From Authorial Mathematics to Studio Mathematics:Ecobiontic Forms of Proof after Large Language Models

Abstract

Mathematics has often been organized around an authorial subject: one person, or a small group, composing proofs through language, notation, and judgment. Large language models, proof assistants, formal libraries, and repositories now make another production unit technically credible: a human-machine assemblage. This article calls that unit a studio ecobiont and asks when it is epistemically legitimate. Its governance thesis is that human participation is substantive only when the system preserves traceable provenance, reconstructible human competence, capacity to challenge the result, effective authority to stop or withdraw it, and public responsibility. These conditions distinguish a governed studio from a degenerate studio whose human oversight is ceremonial. A comparison of Polymath, the Liquid Tensor Experiment, Danus, and the Jacobian counterexample episode shows that collaboration, formalization, technical orchestration, and epistemic governance are independent dimensions. The proposed understanding audit and contribution-authority trace are governance designs, not validated measures. No causal superiority over authorial practice is claimed.