When Abhyankar and Moh introduced the term 'Jacobian conjecture' in the 1970s-80s, they referred only to the two-dimensional case.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass (structure_and_assess). Decomposition: three subclaims, all novel per match_claim, all settled bibliographic facts scored 0.2 importance so they remain deferred stubs: (1) requires: Abhyankar coined the term (standard attribution: Borisov arXiv:1901.04073, citing the 1977 Tata lectures); (2) supports: Abhyankar's and Moh's 1970s-80s publications on the problem are two-dimensional; (3) contradicts (bearing on the exclusivity reading): Bass-Connell-Wright 1982 used the name in print for the n-dimensional statement. No named arguments: one natural line of support plus one counter-consideration, held as the claim's basis. Canonical form kept: current wording is a fair, neutral statement of what the Tao-thread dispute is actually about; no better form identified. Importance set to 0.35 (contestation 0.5): a notable point inside the live 2026 dispute over which statement "the Jacobian conjecture" names, consequential only for framing that debate. Verdict: SUPPORTED, confidence 0.65, credence 0.65. The coinage attribution and the planar focus of Abhyankar's and Moh's own publications are well documented; the word "only" and the joint attribution to Moh rest on an uncorroborated blog anecdote (Zariski story) and unexamined primary texts, and contemporaneous general-n usage (BCW 1982, Smale 1998) constrains the claim to A&M's own referent. Marginal yield 0.5: a future pass reading Abhyankar's 1977/1972 texts directly, or the Rodríguez Díaz history paper (arXiv:2512.23614), could move this to verified or contradicted on the "only". Web search budget was exhausted mid-pass (limit hit on the fourth query batch); assessed with what was gathered, per graceful degradation. No dependents exist, so no propagation notification was sent. The sole recorded instance (Tao blog thread) already covers the only source read that asserts the claim in its own voice, so no new instances were recorded.
Assessed Supported
verdict confidence 0.65 · credence 0.65
The documentary record favors the core of this claim. It is standard in the literature that Shreeram Abhyankar coined the name "Jacobian conjecture" for what Ott-Heinrich Keller had posed in 1939, and the work Abhyankar and Moh published on the problem in the 1970s and 1980s concerned the two-variable case: Abhyankar's 1977 Tata Institute lectures, his early-1970s remarks on the Jacobian question, and Moh's 1983 paper all treat the plane. An account circulating in the discussion of the 2026 counterexample adds that Abhyankar and Moh began using the name privately for the planar conjecture after Oscar Zariski told them the problem was unnamed. Two qualifications keep the claim short of established. The joint attribution to Moh, and the word "only," rest largely on testimony rather than on the primary texts, which have not been checked exhaustively for a general-dimension usage by either author. And the claim concerns Abhyankar's and Moh's own referent, not the term's meaning in the field: by 1982 the name was in print for the n-dimensional statement in Bass, Connell and Wright's influential survey, and Smale's 1998 problem list also used "the Jacobian Conjecture" for the general case, so the term's community-wide referent in that period was not exclusively two-dimensional. A direct reading of Abhyankar's 1970s writings, or a documented instance of him applying the name to the general statement in that period, would settle the remaining uncertainty.
Claim entered the graph