When Abhyankar and Moh introduced the term 'Jacobian conjecture' in the 1970s-80s, they referred only to the two-dimensional case.
Assessment
Evidence favors the claim, but the chain is incomplete or the sources are secondary.
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.
Full reasoning: the evidence and decisions behind this verdict
The claim originates in a comment thread on Terence Tao's July 2026 post digesting the Jacobian conjecture counterexample (terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/), where a commenter asserts it and elaborates that Abhyankar and Moh adopted the name privately, for the two-dimensional conjecture, after Zariski remarked in the 1960s that the conjecture was unnamed. Tao's reply in the same thread disputes the surrounding framing (that the planar case was consensually the fundamental one) but does not directly deny what Abhyankar and Moh themselves meant by the term.
Independent evidence supports the components. Borisov, "Frameworks for two-dimensional Keller maps" (arxiv.org/pdf/1901.04073), states the term was coined by Abhyankar, citing his 1977 Tata lectures; popular exposition (Lipton's blog, 2010) agrees that Keller posed the problem in 1939 and Abhyankar later named it. That supports the coinage subclaim. The bibliographic record supports the two-variable focus of Abhyankar's and Moh's own publications: Abhyankar's Tata lectures (1977), Abhyankar's "Some remarks on the Jacobian question" (1972 lectures), and Moh's 1983 paper on the conjecture for degree up to 100 are all planar.
Weighing against the strong reading, the term was in print for the general n-dimensional statement by the early 1980s: Bass, Connell and Wright's 1982 Bulletin of the AMS survey (projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-7/issue-2/The-Jacobian-conjecture--Reduction-of-degree-and-formal-expansion/bams/1183549636.pdf) states the conjecture for arbitrary n under that name and traces it to Keller 1939. This does not falsify the claim, which is about Abhyankar's and Moh's own usage, but it bounds what the claim can show in the wider naming dispute, and it leaves the "only" unverified: neither Abhyankar's 1970s texts nor a comprehensive usage survey was directly examined in this pass, and the Zariski anecdote is uncorroborated blog testimony.
Verdict: supported rather than verified, because the load-bearing exclusivity ("only") and the joint attribution to Moh rest on secondary testimony rather than examined primary sources. What would change the conclusion: a passage in Abhyankar's 1970s writings applying the name to the general statement (toward contradicted on the "only"), or a corroborated primary account of the coinage (toward verified). The recent historical paper "On the origin of the Jacobian conjecture" (Rodríguez Díaz, arxiv.org/pdf/2512.23614), which traces the problem to Kraus 1884, is a promising source for a future pass on the naming history.
Decomposition
The claims this one rests on directly. ↗︎ opens a subclaim; the map shows how they fit together.
The claims this one rests on directly, not gathered into a named line of reasoning.
- requiresa load-bearing premise: the parent is false without itsteward instructions →Shreeram Abhyankar coined the term "Jacobian conjecture." ↗︎
- supportsthis provides evidence for the parentsteward instructions →Abhyankar and Moh treated the two-variable case of the Jacobian problem in the 1970s and 1980s. ↗︎
- contradictsthis argues against the parentsteward instructions →By the early 1980s the term "Jacobian conjecture" was used in print for the n-dimensional statement. ↗︎
Provenance
Where this claim has been said, linked to its canonical form.
But the fact is, when Abhyankar and Moh named "Jacobian conjecture" in the 1970-80s, they only referred to the 2-dimensional version.
An extended comment thread debates whether the two-dimensional or the general n-dimensional statement is the true 'Jacobian conjecture'; Tao replies that prior to 2026 there was no consensus that the planar case was the more fundamental one, citing Smale, Keller, van den Essen, and Wikipedia.
Cite this claim: a formal citation with its evidence attached
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Created by extractor · Aug 11, 2026. Every judgment on this page is accompanied by a reasoning trace.