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Cite the exact work or archival record that supports the mathematical claim, then explain the credit history separately in your prose. Identify who published, announced, communicated, or independently obtained the result; preserve the chronology; and support any disputed-priority statement with primary records and reliable historical scholarship. A bibliography entry alone cannot show why more than one mathematician deserves recognition.
Start with two separate jobs: source citation and historical credit
A citation answers, “Where can a reader verify this mathematical statement?” A credit explanation answers, “Who contributed what, and when?” Treating those as the same task is the most common reason a delayed or disputed contribution disappears from an otherwise correct bibliography.
For the mathematical claim, cite the item you actually consulted: an original article, proceedings paper, thesis, dated letter, lecture notes, announcement, manuscript, or archival record. Give a locator such as a page, theorem, section, box and folder, or repository identifier when one exists. In a separate sentence, describe the relevant history and name the mathematician whose contribution matters. Cite the evidence for that history as well.
The American Mathematical Society’s Ethical Guidelines of the American Mathematical Society, in Council-minutes material dated January 9, 2015, describes correct attribution as essential because it both encourages creators and informs the community “of when, where, and sometimes how original ideas entered into the chain of mathematical thought.” The same guidelines instruct mathematicians to give appropriate credit “even to unpublished materials and announced results.” These are ethical principles, not a statistic about how often disputes occur.
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Define the exact result before you investigate priority
“The theorem” or “the method” may cover several claims with different histories. Narrow the statement so a reader can tell exactly what is being credited.
Specify the mathematical content
- State the theorem, conjecture, construction, algorithm, counterexample, notation, or proof technique at issue.
- Say whether you are citing the original statement, a proof, a generalization, an application, or an expository formulation.
- Record the version of a result if later papers changed hypotheses, conclusions, or terminology.
Separate contribution types
One mathematician may formulate a conjecture, another may prove a special case, and a third may publish a broader theorem. A person who announced a result may not be the person who first wrote a complete proof. Use a separate attribution for each documented role rather than assigning a single “discovery” label to everyone.
Write a one-sentence scope statement
Before collecting sources, write a sentence such as: “This discussion concerns the first published proof of the stated theorem and an earlier communicated announcement of a restricted case.” That sentence prevents you from treating an announcement date, a private communication, and a publication date as interchangeable.
Build a chronology from records, not from an eponym
A conventional name in textbooks is a lead, not proof of priority. Create a timeline in which every date has an event and a source.
| Event | What it establishes | Evidence to seek |
|---|---|---|
| Private communication | Someone conveyed an idea or result to another person, possibly before any public record. | Dated letter, email, notes, diary, referee report, or testimony preserved in an archive. |
| Public announcement | The result was presented or announced to an audience, without necessarily supplying a complete proof. | Conference program, abstract, lecture notes, society notice, or contemporaneous report. |
| Submission | A manuscript was sent to a journal or publisher; it may not yet have been accepted or available to readers. | Submission receipt, editorial correspondence, dated preprint, or manuscript metadata. |
| Publication | The work appeared in a published venue under that author’s name. | Journal issue, proceedings volume, book, thesis record, or publisher archive. |
| Independent derivation | Another mathematician reached a result without relying on the earlier work, as documented by the record. | Separate dated manuscript, correspondence, announcement, or historical analysis. |
| Later acknowledgment | A subsequent author recognized an earlier contribution or clarified the relationship between results. | Correction, historical note, retrospective article, or correspondence. |
Do not collapse these events into one “discovery date.” A publication can be later than an announcement; an announcement can precede a written proof; and a private communication can be earlier than both while remaining difficult to verify. The wording of your article should match the strongest event the record actually proves.
Choose the source that supports the claim you make
Use primary material whenever it is accessible, and add reputable historical scholarship to interpret a contested record. A source can be authoritative yet still fail to establish the particular proposition you attach to it.
For the mathematical statement
- Cite the original article or proceedings paper when it contains the theorem or proof you describe.
- Use a thesis, lecture notes, or later exposition when that is the item you read, but make clear whether it is reproducing an earlier result.
- Give a page, theorem number, section, equation, or stable manuscript location so readers can check the statement.
For the credit history
- Use dated correspondence, announcements, manuscripts, or archival records for chronology.
- Use historical scholarship to explain context, competing interpretations, and gaps in the surviving record.
- Attribute an interpretation to its author: “Historian A argues …” is different from presenting that interpretation as an undisputed fact.
Match evidence to the strength of the claim
A published paper can establish who published a theorem. It may not establish who first conceived it. A letter can document a communication, but it may not prove that the recipient understood or used the result. State only what the item demonstrates, and identify uncertainty when the record is incomplete.
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How to cite unpublished work
Unpublished material can deserve credit even when it is not formally refereed or widely circulated. Identify it precisely enough that another reader can locate the item and understand its status.
- Identify the creator. Use the name as it appears on the manuscript or in the repository record.
- Describe the item. Give its title if it has one; otherwise provide a concise description such as “notes on [subject]” in your citation template.
- Give the date. Use the date written on the item or the repository’s documented date, and label an approximate date as approximate.
- Identify the collection and repository. For archival material, include collection name, box and folder when available, and the holding repository.
- Explain its role. Say whether it is a manuscript proof, an announced result, correspondence, or notes recording a communication. Do not imply publication or peer review when neither occurred.
- Obtain permission where needed. Copyright, privacy, donor restrictions, and repository rules may limit quotation or reproduction even when attribution is ethically appropriate.
The University of Chicago Libraries’ archival guidance recommends identifying the creator, title or description, date, publication information if applicable, collection, box and folder, and repository. Include the details that lead directly to the item consulted.
{Creator}, “{Title or description},” {date}, {collection}, box {number}, folder {number}, {repository}.In your prose, distinguish the material’s status: “A dated manuscript records an earlier proof” is narrower and safer than “The author published the proof.” If the item is inaccessible, say how you learned of it and rely on a source that reproduces or describes it, while avoiding a claim that you inspected the original.
How to give credit for an earlier result
When a later publication is the source readers will use, cite it for the claim it contains and mention the earlier contribution in the same historical passage. The two citations can be different.
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- Announced: use when a public presentation or notice documents an announcement.
- Communicated: use for a documented private transmission.
- Submitted: use when a dated submission record exists, without implying acceptance.
- Published: use for the appearance of a work in a publication.
- Proved: use when the cited work contains the proof you describe.
- Independently obtained: use only when evidence supports a separate derivation.
- Acknowledged or credited: use when a later source explicitly recognizes the contribution.
State both contributions without erasing either
A useful structure is: “The result was published by [the later author] in [the cited work and date], while [the primary record or historical study] documents an earlier [announcement, communication, or contribution] by [the earlier mathematician]. The record therefore supports crediting both contributions in their distinct roles.” Fill every element with documented facts; do not use this pattern to infer priority from a mere citation or textbook name.
The published proof appears in {later author, work, date, locator}. A {letter/announcement/manuscript} dated {date} documents {earlier mathematician’s specific contribution}; {historical source} describes how the two records relate.How to cite a disputed mathematical result
A priority dispute requires more than adding two names to a reference list. Explain what is agreed, what is contested, and which records support each proposition.
Map the competing accounts
| Question | Account A | Account B |
|---|---|---|
| Who made the relevant contribution? | Name the person and the specific result or role attributed. | Name the alternative attribution and its scope. |
| What date is asserted? | Identify whether it is communication, announcement, submission, or publication. | Identify the event and source claimed by the alternative account. |
| What record supports it? | Give the primary item or historical work and its locator. | Give the competing item and its locator. |
| What remains uncertain? | Note missing dates, incomplete manuscripts, or retrospective testimony. | Explain whether the uncertainty affects priority, influence, or only terminology. |
Attribute interpretations explicitly
Write “Historian A argues that the announcement establishes priority; surviving correspondence confirms that the idea was communicated earlier, but does not show a complete proof.” This tells readers which sentence is an interpretation and which is directly documented. If historians disagree, present the disagreement rather than selecting a winner without evidence.
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Avoid allegations that the record cannot support
The AMS guidelines describe knowingly presenting another person’s mathematical discovery as one’s own as plagiarism. A generic priority dispute, however, is not proof of plagiarism, suppression, or theft. Use those terms only when reliable evidence establishes the specific conduct. Otherwise describe the documented sequence: delayed acknowledgment, overlapping publication, disputed priority, or conflicting recollections.
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Historical fairness does not require inventing a new reference format. Follow the journal, publisher, or archive’s current instructions, and keep the credit explanation in prose.
AMS-style references
The USC Libraries’ AMS guide describes three in-text approaches: bracketed sequential numbers, author-and-year citations, and alphanumeric keys. Select one and use it consistently throughout the manuscript. Its examples show that a book reference can include the author’s name as it appears, title, publisher, publication city, year, and Mathematical Reviews number. An online journal reference can include article title, abbreviated journal title, volume, year, issue, pages, DOI, and MR number when those fields apply.
Do not add a field merely because it appears in an example. Check the destination journal’s current requirements for punctuation, abbreviations, DOI presentation, and required identifiers. A numbered reference such as “[7]” identifies the source; it does not explain why an earlier announcement deserves credit. Add that explanation in the surrounding sentence.
{Author}. “{Article title}.” {Abbreviated journal} {volume} ({year}), no. {issue}, {pages}. DOI: {doi}. MR {number}.Chicago notes and bibliography
For historical writing using Chicago notes and bibliography, the official sample guide demonstrates full notes, shortened notes, and bibliography entries, with fuller rules in the 18th edition (2024). Use a full note the first time you identify a source, then the required shortened form. Chicago’s official guidance says the primary purpose of a source citation is to identify, concisely and unambiguously, the source of a quotation or idea that is not your own.
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For a manuscript, adapt the archival details to Chicago’s model: creator, title or description, date, publication information if applicable, collection, box and folder, and repository. If the archive supplies a call number or digital identifier, include it when the repository or target publication expects one.
Do not mix styles to signal authority
AMS, Chicago, and other systems are navigational conventions. Switching from one to another because a format looks more prestigious can make a source harder to find. Use the required style for the venue and reserve historical explanation for clear narrative prose.
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Compare sources by provenance, chronology, and scope
When accounts conflict, evaluate them on the same axes rather than counting citations or choosing the newest retelling.
| Comparison axis | Questions to ask |
|---|---|
| Provenance | Is this a contemporaneous paper, dated letter, announcement, archive item, or retrospective account? Who created and preserved it? |
| Chronology | Does the source document communication, announcement, submission, publication, or later acknowledgment? |
| Content | Does it contain the theorem, a complete proof, a special case, a conjecture, or only a reference to an idea? |
| Independence | Does the record show a separate derivation, or only parallel publication with no evidence about influence? |
| Retrospection | Was the account written at the time, or many years later after reputations and terminology had formed? |
| Locator quality | Can readers find the exact page, theorem, folder, or repository item you rely on? |
A later historical article may reconcile records that are individually ambiguous, but it cannot turn an unsupported assertion into a primary fact. Describe the historian’s argument as an argument and retain the underlying record wherever possible.
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Common citation failures and their fixes
Failure: citing only the famous later paper
Why it fails: the paper may support the theorem but conceal an earlier announcement or communication.
Fix: retain the later paper for the proof and add the dated record that documents the earlier contribution.
Failure: treating an announcement as a publication
Why it fails: an announcement may not include a complete proof or a stable text.
Fix: call it an announcement, give its date and venue, and say what it actually disclosed.
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Why it fails: readers cannot infer why the source matters or which person contributed what.
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Fix: name the mathematician and role in the sentence where the history is relevant.
Failure: converting uncertainty into an accusation
Why it fails: missing records do not prove misconduct.
Fix: describe the gap, identify competing interpretations, and use neutral verbs until evidence supports a stronger claim.
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Why it fails: “private papers” or “unpublished notes” is not enough for verification.
Fix: add collection, repository, date, box, folder, call number, or digital identifier as available.
Failure: mixing citation systems
Why it fails: inconsistent formatting makes sources difficult to locate and may violate journal rules.
Fix: choose the destination’s required system before finalizing references and apply it uniformly.
A repeatable workflow for authors and editors
- Define the claim. Write the narrow theorem, method, or historical proposition you will make.
- List every relevant event. Create separate entries for communication, announcement, submission, publication, independent derivation, and acknowledgment.
- Collect primary records. Locate the original paper, dated correspondence, announcement, manuscript, or archive item for each event.
- Add historical interpretation. Consult reputable scholarship and record which conclusions are arguments rather than direct observations.
- Assign roles. For each mathematician, state whether the evidence supports formulation, communication, announcement, proof, publication, generalization, or another contribution.
- Draft the mathematical citation. Give the exact source and locator for the result itself.
- Draft the credit sentence. Explain the chronology and name the relevant mathematician in prose.
- Choose one style. Apply the target venue’s AMS, Chicago, or other required format consistently.
- Audit wording. Replace unsupported verbs such as “discovered” or “stole” with the precise documented verb.
- Check retrieval. Confirm that every reference, archive detail, page, theorem number, and identifier leads a reader to the material you used.
Model language you can adapt
These patterns are templates, not evidence. Replace every variable with a documented person, work, date, and locator before publication.
{Result} is proved in {published work}, {date}, {page/theorem}. A dated {letter/announcement/manuscript} records {earlier mathematician}’s {specific contribution} on {date}. {Historical source} interprets the relationship as {carefully attributed interpretation}; the surviving record does not establish {uncertain point}.{Author} announced {result or special case} at {venue} on {date}; {later author} published a proof in {work}, {publication date}. Because the records document different events, this account credits the announcement and the published proof separately.Do not retain the braces or any unverified wording in a finished article. The final text should state the actual evidence and its limits.
Final verification checklist
- Is the mathematical claim narrow enough to identify its credit history?
- Does the citation point to the work or record actually consulted?
- Is there a page, theorem, section, folder, or other useful locator?
- Are communication, announcement, submission, publication, and independent derivation kept distinct?
- Does the prose name each mathematician’s documented role?
- Are contested interpretations attributed to their sources?
- Does the wording avoid unsupported allegations of plagiarism, suppression, or theft?
- Are unpublished materials identified with creator, description, date, collection, repository, and archival location where available?
- Does the reference list follow the destination’s current style without mixing systems?
- Can a reader distinguish what is established from what remains uncertain?
What a responsible citation accomplishes
A well-documented citation lets readers verify the mathematics and understand how the idea entered the historical record. It preserves the difference between a private communication and a public announcement, between an announcement and a proof, and between publication and later acknowledgment. When evidence supports more than one contribution, crediting those roles in prose is not an optional embellishment: it is the clearest account of the mathematics and its history.
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