Banach–Tarski paradox

theorem that there exists a decomposition of a unit solid ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the unit sphere
Intangible theorem Q737851
Banach–Tarski paradox
Benjamin D. Esham (bdesham) · Public Domain · Wikimedia
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Banach–Tarski paradox

Summary

Banach–Tarski paradox is a theorem[1]. It ranks in the top 0.38% of theorem entities by monthly Wikipedia readership (4,789 views/month, #5 of 1,306).[2]

Key Facts

  • Banach–Tarski paradox's instance of is recorded as theorem[3].
  • Stefan Banach is named after Banach–Tarski paradox[4].
  • Alfred Tarski is named after Banach–Tarski paradox[5].
  • Banach–Tarski paradox is part of list of theorems[6].
  • Banach–Tarski paradox's Commons category is recorded as Banach-Tarski paradox[7].
  • Banach–Tarski paradox's time of discovery or invention is recorded as 1924[8].
  • Banach–Tarski paradox was released on 1924[9].
  • Banach–Tarski paradox's proved by is recorded as Stefan Banach[10].
  • Banach–Tarski paradox's proved by is recorded as Alfred Tarski[11].
  • Banach–Tarski paradox's Stack Exchange tag is recorded as https://mathoverflow.net/tags/banach-tarski[12].
  • Banach–Tarski paradox's maintained by WikiProject is recorded as WikiProject Mathematics[13].

Body

Definition and Type

Banach–Tarski paradox's instance of is recorded as theorem[3].

Origins

Things named after include Stefan Banach[4], a mathematician[14], 1892–1945[15], of Cisleithania[16], awarded the Order of the White Eagle[17], specialised in mathematics[18] and Alfred Tarski[5], a mathematician[19], 1901–1983[20], of Russian Empire[21], awarded the Guggenheim Fellowship[22], specialised in logic[23].

Use and Application

Banach–Tarski paradox is part of list of theorems[6].

Why It Matters

Banach–Tarski paradox ranks in the top 0.38% of theorem entities by monthly Wikipedia readership (4,789 views/month, #5 of 1,306).[2] It has Wikipedia articles in 22 language editions, a strong signal of global cultural recognition.[24] It is known by 41 alternative names across languages and contexts.[25]

References

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

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.

Inline context (facts about related entities)

  1. [14] . Wikidata. wikidata.org. → on this site
  2. [15] . Wikidata. wikidata.org. → on this site
  3. [16] . Wikidata. wikidata.org. → on this site
  4. [17] . Wikidata. wikidata.org. → on this site
  5. [18] . Wikidata. wikidata.org. → on this site
  6. [19] . Wikidata. wikidata.org. → on this site
  7. [20] . Wikidata. wikidata.org. → on this site
  8. [21] . Wikidata. wikidata.org. → on this site
  9. [22] . Wikidata. wikidata.org. → on this site
  10. [23] . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [24] . Wikidata sitelinks. wikidata.org.
  3. [25] . Wikidata aliases. 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). Banach–Tarski paradox. Retrieved May 3, 2026, from https://4ort.xyz/entity/banach-tarski-paradox
MLA “Banach–Tarski paradox.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/banach-tarski-paradox.
BibTeX @misc{4ortxyz_banach-tarski-paradox_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Banach–Tarski paradox}}, year = {2026}, url = {https://4ort.xyz/entity/banach-tarski-paradox}, note = {Accessed: 2026-05-03}}
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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. 17d ago · Twofivesixbot bot · 2026-05-26 view diff on Wikidata ↗
    Publication date +1924-00-00T00:00:00Z
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    Part of
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    + 8 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|2 */ [[Property:P8189]]: 987007282589105171, mv to monolingual text names on J9U statements"
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