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In `F33f`_`[science`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Science]`_`f and `F33f`_`[mathematics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Mathematics]`_`f, an `!open problem`! or an `!open question`! is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known).

In the `F33f`_`[history of science`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=History_of_science]`_`f, some of these supposed open problems were "solved" by means of showing that they were not well-defined. In mathematics, many open problems are concerned with the question of whether a certain definition is or is not consistent.

Two notable examples in `F33f`_`[mathematics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Mathematics]`_`f that have been solved and `*closed`* by researchers in the late twentieth century are `F33f`_`[Fermat's Last Theorem`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Fermat's_Last_Theorem]`_`f`:cite-ref-1[`F5bf`_`[1`#cite-note-1]`_`f] and the `F33f`_`[four-color theorem`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Four-color_theorem]`_`f.`:cite-ref-appel1977a-2-0[`F5bf`_`[2`#cite-note-appel1977a-2]`_`f]`:cite-ref-appel1977b-3-0[`F5bf`_`[3`#cite-note-appel1977b-3]`_`f] An important open mathematics problem solved in the early 21st century is the `F33f`_`[Poincaré conjecture`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Poincaré_conjecture]`_`f.

Open problems exist in all scientific fields. For example, one of the most important open problems in biochemistry is the `F33f`_`[protein structure prediction`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Protein_structure_prediction]`_`f problem`:cite-ref-vendruscolo1999-4-0[`F5bf`_`[4`#cite-note-vendruscolo1999-4]`_`f]`:cite-ref-dill2007-5-0[`F5bf`_`[5`#cite-note-dill2007-5]`_`f] – how to predict a `F33f`_`[protein`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Protein]`_`f's structure from its sequence. In 2024, `F33f`_`[David Baker`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=David_Baker_(biochemist)]`_`f and `F33f`_`[Demis Hassabis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Demis_Hassabis]`_`f were awarded the `F33f`_`[Nobel Prize in Chemistry`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Nobel_Prize_in_Chemistry]`_`f`:cite-ref-6[`F5bf`_`[6`#cite-note-6]`_`f] for their contributions to protein structure prediction.

>>Contents

• `F0af`_`[See also`#see-also]`_`f

• `F0af`_`[References`#references]`_`f

• `F0af`_`[External links`#external-links]`_`f

-─

>>See also

• `F33f`_`[Lists of unsolved problems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Lists_of_unsolved_problems]`_`f (by major field)

• `F33f`_`[Hilbert's problems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hilbert's_problems]`_`f

• `F33f`_`[Millennium Prize Problems`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Millennium_Prize_Problems]`_`f

• `F33f`_`[Conjecture`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Conjecture]`_`f

• `F33f`_`[Wikenigma`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Wikenigma]`_`f, wiki for open problems

>>References

`:cite-note-1`!1.`! `F0af`_`[↑`#cite-ref-1]`_`f `:citereffaltings1995`aFaltings, Gerd (July 1995), "The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles" (PDF), `*Notices of the AMS`*, `!42`! (7): 743–746, `F33f`_`[ISSN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISSN_(identifier)]`_`f 0002-9920

`:cite-note-appel1977a-2`!2.`! `F0af`_`[↑`#cite-ref-appel1977a-2-0]`_`f K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", `*Illinois J. Math`* `!21`!: 429–490. `F33f`_`[MR`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=MR_(identifier)]`_`f 0543795

`:cite-note-appel1977b-3`!3.`! `F0af`_`[↑`#cite-ref-appel1977b-3-0]`_`f K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", `*Illinois J. Math`* `!21`!: 491–567. `F33f`_`[MR`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=MR_(identifier)]`_`f 0543795

`:cite-note-vendruscolo1999-4`!4.`! `F0af`_`[↑`#cite-ref-vendruscolo1999-4-0]`_`f `:citerefvendruscolonajmanovichdomany1999`aVendruscolo, M.; Najmanovich, R.; Domany, E. (1999), "Protein Folding in Contact Map Space", `*Physical Review Letters`*, `!82`! (3): 656–659, `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:cond-mat/9901215, `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:1999PhRvL..82..656V, `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1103/PhysRevLett.82.656, `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 6686420

`:cite-note-dill2007-5`!5.`! `F0af`_`[↑`#cite-ref-dill2007-5-0]`_`f `:citerefdillozkanweiklchodera2007`aDill, K.A.; Ozkan, S.B.; Weikl, T.R.; Chodera, J.D.; Voelz, V.A. (2007), "The protein folding problem: when will it be solved?" (PDF), `*Current Opinion in Structural Biology`*, `!17`! (3): 342–346, `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1016/j.sbi.2007.06.001, `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 17572080, archived from the original (PDF) on 2011-07-20

`:cite-note-6`!6.`! `F0af`_`[↑`#cite-ref-6]`_`f "Nobel Prize in Chemistry 2024". `*NobelPrize.org`*. Retrieved 2025-02-03.

>>External links

• `:citerefkennedynorman2005`aKennedy, Donald; Norman, Colin (2005), "What Don't We Know?", `*Science`*, `!309`! (5731): 75, `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1126/science.309.5731.75, `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 15994521

• "So much more to know", `*Science`*, `!309`! (5731): 78–102, July 2005, `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1126/science.309.5731.78b, `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 15994524

• Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ("wiki") site

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