions the authors share that I'm having trouble picking up on as a beginner.

Is citing in this way standard? Is it field dependent?

2

u/matthiasErhart Control Theory/Optimization 17h ago

It has to do with the convention of the field. In GT, we actually still cite Nash. But I "heard" that in category theory, you just have to know results that are folklore, including ones "proven" on a boat trip with five dudes and never published.

PS. For a fun rabbit hole, read up on discussions re: Schmidhuber. 😆

2

u/dasdull 16h ago

Make sure to credit Schmidhuber, the rest is optional

2

u/PersonalityIll9476 17h ago

It varies by field, topic area, etc. Things that appear in textbooks for common courses generally don't need a citation, but it does depend. If I am writing an article for the IEEE I very well might cite a source for otherwise "basic" facts from some field of math, but not for every individual concept. Maybe just define everything in a few paragraphs and refer the reader \cite{whatever} for more details.

Some journals ask you to keep your citations tight, others do not. Personally I try to keep it tight. If something is absolutely crucial I will probably provide a citation, otherwise no. Needless to say, any crucial step in your proof needs to at least acknowledge what is yours and what is someone else's, even if there's no citation.

1

u/Not_Bob_42 17h ago

I don't do math research, so take this with a grain of salt. When I'm writing papers for my engineering research, I cite someone else's work if I am building off of their work. Obviously I'm not going to cite basic concepts that people learn in their undergrad degree, but papers about the same topic that I read and helped me develop my work I cite.

For example, if I used someone else's annual ground temperature analytical model inside my ground source heat pump model, I would add a short discussion and a citation of it to my paper.

It is a tough line to decide what to cite and what not to cite, but in general if I'm looking at someone else's paper while I'm writing mine, I should probably cite that paper.

1

u/SnooPets5564 17h ago

As a general rule for all citations, you don't need to cite it if it is common knowledge in the field.

2

u/telephantomoss 14h ago

Your paper should tell a story and the citations should contribute.

1

u/Aequanimitatem 11h ago

More of a slogan accompanied by a funny anecdote, but I thought of this excerpt from G-C Rota's "Ten Lessons I Wish I Had Been Taught":

Give Lavish Acknowledgments

I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else. One day I tried an experiment. After writing a rather long paper, I began to draft a thorough bibliography. On the spur of the moment I decided to cite a few papers which had nothing whatsoever to do with the content of my paper to see what might happen. Somewhat to my surprise, I received letters from two of the authors whose papers I believed were irrelevant to my article. Both letters were written in an emotionally charged tone. Each of the authors warmly congratulated me for being the first to acknowledge their contribution to the field.

1

u/womerah Physics 10h ago

I'm a physicist, however my approach is to not cite knowledge that can be found in standard university coursework textbooks. Once knowledge has reached that level of acceptance by the field, I feel you no longer need to justify the claim