AI as Tool, Epistemic Agent,
and Quasi-Author

An Unresolved Tension in the Leiden Declaration

Krzysztof Burdzy

September 2026

The Leiden Declaration on Artificial Intelligence and Mathematics combines two positions that are individually understandable but difficult to reconcile. It asks mathematicians to disclose their use of artificial intelligence, including substantive uses in research. At the same time, under the heading “Affirm the humanity of authorship,” it declares that credit and responsibility belong to humans and “should not be given to automated systems.”[1]

This is not a formal logical contradiction. It is, however, a serious conceptual tension. The Declaration treats AI as sufficiently important to the intellectual history of a paper that its involvement must be reported, while denying that AI can receive intellectual credit. AI is treated as a tool when authorship is discussed, as an agent when disclosure is demanded, and as something between the two when it makes an original contribution.

1. From tool use to epistemic agency

If AI is merely a tool, the demand for universal disclosure is difficult to justify. Mathematicians use search engines, symbolic-algebra programs, databases, spellcheckers, electronic libraries, videoconferencing systems, and many other services without providing a history of every interaction with them. When software performs a computation essential to a result, identifying the software may be necessary for verification or reproducibility. But when a tool merely helps an author think, locate a reference, improve exposition, or check a routine step, its use is normally regarded as part of the research process rather than as a contribution requiring attribution.

The situation changes when AI proposes a decisive lemma, discovers the central construction, identifies an unexpected connection, or generates the first proof of a principal theorem. In such a case, the AI is not functioning like a spellchecker. It is performing an activity that, when performed by a human being, would ordinarily be regarded as an intellectual contribution.

This amounts to assigning AI a form of epistemic agency. Epistemic agency is the capacity—or at least the functional role—of producing, selecting, organizing, or justifying claims that contribute to knowledge. It does not necessarily imply consciousness, moral worth, legal personality, or human rights. A system may be treated as an epistemic agent in a limited sense because its output plays the role that a human idea or argument would otherwise have played.

Once AI is treated as possessing epistemic agency, it begins to occupy the position of a quasi-author. It may not qualify as an author under existing legal or professional rules. It cannot sign a copyright agreement, accept a university appointment, answer an allegation of misconduct, or defend a proof at a seminar. Nevertheless, it may perform some of the intellectual functions traditionally associated with authorship. It is therefore neither an ordinary tool nor a recognized author. It is a quasi-author: an entity that performs author-like intellectual work without receiving authorial status.

The Declaration seems to recognize the causal importance of this quasi-author while categorically denying it intellectual credit. An author must disclose that AI supplied an important idea, but the AI must not be credited for supplying it. The system is treated as sufficiently agent-like for its participation to require disclosure, but insufficiently agent-like for attribution.

2. The unusual culture of mathematical authorship

The traditional culture of mathematical authorship makes this intermediate category especially problematic.

In most areas of pure mathematics, coauthors are listed alphabetically rather than ranked according to the importance of their contributions. Papers generally do not say that one author supplied 70 percent of the ideas, another supplied 20 percent, and a third contributed 10 percent. The author list does not distinguish the person who discovered the main theorem from the person who supplied a technical lemma or wrote most of the exposition.

The American Mathematical Society has defended this convention on the ground that mathematical collaboration usually involves an intermingling of ideas that cannot meaningfully be separated. An idea proposed by one participant may be corrected by another, reformulated by a third, and recognized as important only after a collective discussion. Asking who “owns” the resulting idea may misrepresent how the mathematics actually developed.[2]

Consequently, mathematical authorship is ordinarily indivisible. Each coauthor receives the status of an author of the whole paper. When publications are considered in hiring, promotion, tenure, salary, or prize decisions, the paper appears as a publication of every author rather than as a fraction of a publication assigned according to a published contribution percentage. Committees may informally try to determine who did what, especially when evaluating junior mathematicians or unusually large collaborations, but the publication itself normally provides no official division of credit. In this important sense, each coauthor receives 100 percent authorship credit.

This does not mean that every mathematician believes that every coauthor contributed equally, or that evaluators are forbidden to seek additional information. It means that the byline does not encode a hierarchy. Once a person qualifies as an author, the paper itself grants that person undivided authorship status.

3. Two revealing extremes within mathematics

The boundaries of this convention can be understood by considering two rather different practices.

At one extreme, mathematical authorship can be interpreted expansively. Workshops at the American Institute of Mathematics are commonly organized around small research groups. When such a group produces a paper, all active participants in the group may become coauthors, even though their individual contributions were undoubtedly different.

One of my own papers provides an example:

T. Beck, B. Brandolini, K. Burdzy, A. Henrot, J. J. Langford, S. Larson, R. G. Smits, and S. Steinerberger, “Improved Bounds for Hermite–Hadamard Inequalities in Higher Dimensions,” Journal of Geometric Analysis 31 (2021), 801–816.[3]

The research began at the 2019 AIM workshop “Shape Optimization with Surface Interactions,” and the paper has eight alphabetically listed authors.[4] It does not assign percentages or rank the authors by contribution. Each participant appears simply as an author of the paper.

One may regard this practice as stretching the ordinary convention of authorship. But it also expresses an attractive feature of mathematical culture: collaborative work is treated as the achievement of the group rather than converted into a bureaucratic accounting of individual intellectual property. The convention deliberately declines to distinguish the person who first stated an idea from those who helped turn it into a correct and publishable argument.

At the opposite extreme stands the Polish habilitacja system. The habilitacja is a postdoctoral academic degree awarded on the basis of a substantial body of independent research. It certifies scholarly independence beyond the doctorate and has traditionally been important for advancement to senior academic status and for eligibility to supervise doctoral research.[5]

In habilitation proceedings, candidates have been required or expected to describe their personal contributions to jointly authored publications. Publicly available mathematics dossiers sometimes assign numerical percentages to the contributions of the applicant and the coauthors. A dataset extracted from Polish habilitation records contains precisely such percentage declarations.[6]

This practice tries to replace the indivisible mathematical convention with explicit fractional accounting. It assumes that the contribution to a joint mathematical paper can be decomposed—for example, 40 percent to one author, 35 percent to another, and 25 percent to a third. Whether these numbers describe anything objective is doubtful. They may reflect negotiation, memory, institutional expectations, or strategic presentation as much as measurable intellectual contribution.

The AIM-style paper and the Polish habilitation dossier represent opposite responses to the same problem. The first treats a collaborative achievement as essentially indivisible and extends full authorship to everyone in the research group. The second demands that the collaboration be decomposed into individual percentages. Mainstream mathematical practice lies between these extremes: authorship is restricted to those regarded as genuine contributors, but once a person becomes an author, the paper normally does not quantify that person’s share.

4. The contrast with biology and physics

This convention is not universal across science.

In much of biology and biomedicine, the position of a name in the author list conveys information. The first author is ordinarily understood to have made the principal hands-on contribution. The last author is often the laboratory director or senior investigator. The corresponding author has a separate organizational role. Nature describes the first author as “typically the primary contributor,” and many journals require an author-contribution statement specifying what each person did.[7]

The CRediT taxonomy formalizes such information through categories including conceptualization, methodology, software, data curation, supervision, funding acquisition, and writing.[8] The same person may be credited in several categories, and several people may share a category. The biological model is therefore substantially different from the mathematical one. A biologist can be a coauthor without receiving the same professional credit as the first or last author. Position in the author list, corresponding-author status, equal-contribution notices, and detailed contribution statements all help evaluators reconstruct a hierarchy of contributions.

Physics contains several different cultures. In small and medium-sized collaborations, author order may be negotiated or based on contribution. The American Physical Society recommends limiting authorship to people who made significant contributions and advises research teams to decide who will be an author and in what order.[9] APS journals also permit explicit author-contribution statements.

High-energy experimental physics lies at the opposite extreme. Collaborations such as ATLAS and CMS may have hundreds or thousands of authors. Their papers commonly use alphabetical, collaboration-wide author lists determined by membership and service rules rather than by attempting to measure each person’s contribution to each individual paper. An international physics report describes alphabetical author lists as the usual practice in large high-energy-physics collaborations.[10]

This resembles mathematical alphabetical authorship only superficially. A high-energy-physics paper is the product of a vast experimental organization involving detectors, engineering, software, data collection, calibration, and analysis. Membership-based collective authorship reflects the impossibility of publishing the result without that infrastructure. Traditional mathematical collaboration, by contrast, usually involves a small group whose ideas develop through direct intellectual interaction. Mathematics combines alphabetical order, small groups, and the absence of formal contribution statements. That combination makes its authorship culture distinctive.

5. Credit and responsibility are different

The Declaration appears to justify its position partly by joining credit to responsibility. Human authors can take responsibility for correctness, citations, and exposition; an AI system cannot. Human authors should indeed remain responsible for everything they publish. But responsibility and credit are not identical.

A mathematician may deserve credit for suggesting the central idea without assuming responsibility for the final paper. A deceased mathematician can be credited for an unpublished insight although that person can no longer verify the authors’ use of it. A colleague thanked in the acknowledgments may deserve intellectual credit without accepting responsibility for the theorem. Conversely, an author can assume responsibility for checking and publishing a proof without having originated every important idea in it.

The inability of AI to bear professional or legal responsibility therefore does not show that its causal intellectual contribution is nonexistent. It shows only that AI cannot satisfy every condition traditionally associated with authorship. That is precisely why the notion of quasi-authorship arises.

The Declaration recognizes AI’s causal importance while categorically denying it intellectual credit. It grants epistemic agency when disclosure is demanded and denies epistemic agency when credit is allocated. Mathematical authorship makes the asymmetry especially conspicuous: human collaborators are protected by a convention under which their contributions need not be measured, ranked, or assigned percentages, while the AI contribution must be isolated and described even though AI is prohibited from receiving authorship credit.

6. Disclosure is not necessarily attribution

A defender of the Declaration might respond that disclosure is not credit. It is merely information about the research process. This answer is plausible when disclosure is necessary for verification—for example, when a result depends on an extensive computer calculation. It is less persuasive when AI use consists of an unrecorded conversation that leads to a new idea.

If AI cannot be credited and its output does not need to be reproduced, why must its role be reported when analogous intellectual influences from books, seminars, private conversations, search engines, and unsuccessful calculations are not reported systematically?

Nor is it enough to say that AI disclosure protects the credit owed to the human works on which the model was trained. If the relevant human sources can be identified, they should be cited whether or not AI was used. If they cannot be identified, merely stating that an AI system was consulted does not restore credit to the unknown human sources. It only identifies the intermediary.

The comparison with other disciplines suggests that the Leiden Declaration is importing a contributorship model into mathematics. It asks authors to identify whether AI corrected prose, suggested a lemma, developed a proof, or supplied a central idea. Yet it simultaneously denies AI the status that contribution statements ordinarily help to allocate.

7. The unresolved trilemma

The Declaration therefore faces a trilemma.

First, AI might possess authorship-grade epistemic agency. If so, it is performing the kind of intellectual work that qualifies a human being for authorship. Under the traditional mathematical convention, it should be listed as a contributor and receive the same undivided authorship status as every other coauthor. If AI is to be regarded as possessing personhood for purposes of intellectual attribution, it cannot consistently be denied the credit ordinarily attached to that status.

Second, AI might be only a nonperson tool or service. If so, its mere use should no more require disclosure than the use of other machines or services. Authors may still need to report a computational dependency essential for verification, just as they may need to identify specialized software, hardware, or numerical data. But what should be disclosed is the mathematically relevant dependency, not every tool that influenced the private process of discovery.

Third, AI might be placed in the special category of quasi-author: capable of intellectual contributions important enough to require disclosure, but categorically ineligible for authorship or credit. This is effectively the position adopted by the Leiden Declaration, but it is the position most in need of justification.

The two extremes within mathematics show why percentage accounting does not solve the problem. An AIM-style conception of collaboration treats the product as a collective whole. A Polish-habilitation-style conception asks for numerical shares that may have no objective meaning. Trying to assign a percentage to AI would add an almost impossible counterfactual question: what portion of the final theorem belongs to the system, and what portion belongs to the human who chose the problem, designed the prompts, rejected false suggestions, recognized the valuable idea, repaired the proof, and placed it in mathematical context?

The traditional mathematical convention avoids this pseudo-precision. It recognizes authorship as a status rather than a measured quantity. That convention may be worthy of analysis, preservation, and perhaps extension in the age of AI.

The mathematical community may eventually decide that AI requires a genuinely new category. But such a category cannot simply be assumed. Its principles must be stated and defended. Until then, the Declaration’s position remains unstable: if AI is an intellectual participant, credit it; if it is a machine, treat it like a machine. Requiring authors to disclose AI’s intellectual participation while forbidding them to recognize AI as an intellectual participant combines the obligations associated with authorship with a categorical denial of authorship itself.

References