Open problem

In science and mathematics, 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 history of science, 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 mathematics that have been solved and closed by researchers in the late twentieth century are Fermat's Last Theorem^[1] and the four-color theorem.^[2]^[3] An important open mathematics problem solved in the early 21st century is the Poincaré conjecture.

Open problems exist in all scientific fields. For example, one of the most important open problems in biochemistry is the protein structure prediction problem^[4]^[5] – how to predict a protein's structure from its sequence. In 2024, David Baker and Demis Hassabis were awarded the Nobel Prize in Chemistry^[6] for their contributions to protein structure prediction.

References

^ Faltings, 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, ISSN 0002-9920
^ K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", Illinois J. Math 21: 429–490. MR 0543795
^ K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", Illinois J. Math 21: 491–567. MR 0543795
^ Vendruscolo, M.; Najmanovich, R.; Domany, E. (1999), "Protein Folding in Contact Map Space", Physical Review Letters, 82 (3): 656–659, arXiv:cond-mat/9901215, Bibcode:1999PhRvL..82..656V, doi:10.1103/PhysRevLett.82.656, S2CID 6686420
^ Dill, 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, doi:10.1016/j.sbi.2007.06.001, PMID 17572080, archived from the original (PDF) on 2011-07-20
^ "Nobel Prize in Chemistry 2024". NobelPrize.org. Retrieved 2025-02-03.

External links

Kennedy, Donald; Norman, Colin (2005), "What Don't We Know?", Science, 309 (5731): 75, doi:10.1126/science.309.5731.75, PMID 15994521
"So much more to know", Science, 309 (5731): 78–102, July 2005, doi:10.1126/science.309.5731.78b, PMID 15994524
Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ("wiki") site

[1] Faltings, 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, ISSN 0002-9920

[Appel1977a-2] K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", Illinois J. Math 21: 429–490. MR 0543795

[Appel1977b-3] K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", Illinois J. Math 21: 491–567. MR 0543795

[Vendruscolo1999-4] Vendruscolo, M.; Najmanovich, R.; Domany, E. (1999), "Protein Folding in Contact Map Space", Physical Review Letters, 82 (3): 656–659, arXiv:cond-mat/9901215, Bibcode:1999PhRvL..82..656V, doi:10.1103/PhysRevLett.82.656, S2CID 6686420

[Dill2007-5] Dill, 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, doi:10.1016/j.sbi.2007.06.001, PMID 17572080, archived from the original (PDF) on 2011-07-20

[6] "Nobel Prize in Chemistry 2024". NobelPrize.org. Retrieved 2025-02-03.

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