Home › Entities › conjecture › Jacobian conjecture

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
Place conjecture Q2605695
Press Enter · cited answer in seconds

Jacobian conjecture

Summary

Jacobian conjecture is a conjecture[1]. It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[2]

Key Facts

  • Jacobian conjecture is credited with the discovery of Ott-Heinrich Keller[3].
  • Jacobian conjecture's instance of is recorded as conjecture[4].
  • Jacobian conjecture's instance of is recorded as Smale's problems[5].
  • Carl Gustav Jacob Jacobi is named after Jacobian conjecture[6].
  • Jacobian conjecture's maintained by WikiProject is recorded as WikiProject Mathematics[7].

Body

Designation and Status

Recorded instance of include conjecture[4] and Smale's problems[5].

History and Context

Carl Gustav Jacob Jacobi is named after Jacobian conjecture[6].

Why It Matters

Jacobian conjecture has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[2]

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. [5] ↑ . wikidata.org.
  3. [3] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikidata sitelinks. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Jacobian conjecture. Retrieved May 3, 2026, from https://4ort.xyz/entity/jacobian-conjecture
MLA “Jacobian conjecture.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 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: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Jacobian conjecture — https://4ort.xyz/entity/jacobian-conjecture (retrieved 2026-05-03)

Canonical URL: https://4ort.xyz/entity/jacobian-conjecture · Last refreshed:

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. 4w 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"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.