User:XOR'easter/So, you've decided to write about physics and/or mathematics on Wikipedia

So, you've decided to write about physics and/or mathematics on Wikipedia!

Maybe you're a student in one of those fields, or even a professor. Or maybe you came to Wikipedia for other reasons, have experience with how the project works, and suddenly find yourself dealing with a science topic in the news or a physicist who's shown up to edit. The peculiarities of Wikipedia and those of the academic world can intersect in strange and frustrating ways, causing even people of good will to work at cross-purposes.

Wikipedia works by summarizing, as fairly as possible, the content of reliable sources. In subject areas that require considerable education to master, identifying which sources might be reliable can be a difficult task, and indeed, learning to do so can be a significant part of that education. On the flipside, there are things about writing on Wikipedia that aren't necessarily obvious to new arrivals, no matter how much subject-area expertise they have. This essay provides some pragmatic advice for identifying reliable sources about physics and mathematics, deciding how much emphasis to give a topic, and organizing the coverage of those subjects in a clarifying way.

Introduction to Wikipedian jargon
Wikipedians have given some ordinary words new, specialized definitions that are related to but distinct from their everyday meanings. Physicists and mathematicians should feel right at home with this.


 * Reliable sources: published sources of information that are trustworthy enough for our purposes. Thanks to complexities of the sort we will explore below, deciding which sources are "RS" and which aren't requires care.
 * No original research: Wikipedia isn't set up to evaluate claims about new ideas or discoveries. So, we have a rule that we don't say anything unless someone else has said it first. This also means that we don't put together ideas to draw new conclusions: no synthesis, even if the component ideas are already out there on the record.
 * Neutral Point Of View (NPOV): taking the viewpoints present in reliable sources and representing them "fairly, proportionately, and, as far as possible, without editorial bias". This is not "neutrality" in the sense of saying one bad thing for every good thing, which would lead to absurdities.
 * Notability: similar to, but more specific than, the everyday idea of "noteworthiness". A topic is "notable" if it deserves a Wikipedia article about it. This mostly boils down to the question, "Has it been written about a lot before?"
 * Due weight: related to, but distinct from, "notability". This refers to the question of how much emphasis to give a point within an article.
 * Good articles (GAs): articles that have gone through an assessment process and been designated well-written and well-cited, though not necessarily comprehensive. Featured articles (FAs) are a level beyond that.

Writing about your own work
It is generally a bad idea to write about your own research here. For one thing, Wikipedia has strict rules about conflicts of interest. Wikipedia is nobody's publicity department or advertising platform, and the prohibition against promotional content includes content that is intended to bulk up one's reputation whether or not immediate financial gain is involved. Of course, it is tempting to get ahead in the academic rat race by any means possible, and each of us naturally feels that our work deserves to be covered here — if we didn't think it was important, we wouldn't be plugging away at it! When faced with this temptation, consider how you would feel about anyone else puffing themselves up in this manner, and recognize that (to paraphrase Calvin and Hobbes) we are all someone else to somebody.

Rather than advertise one's own super-specialization, why not work on explaining the prerequisites to understanding it? What articles would a student read in order to understand the background and broader context of your research? We can guarantee that some fraction of those articles need attention.

When do we need an article?
Wikipedia is an encyclopedia, not a dictionary. Generally, we organize material by what things are, rather than what they're called. Creating a new article dedicated to a specific jargon term can be a bad idea, because it isolates that term from its context. For example, prime numbers with at least 10,000 digits have sometimes been called "gigantic primes", but there is little more to say about "gigantic primes" than that, so we define the term within another article rather than giving it a page unto itself. Likewise, there's not enough to say about "helvetium" beyond what is said in the history of the discovery of astatine, so having a separate "helvetium" page would be a distraction. In kinematics, one can differentiate position an arbitrary number of times, but we only need one page for all the derivatives above the third, because they are typically discussed together and there is not so much to discuss about them individually. When adding and organizing content, consider when ideas form a "package deal".

We have biographical articles on physicists and mathematicians when they are influential or significant in a way that we can back up with documentation. In fact, we have a whole guideline on how to tell if that is the case. If you want to write an article about yourself, first, don't, and second, ask yourself if that is something you really want. If someone is offering to write an article about you for payment, they are a scam artist.

How do we organize an article?
Wikipedia articles are not written like textbooks: a textbook may lead the reader with probing questions, work step-by-step through examples, and so forth. Textbooks have the advantage over us in that they can be targeted to a specific audience (e.g., Introductory Category Theory for Undergraduate Physics), whereas our articles often have to serve multiple audiences simultaneously. This poses difficulties that scientists and science writers may be unfamiliar with. It is not in general possible to learn physics or mathematics merely by reading encyclopedia articles and nodding along; one must work problems. However, for reasons going deep into the kind of project that Wikipedia is, it is ill-suited to provide them.

We aim to write "one level down": if a topic is generally studied at stage $$N$$ of an education, our article on it should be at least somewhat useful to people at stage $$N - 1$$. We don't avoid technicalities, but ideally, we do take care how to present them. It is generally best to put the less technical portions of an article up front. Above all, the introductory paragraphs, also known as the lede, should be as widely accessible as possible while still giving a fair summary of the article that follows. It is rather rare that we step through the details of a proof; instead, we explain its context, the assumptions that go into it, and what it demonstrates. See the article on Gleason's theorem for an example of this style. We go into more detail about the steps when they themselves are of historical or conceptual interest. For example, it is reasonable to detail Nicole Oresme's proof that the harmonic series diverges, because it dates back to Nicole Oresme, and it generalizes to the Cauchy condensation test.

The history of a topic is often isolated within a devoted section of an article. There is no official guideline on where to put a "History" section: one can be placed near the beginning, in the middle, or at the end, depending on what works best, and it may not be obvious what actually does work best. An accurate history may be more intimidating than a crisp presentation of the current state of a subject.

Types of sources
Unlike the case of medical subjects, when it comes to mathematics and physics, the undesirable sources are typically more mediocre than actively harmful to human well-being. We do, however, have incidents where things get hyped up because a press release said it was the most amazing discovery ever, or a random website is used as a source when perfectly good textbooks covered the topic in depth, or something fringe-y is cited to a journal that looked respectable but wasn't, etc. The goal of this section is to gather the editing community's experience with such problems into one place.

Textbooks
As mentioned above, Wikipedia articles aren't written like textbooks. However, this is a difference of style and structure, not subject matter. When the standard textbooks for a field cover a topic, it's fair to presume that Wikipedia should cover it too. Whether that topic deserves a stand-alone article or is better treated as part of an article with a broader scope must be decided on a case-by-case basis. Standard textbooks can be presumed generally reliable. They are also almost certainly wiki-notable, and linking to the article on the textbook when that textbook is cited is a good way to provide the reader with further information, like the level at which the book was written and the background knowledge it presumes.

Textbooks can be roughly grouped according to the stage in a student's education in which they are assigned. Typically, we deal with post-secondary educational resources, meaning that textbooks can be divided between undergraduate and postgraduate levels. The following lists are certainly incomplete, but they do reflect what physics and mathematics enthusiasts have been most motivated to contribute to Wikipedia.


 * List of textbooks on classical mechanics and quantum mechanics
 * List of textbooks in thermodynamics and statistical mechanics
 * List of textbooks in electromagnetism

Not every word in a standard textbook is golden. Even in widely-used and well-regarded texts, there can be a penumbra of material that other, more specialized sources might supersede. For example, physics and mathematics textbooks are principally written to explain the current state of the field, and they do not focus so much upon the history; when they do cover the history of a subject, they may oversimplify. A brief synopsis of the conflict between Newton and Leibniz regarding the discovery of calculus is no substitute for in-depth works by historians of mathematics. By the same token, if standard textbooks only treat the history of a subject in a cursory manner, that may indicate that Wikipedia should address the history separately, e.g., in a biographical article on a researcher or in a "History of..." page.

In addition to texts on broad topics like electromagnetism or differential equations, which might be used for semester-long required courses, there also exist more specialized volumes that might be used in higher-level elective courses or as references for active researchers. This territory overlaps with the scholarly monograph; the latter term carries more of a connotation that the text presents original ideas of its author. Specialized textbooks and monographs can also be assumed reliable for Wikipedia's purposes.

Books printed with self-publishing services like Lulu.com and vanity presses like Cambridge Scholars Publishing are, by default, not reliable sources. In rare cases, they may be the serious work of a subject-matter expert and can then be used with caution, but it is much more likely that reliance on such sources is an indicator of fringe physics or pseudomathematics (perpetual motion machines, quantum mysticism, golden ratio crankery...).

Journal articles
Journal articles are the common currency of physics and mathematics. They come in multiple types, the distinctions between which might not be clear to an outside observer. Many articles begin as preprints posted to an online repository like the arXiv. Making their writing public in this way allows a researcher (or group thereof) to claim priority, proving to the world that they knew the results in the paper by the date the paper appeared, and it facilitates discussion among scientists. However, preprints are not guaranteed to be reviewed in any formal way, and consequently, they should be taken as self-published sources. They might represent the opinion of a subject-matter expert, but they are generally not suitable for most purposes when it comes to writing Wikipedia articles.

Research papers
Once a paper is written, and possibly after it has been posted as a preprint, it is submitted to a journal, where it undergoes a process called peer review. This process acts as a filter to keep unfounded claims from appearing in journals. It is not an infallible guarantee of correctness. Results can slip through peer review that are subtly erroneous or outright fraudulent. Even mathematics is not immune.

It is usually a bad idea to make a big deal out of research that hasn't been cited by anyone other than the original authors, even if it has technically been peer-reviewed. Remember, peer review is the opinion of a few people, while citations are the opinion of a community. This matters both when evaluating wiki-notability to see whether an article should exist or not, and when deciding how much weight to give a topic within an article. The number of marginal ideas that the scientific community has not found interesting enough to criticize is far higher than outsiders realize. (A 2019 study found that about 11% of physics and astronomy articles, and 16% of mathematics articles, received no citations at all. If one considers also those articles which receive only perfunctory mentions, the fraction would doubtless be larger.)

MathSciNet and zbMATH provide post-publication commentary on mathematics articles.

Some journals have a pedagogical focus, printing papers meant to be read by students and/or those actively involved in teaching them. Examples include the American Journal of Physics and the American Mathematical Monthly.

Papers published in predatory journals are not reliable sources. Predatory journals provide the superficial appearance of having been published, but they do not conduct a meaningful review process. The term "predatory" is not universally embraced, as it may be that some scientists deliberately choose to publish in these journals even while knowing that the journals have no standards to speak of, in order to meet the pressure of a publish or perish culture. Whatever we call them, these platforms allow purveyors of fringe physics or pseudomathematics to publish their work in something that looks like an academic journal. Work that was published in a "journal" that provides no actual quality control and which has attracted no attention beyond its own authors is, in essence, "original research", just like a circle-squaring that was posted on the inventor's website. (The No original research policy was originally written with physics cranks and crackpots specifically in mind. )

Review articles
A review article summarizes the current state of knowledge about a topic, gathering together the results of previously-published work rather than introducing new ideas or discoveries. Journals like Reviews of Modern Physics specialize in articles like these. The "What is...?" essays published in the Notices of the American Mathematical Society also fit under this heading. Review articles are typically narrower in scope than textbooks and are likely to be more up-to-date.

Conference proceedings
In physics, conference proceedings are typically the lowest tier of journal publication, in terms of the standard of peer-review applied. Conference proceedings are also more likely to go uncited by later work. This is not necessarily the case in other fields.

Conference websites typically list abstracts of the talks given there. The material in a talk is hardly ever reviewed prior to the talk being given, and getting the chance to present at a conference can be a very low bar to pass. Video recordings of conference and seminar presentations are sometimes available, particularly when the meeting was held online. These recordings should be regarded as self-published sources. Recordings of presentations have all the problems of preprints, with the added complexities of extemporaneous speech. Videos tend to go up without the kind of work that goes into peer-reviewing and editing written material. An editor at a journal solicits opinions from experts in the field, who can point to specific parts of a paper and ask that they be revised. Nobody checks a lecture video to see if it is careless, confusing, oversimplified, or meandering. If you're very lucky, they'll get an intern to splice the speaker's slides into the video so they're easier to read, and maybe trim the Zoom-fumbling from the start of the recording; that's about it.

Theses
A thesis, also called a dissertation, is a written document produced as a central part of obtaining an academic degree. The degree in question can be a bachelor's, a master's, or a doctorate. (In countries where obtaining a Habilitation is the custom, this also requires a thesis.) Particularly at the doctoral level, a thesis is supposed to be an original contribution to scholarship. A thesis must be approved in order for its author to obtain a degree, though the details of this process vary across institutions. In most cases, success only requires approval by scholars within the student's university. Consequently, theses should be regarded as primary sources and used with caution.

Theses may be published as monographs or broken up into smaller portions that are published as journal articles. (For an interesting example of the former, see The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields.) When available, these are generally preferred, due to the extra steps of review involved. Alternatively, some theses may be assembled by joining together several journal articles in which the student had been involved, perhaps with new framing material. The introduction or preface of the thesis should make this clear. The separate articles may, in practice, be easier to access online than the conjoined thesis; keep this in mind when deciding which to cite.

Popular press
Unfortunately for us all, the popular press is typically not a good source for scientific information that we can use in writing Wikipedia articles. Newspapers, television, pop-science websites and their kin generally oversell the novelty and the certainty of whatever they "report" upon. They also rush to press with stories about scientific results before the scientific community itself has been able to reproduce them, or even before the results have survived peer review. Sometimes, the "story" is merely a thinly-disguised press release. Even high-quality popular press may lack the institutional knowledge to evaluate scientific claims critically, and they may choose not to devote their limited resources to deeply reporting a story they see as having only niche interest. Considering all these factors, it is best not to use a news article as the sole source for any scientific claim. Instead, go the extra step and find the scholarly research behind the slick video. Having done this, you can point to the original for the details and the more accessible popularization for an overview, if the latter is not a travesty. In topics that are very "photogenic", like space exploration, it is common to find old content that was based on rather breathless pop-science press ("NASA finds life signs on Io!"); such content should be checked for consistency with follow-ups in the peer-reviewed literature.

Conversely, those outlets in the popular press that do put forth an effort can provide good sources for "penumbra" material, like biographical aspects and the social context of research. For example, pop-science publications such as Quanta Magazine and Scientific American are in the business of simplifying, and while this comes with its inevitable downsides, they have their uses as well. It can also be helpful to check whether the author of a popular-press item has physics or mathematics as their beat; a reporter with a track record of success may be a better source for a plain-English summary than one who does not.

Some physicists and mathematicians themselves write popularizations. These can generally be taken as acceptable simplifications which may be helpful in writing the less technical portions of Wikipedia articles (as noted above, it's usually best to put the least obscure parts of an article up front). The same cautions about transmitting oversimplifications described above regarding textbooks also apply here. Detailed studies by historians of physics are preferred over a "physicist's history" further stripped down for a general audience.

Websites, social media, and discussion groups
Physicists and mathematicians have been making websites for as long as there have been websites, and many are users of social media. Their websites and social-media posts constitute self-published sources. These may be considered reliable when the topic they address is one in which the author is an established subject-matter expert. This means, for a start, that the author must have a prior history of non-self-published work on the topic. Self-published writings by subject-matter experts can be used for commentary upon ideas, but not for biographical claims about other people.

Sooner or later, editing Wikipedia articles on physics or mathematics will bump into fringe physics or pseudomathematics. In these areas, self-published sources by subject-matter experts may be the best available option for giving the mainstream position. See the guideline for covering fringe theories and in particular the parity of sources section.

Discussion sites like MathOverflow, PhysicsOverflow, and the mathematics and physics sections of StackExchange and Reddit are user-generated content and thus for the most part unreliable. Commentary in these forums by recognized subject-matter experts can be reliable, per the provisos above, but that commentary is likely to include pointers to the more formal literature, which is the kind of reference we generally prefer. Before investing your time in reading a forum, check whether its moderators have gone on strike, or if there are other indications that management is burning the place down for the insurance money to satisfy investors.

The On-Line Encyclopedia of Integer Sequences is manually curated by experts and can be considered a reliable source. Whether an OEIS listing means that a Wikipedia article should discuss a sequence may depend on whether the OEIS designates the sequence as "nice", "core" (of central importance to some topic), or "hard" (often pertaining to an unsolved problem). The Stanford Encyclopedia of Philosophy contains articles written by subject-matter experts that may be useful for mathematical logic, the Interpretation of quantum mechanics, and other such topics on the more philosophical side. The nLab is mostly written by subject-matter experts, but because it is a wiki, figuring out who contributed what is time-consuming, and it is probably best to use it as a collection of pointers into the more formal literature. The fact that a topic has an article in MathWorld does not imply that it should have an article here; nor should MathWorld's choice of terminology be taken as definitive. For past discussions on this point, see the following:
 * Articles for deletion/Swirl function
 * Articles for deletion/Carol number (2nd nomination)
 * Minimal axioms for Boolean algebra and its Talk page
 * Articles for deletion/Rhonda number
 * Articles for deletion/Smarandache number
 * Articles for deletion/Florentin Smarandache (2nd nomination)
 * Articles for deletion/Alladi–Grinstead constant

Press releases
Press releases might not lie, exactly, but they do report the truth selectively. It is the job of a university's public relations department to present that university in the best light possible. Consequently, they will portray work from their university as "novel", "innovative", "unprecedented", or even "revolutionary". We are under no obligation to honor their enthusiasm.

Be wary of websites that churn press releases, presenting them in lightly-modified form without doing actual journalism. EurekAlert, Futurism.com, phys.org, and ScienceDaily are known for "reporting" of this kind. A useful warning sign for churnalism is the absence of a comment or quotation from a scientist not involved in the original study.

On occasion, press releases might contain material meant to "humanize" the research they present or give it a "hook" for a wider audience:"The collaboration between Smith and Jones began by accident, when they happened to meet while queuing for their COVID jabs."It may be tempting to incorporate this material into an article for the same reasons it was included in the press release. However, before trying to add "charming detail" to a page, consider whether sources that are actually independent and reliable have reported on that biographical or historical information. If no source of higher quality than a press release has cared, the presumption is that we shouldn't either.

Faculty directories and CVs
Writing biographical articles about physicists and mathematicians poses challenges. If the subject of the article is alive (or but recently deceased), the Biographies of living persons policy is of paramount importance.

Sources affiliated with an article's subject, like the university where they are employed, are generally acceptable for information that is not likely to be challenged, or for which a challenge would constitute a serious effort in investigative journalism. For example, it's fine to cite a department's own website for the year in which a faculty member was hired, and it's no problem to cite a person's own CV for the date they earned their PhD. Fraud on such documents is always possible, but we should assume them reliable unless substantial evidence exists to the contrary (e.g., if a CV lists membership in "honorary societies" that don't actually exist). Rooting out that kind of deception is (usually) not our job, and the encyclopedia as a whole benefits by our being able to write about people who don't have lengthy biographical profiles in secondary sources. That said, we're not a CV host. Lists of every grant won, every student mentored, every abstract for a conference talk — no, that's not what we do. A CV is typically list-based and all-inclusive, while we write prose and exercise a degree of editorial judgment.

Large language models
Large language models, known for marketing reasons as "AI", work by generating at great expense a worse version of their input data. They are not reliable sources of scientific or mathematical knowledge. Generating text that follows the statistical patterns of mathematical prose is blind to the actual logic.

The situation is rather like that of social media and press releases discussed above. Wikipedia must not rely upon the writing of people whose knowledge was itself cribbed from Wikipedia. Similarly, Wikipedia cannot rely upon text generated by a machine that potentially used Wikipedia for input. Moreover, trusting a text-generation machine to do your writing opens you to the risk of committing plagiarism by overly close paraphrasing, should the machine cough up a text string too close to one of the sources it drew upon.

Technical names and the "bag of words" problem
Ideas in physics and in mathematics might be named after the people who discovered them. (Sometimes, the conventional name is that of the second person to make the discovery, because otherwise, everything would be named for Leonhard Euler. ) But the connection is not always direct; see, for example, Newton fractal and Leibniz algebra. It is easy for a casual search to find false positives due to a "bag of words" effect. Suppose, for example, that an article on the "Leibniz–Einstein–Hamilton equations" were brought to Articles for deletion. The literature will be full of mentions of Leibniz's equations, Einstein's equations, and Hamilton's equations, but the article itself is actually about something distinct and much more specific and obscure. Evaluating the wiki-notability of the topic would require sifting out the true positives from the false ones.

Citogenesis
It is possible for a claim to be invented on Wikipedia, spread to the wider world, and then return to Wikipedia. Be careful not to use sites that copy Wikipedia content as sources. This goes for books, too! Take care to verify claims that may have originated from an enthusiast pushing their pet project, e.g., preferred choices of terminology or lengthy calculations on a recreational mathematics topic. Look for sources that predate the appearance of claims in the history of a Wikipedia article.

Dubious journals and websites
Lots of publications look like journals but aren't to be trusted. Sadly, expert judgment about such things doesn't always get written down: folklore about which journals are worthwhile gets passed from advisor to student, crank papers get chuckled over and their habitual homes accrue a reputation, but there is (understandably) a reluctance to spend time spelling out exactly how nonsensical the nonsense is. The following journals publish physics and/or mathematics content but have been called into question for having lapses in or apparently low standards of review. Results published in these journals are not necessarily incorrect, but it may be prudent to treat them on a level with preprint repositories.


 * Entropy
 * International Journal of Theoretical Physics (see discussion)
 * Scientific Reports
 * Physica Scripta — it may look respectable at first glance, but it's published plasma universe stuff, Myron Evans-related "free energy from the vacuum" oddities, etc.
 * Journal of Physics: Conference Series

Of lower rank still are the venues where meaningful review is so lacking that publication there is actively a bad sign. For example, Physics Essays was founded in 1988 and was described as a home for "unorthodox thought" in 1993; nowadays, it is a haven for relativity denial and the like, including the claim that biological beings consist of a physical body in the physical universe plus entangled bodies in the three nonphysical universes. Or the paper claiming that bodiless consciousness perceives the physical world as nonlocal 4D as revealed by a special kind of perception that takes place in near-death-experiences. Or the paper asserting that the conservation of energy and the hydrogen spectrum can be derived from an equation that says "The universe equals the sum of all things". If a news story comes your way that is based upon "research" published there, you can stop reading and move on with your life. This tier is where we find the following: The publication process for conference proceedings is also susceptible to abuse.
 * Apeiron (not to be confused with the philosophy journal of the same name)
 * Chaos, Solitons & Fractals
 * Journal of Cosmology
 * Journal of Scientific Exploration
 * NeuroQuantology
 * Physics Procedia (see discussion)
 * Progress in Physics
 * The viXra repository