List of incomplete proofs

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A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail.

Contents

Vladimir Voevodsky, [1]

This page lists notable examples of incomplete or incorrect published mathematical proofs. Most of these were accepted as complete or correct for several years but later discovered to contain gaps or errors. There are both examples where a complete proof was later found, or where the alleged result turned out to be false.

Results later proved rigorously

Incorrect results

Theories proven inconsistent

Status unclear

See also

Notes

  1. 1 2 Voevodsky, Vladimir (March 26, 2014). "Univalent Foundations" (PDF). Institute for Advanced Study .
  2. Saaty, Thomas L.; Kainen, Paul C. (1986). The four-color problem: assaults and conquest. New York: Dover Publications. ISBN   978-0-486-65092-0.
  3. Schröder, Ernst (1898). Kaiserliche Leopoldino-Carolinische Deutsche Akademie der Naturforscher (ed.). Ueber zwei Definitionen der Endlichkeit und G. Cantor'sche Sätze. Vol. 71. Johann Ambrosius Barth Verlag. pp. 303–376 (proof: p.336–344).
  4. Korselt, A. (June 1911). Klein, Felix; Walther von Dyck; David Hilbert; Otto Blumenthal (eds.). "Über einen Beweis des Äquivalenzsatzes". Mathematische Annalen (in German). 70 (2). Leipzig: B. G. Teubner: 294–296. doi:10.1007/BF01461161. ISSN   0025-5831. S2CID   119757900.
  5. Hausdorff, Felix; Brieskorn, Egbert (2001). Gesammelte Werke: einschliesslich der under dem Pseudonym Paul Mongré erschienenen philosophischen und literarischen Schriften und ausgewählter Texte aus dem Nachlass (1. ed.). Berlin ; New York: Springer. p. 587. ISBN   978-3-642-25598-4. OCLC   57368353.Original edition (1914)
  6. Korselt 1911 , p. 295
  7. Kolata, Gina (24 June 1993). "At Last, Shout of 'Eureka!' In Age-Old Math Mystery". The New York Times. Archived from the original on 26 July 2023. Retrieved 21 January 2013.
  8. "The Abel Prize 2016". Norwegian Academy of Science and Letters. 2016. Archived from the original on 20 May 2020. Retrieved 29 June 2017.
  9. 1 2 Yulij Ilyashenko (2002). "Centennial History of Hilbert's 16th problem" (PDF). Bulletin of the AMS. 39 (3): 301–354. doi: 10.1090/s0273-0979-02-00946-1 .
  10. Zubkov, A. M. (2011). "Euler and combinatorial calculus". Proceedings of the Steklov Institute of Mathematics. 274: 162–168. doi:10.1134/s0081543811070030. S2CID   121881906.
  11. Legendre, Adrien-Marie (1798). Essai sur la théorie des nombres. Paris: Duprat.
  12. Grünbaum, Branko (2010), "The Bilinski dodecahedron and assorted parallelohedra, zonohedra, monohedra, isozonohedra, and otherhedra" (PDF), The Mathematical Intelligencer , 32 (4): 5–15, doi:10.1007/s00283-010-9138-7, hdl: 1773/15593 , MR   2747698, S2CID   120403108, archived from the original (PDF) on 2015-04-02.
  13. "Ho.history overview - Widely accepted mathematical results that were later shown to be wrong?".
  14. Boerger, Egon; Grädel, Erich; Gurevich, Yuri (1997). The Classical Decision Problem. Springer. p. 188. ISBN   3-540-42324-9.
  15. Goldfarb, Warren (1986). Feferman, Solomon (ed.). Kurt Gödel: Collected Works. Vol. 1. Oxford University Press. pp. 229–231. ISBN   0-19-503964-5.
  16. Roos, Jan-Erik (1961). "Sur les foncteurs dérivés de lim. Applications". C. R. Acad. Sci. Paris. 252: 3702–3704. MR   0132091.
  17. Neeman, Amnon (2002). "A counterexample to a 1961 "theorem" in homological algebra". Inventiones Mathematicae. 148 (2): 397–420. Bibcode:2002InMat.148..397N. doi:10.1007/s002220100197. MR   1906154. S2CID   121186299.
  18. Roos, Jan-Erik (2006), "Derived functors of inverse limits revisited", J. London Math. Soc. , Series 2, 73 (1): 65–83, doi:10.1112/S0024610705022416, MR   2197371, S2CID   122666355
  19. Porter, Roy (2003). The Cambridge History of Science . Cambridge University Press. p.  476. ISBN   0-521-57199-5.
  20. G. D. Birkhoff and W. J. Trjitzinsky (1933). "Analytic theory of singular difference equations". Acta Math. 60 (1): 1–89. doi: 10.1007/BF02398269 . S2CID   121809579.
  21. J. Wimp and D. Zeilberger (1985). "Resurrecting the asymptotics of linear recurrences". J. Math. Anal. Appl. 111 (1): 162–176. doi: 10.1016/0022-247X(85)90209-4 .
  22. P. Flajolet and R. Sedgewick (2009). Analytic Combinatorics. Cambridge University Press. pp. 582/683. ISBN   9780521898065.
  23. "Geometry - Has anyone ever actually seen this Daniel Biss paper?".
  24. Mnev, N. (2007). "On D.K. Biss' papers 'The homotopy type of the matroid Grassmannian' and 'Oriented matroids, complex manifolds, and a combinatorial model for BU'". arXiv: 0709.1291 [math.CO].
  25. Bordg, Anthony (December 2021). "A Replication Crisis in Mathematics?". The Mathematical Intelligencer. 43 (4): 48–52. doi:10.1007/s00283-020-10037-7. ISSN   0343-6993. PMC   8700325 . PMID   34966193.

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