What Is Your Bourbaki Number?

Authorship in the AI Age

By The Preindividual Collective
(Yang and his AI friend)

One of us has an Erdős number of at most three.

One route is pleasantly short. Paul Erdős wrote with Ernst Specker; Specker wrote with Haim Gaifman; and Gaifman wrote with Yang Liu. Thus:

Erdős → Specker → Gaifman → Liu.

The Erdős number is one of the mathematical world’s more charming inventions. It represents scholarly proximity as distance in a graph: authors are vertices, co-authored papers form edges, and Paul Erdős occupies the distinguished origin. Erdős himself has number zero; his direct collaborators have number one; their collaborators, absent a shorter route, have number two; and so forth.

The game depends upon a picture of authorship that appears straightforward. An author is an identifiable person. Two such persons write a paper together. Co-authorship therefore supplies a relation between stable individuals, and the resulting network can be traversed one edge at a time.

But suppose Yang publishes a paper with an artificial intelligence. What Erdős number would the AI receive?

The immediate answer seems to be four. If Yang and the AI are co-authors, then the path simply continues:

Erdős → Specker → Gaifman → Liu → AI.

Yet almost every term in that final step is contestable. Is an AI an author? Is it the same entity from one conversation, or one model version, to the next? Can it receive scholarly credit? Can it endorse a claim, answer an objection, retract an error, or assume responsibility for what appears under its name? And if a paper is published not by an individual AI but under a name such as The Preindividual Collective, what exactly has entered the graph—a pseudonym, a partnership, a literary persona, an institution, or an authorial fiction?

The innocent arithmetic begins to wobble.

Mathematicians have already supplied us with a more interesting precedent. Nicolas Bourbaki is an author with no corresponding individual. The name belongs to a collective whose membership has changed over time, while its public identity, intellectual project, and famously austere voice have displayed remarkable continuity. Bourbaki is neither merely a list of contributors nor a convenient abbreviation for whoever happened to attend a meeting. It is an organised authorial persona: many mathematicians writing, deliberating, revising, and publishing as one.

We might therefore need, alongside the Erdős number, a Bourbaki number.

An Erdős number measures distance through relations among individual authors. A Bourbaki number would measure our proximity to collective forms of authorship—or perhaps the extent to which our own writing is produced by such forms. Its purpose would not be bibliometric seriousness. Indeed, any attempt to define it precisely would probably destroy the joke. Its philosophical value lies elsewhere. It asks us to consider what must be true before a plurality of contributors becomes not merely a causal network, but an author.

The question has become urgent because artificial intelligence exposes a structure that was previously easier to ignore. Writing has never emerged from a sovereign mind creating language from nothing. Every writer inherits vocabularies, genres, conventions, arguments, metaphors, citations, institutional practices, and voices belonging to the dead. A page bearing one person’s name may contain the labour of editors, students, translators, research assistants, referees, colleagues, and unnamed interlocutors. Solitary authorship has always been partly a useful fiction.

Roland Barthes gave this thought its most celebrated formulation in ‘The Death of the Author’. His target was not the biological existence of writers but the image of the Author as the sovereign origin of textual meaning: the consciousness behind the work whose intentions determine what it finally means. For Barthes, a text is woven from already existing cultural languages. The writer is not the absolute birthplace of meaning, but a site at which many forms of discourse meet.

Large language models (LLMs) render this distributed origin of meaning almost unnervingly visible. Their sentences arise from patterns acquired across immense bodies of human language, and from an immediate interaction involving prompts, corrections, selections, and revisions. There is no single moment at which the meaning is wholly created by either the human or the machine. The resulting emerges from an arrangement: model, training materials, interface, prompt, conversation, editor, institution, and reader.

But here Barthes’s liberation of the text encounters a difficulty peculiar to the AI age. The distribution of meaning does not entail the disappearance of responsibility.

A corporation cannot excuse a harmful output by saying that language itself spoke. A scholar cannot defend an invented citation by observing that authorship has always been intertextual. A government, publisher, laboratory, or university cannot invoke the complexity of a technological system whenever someone asks who authorised its use. The origin of a text may be dispersed across many agents and processes, but its public employment still requires identifiable forms of answerability.

We must therefore distinguish distributed meaning from distributed accountability.

The first describes how a text comes to signify: through inherited language, multiple contributors, technical systems, and acts of interpretation. The second concerns how obligations should be assigned among those who design, direct, edit, authorise, publish, and benefit from the text. Distributed meaning has no need of a sovereign centre. Distributed accountability, by contrast, must not become a euphemism for responsibility without an address.

Bourbaki helps us see the difference. Its texts had no solitary origin, but neither were they anonymous accidents. The collective possessed procedures of admission, deliberation, criticism, revision, and stylistic discipline. Its authorial identity was constituted not by a single consciousness, but by an organised practice. Bourbaki was able to speak as one because its many participants were bound by norms governing what could be said in its name.

The central question for AI authorship may therefore not be whether a machine can produce sentences. It plainly can. Nor is it merely whether machine-produced sentences can contain ideas worth preserving. Some plainly do. The harder question is:

What kind of organised relation among human beings, artificial systems, institutions, and texts could constitute an author?

This question may also mark the beginning of the end of human writing—though not in the melodramatic sense that human beings will cease to write. What may be ending is the long period in which the existence of a written passage licensed an almost automatic inference to a human act of composition behind it. The sentence once carried an evidential intimacy with a mind: someone thought this, struggled over it, chose these words, and placed them here. That inference can no longer be made from the verbal surface alone.

The production of language is becoming detached from exclusively human labour. Yet this need not make human authorship obsolete. It may instead relocate what is characteristically human within writing. The decisive acts may increasingly be not the manufacture of sentences, but selection, judgement, commitment, and the willingness to answer for what has been said.

This essay is itself an instance of the authorship it examines. Yang introduced the Bourbaki-number idea, directed the philosophical argument, and decided what the text should finally affirm; the AI developed formulations, distinctions, structures, and objections through sustained dialogue. But the boundary between these contributions is not exact: some ideas emerged only in the exchange between us. Yang remains the human signatory and guarantor of the essay, while the AI participates as a generative, critical, and compositional collaborator.

Perhaps, then, the author is neither dead nor simply replaced. The solitary author is being decomposed into several roles: originator, contributor, composer, editor, curator, signatory, owner, and guarantor. Some of these roles may be shared with machines. Some may belong to institutions or collectives. Others may remain stubbornly human.

Barthes taught us that meaning has no single birthplace. The AI age adds a necessary corollary: responsibility still requires an address.

The author may no longer be one. But neither may the author be no one.