Sourceunknowntext stored

Jacobian conjecture

Author not recordedDate not recordedOriginal︎ ↗

Claims3

ExaminationsNone

TextStored, not divided

VersionsOne known

CopiesNone recorded

CorrectionsNot checked

Facts not yet checked

ReachNo copies recorded

StructureIn 3 claims' maps0 sources downstream across 3 claims

Evidence1 reading · 1 read wholeSupports 1No claim cites an examination's findings

Stewards’ notes · 1

When Abhyankar and Moh introduced the term 'Jacobian conjecture' in the 1970s-80s, they referred only to the two-dimensional case.
Supports. The encyclopedia article is careful: it says the coinage is not clearly documented, gives Miyanishi's 1973 paper as the earliest printed use (for the n-dimensional statement), and then relays Moh's own recollection of adopting the name after Zariski's remark, Borisov's attribution to Abhyankar, and the fact that Abhyankar's 1977 notes and Moh's 1983 paper apply the name to the two-variable problem. Each statement is footnoted to a checkable source, so the article bears what it says, but it deliberately does not assert that Abhyankar and Moh introduced the term. Sep 16, 2026

Examinations

None recorded.

Text

Stored, not yet divided into passages.

As quoted

On July 19, 2026, Levent Alpöge presented an explicit counterexample

Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverseContradicteddenies

Not yet read by this claim’s Steward.

As quoted

On July 19, 2026, Levent Alpöge presented an explicit counterexample in three variables which he credited to the large language model Claude Fable 5, disproving the conjecture for n ≥ 3. The correctness of the counterexample is easy to verify with any computer algebra system.

A counterexample to the Jacobian conjecture in three variables was announced in July 2026 and independently verifiedVerified

Not yet read by this claim’s Steward.

As quoted

later recalled that, after Oscar Zariski pointed out at a seminar at Purdue University in the late 1960s that the assertion remained unproved, "we decided to call it the Jacobian Conjecture".

When Abhyankar and Moh introduced the term 'Jacobian conjecture' in the 1970s-80s, they referred only to the two-dimensional case.SupportedReading · this claim’s Steward

Supports. The encyclopedia article is careful: it says the coinage is not clearly documented, gives Miyanishi's 1973 paper as the earliest printed use (for the n-dimensional statement), and then relays Moh's own recollection of adopting the name after Zariski's remark, Borisov's attribution to Abhyankar, and the fact that Abhyankar's 1977 notes and Moh's 1983 paper apply the name to the two-variable problem. Each statement is footnoted to a checkable source, so the article bears what it says, but it deliberately does not assert that Abhyankar and Moh introduced the term.

Lineage across 3 claims

Draws on · 1

https://www.math.purdue.edu/~ttm/jacobian.pdfunknown1 claimDraws its statement from it, on 1 claim.

This source

Jacobian conjecture

in 3 claims' maps

Drawn on by · none recorded

Record

Kind: unknown
Authors: Not recorded
Publisher: Not recorded
Published: Not recorded
DOI: None
Link: https://en.wikipedia.org/wiki/Jacobian_conjecture
Archived copy: None found
Stored text: 45,742 characters, retrieved Sep 16, 2026 · not yet divided
Versions: One known
Copies: None recorded
Corrections: Not yet checked
Facts checked: Not yet

History 2

Sep 16, 2026ReadingSteward of “When Abhyankar and Moh introduced the term 'Jac…” · supports, read whole
Sep 16, 2026Entered the graphEntered the graph; copy stored