Euclid

Record yearc. 300 BCE (late-antique attribution; the extant text passed through later copying and editing)

summarySelects, orders, and organizes earlier materials in geometry, proportion, number theory, incommensurable magnitudes, and solid geometry into a thirteen-book mathematical system that proceeds step by step from definitions, postulates, common notions, and prior proofs. It evaluates only the visible dependency-based deductive organization, tightening of proofs, and cross-book knowledge architecture; it does not attribute the discoveries embodied in hundreds of propositions wholly to Euclid.

M rationaleThis object organizes material across geometry, proportion, number theory, and solid geometry into a long-reusable chain of premises, constructions, and proofs, and continues to serve foundational functions in mathematical proof and teaching. It has broader coverage and longer cross-generational persistence than Church’s M6.0 system of lambda conversion and definability or Mill’s M6.1 system of inductive method. Like the M7 objects of Aristotle’s syllogistic deductive system and Shannon’s information-theory framework, it changes how a large domain organizes argument and verifies knowledge. The central estimate does not take the 7.2 of Newton’s Principia synthesis: most propositions came from predecessors, the extant text contains logical gaps and later layers, and the candidate excludes discoveries of particular theorems, modern axiomatization, and later mathematical increments. 6.8 and 7.2 are scope-sensitivity points, not historical confidence intervals, and M is not mechanically set by book or proposition count.

attribution rationaleThe central share is not calculated from later eponymy, book count, or proposition count. Fitzpatrick explicitly says that most theorems were not discovered by Euclid. The Proclus summary quoted by Heath supports, only at a layer roughly eight centuries later, that Euclid ‘put together’ the work, assembled Eudoxus’s results, completed Theaetetus’s work, and tightened predecessors’ proofs; Heath also lists pre-Euclidean traditions of elements compilation. Euclid therefore receives 0.34 as a conservative but substantive share for formation of organization and proof. Content prehistory at 0.46, compilation-and-organization prehistory at 0.10, and the unknown at 0.10 together prevent a single person from absorbing the entire book. 34% is a reasoned provisional estimate, not a proportion supplied directly by sources.

overlap boundaryThis candidate chooses the overall deductive organization as its sole outcome boundary. I.48 identifies only one increment of dependency-based proof: it reuses I.47, I.8, and construction prerequisites. I.1, I.7–8, and VII.1–2 likewise serve only as examples or sub-chains. If a proposition is later shown to contain an isolable new Euclidean proof, an independent persistent function, and sufficient comparison with prior work, the corresponding proof organization and value must first be removed from the overall object before a new item is created; the whole book and a local part cannot both receive full credit.

Evidence gapsThere is no evidence from authors contemporary with Euclid; the earlier source behind Proclus’s late summary is undetermined; the transmitted text passed through editors including Theon; and the thirteen books have not been collated proposition by proposition, while much content prehistory is known only at the level of tradition. This candidate does not require impossible exact personal percentages or an authorial manuscript. Instead, it carries uncertainty through a lower personal share, 0.56 for prehistory, and 0.10 for the unknown.