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Jacobian conjecture

conjecture asserting that, over a characteristic-zero field K, given a polynomial map f: Kⁿ → Kⁿ, if its Jacobian determinant J: Kⁿ → K is a nonzero constant map, then f admits a polynomial inverse g: Kⁿ → Kⁿ
Intangible conjecture Q2605695
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Summary

Jacobian conjecture is a conjecture[1]. It draws 10,081 Wikipedia views per month (conjecture category, ranking #14 of 128).[2]

Key Facts

  • Discoverer or inventor: Ott-Heinrich Keller[3]
  • Instance of: Smale's problems[4]
  • Named after: Carl Gustav Jacob Jacobi[5]
  • Maintained by WikiProject: WikiProject Mathematics[6]

Why It Matters

Jacobian conjecture has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[7] It is known by 17 alternative names across languages and contexts.[8]

Related Entities

Carl Gustav Jacob Jacobi

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [4] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [7] ↑ . Wikidata sitelinks. wikidata.org.
  3. [8] ↑ . Wikidata aliases. wikidata.org.

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APA 4ort.xyz Knowledge Graph. (2026). Jacobian conjecture. Retrieved October 28, 2026, from https://4ort.xyz/entity/jacobian-conjecture
MLA “Jacobian conjecture.” 4ort.xyz Knowledge Graph, 4ort.xyz, 28 Oct. 2026, https://4ort.xyz/entity/jacobian-conjecture.
BibTeX @misc{4ortxyz_jacobian-conjecture_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Jacobian conjecture}}, year = {2026}, url = {https://4ort.xyz/entity/jacobian-conjecture}, note = {Accessed: 2026-10-28}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 12w ago · MatSuBot bot · 2026-08-03 view diff on Wikidata ↗
    Instance of → conjecture, Smale's problems
    Discoverer or inventor → Ott-Heinrich Keller
    Aliases → —
    Maintained by wikiproject → WikiProject Mathematics
    + 3 other properties edited (see Wikidata diff for full list)
    "/* wbeditentity-update-languages-short:0||pt, vi, pl */ import labels from sitelinks"
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