Open problem

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"Open question" redirects here. For information on open-ended questions, see closed-ended question.

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 (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, after all, well-defined. Many open problems in mathematics are in fact concerned with the question 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 map theorem.[2][3] An important mathematics open problem solved in the early 21st century is the Poincaré conjecture.

Important 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.

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  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 
  2. ^ K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", Illinois J. Math 21: 429–490. MR 58:27598d
  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 58:27598d
  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 
  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?", Current Opinion in Structural Biology 17 (3): 342–346, doi:10.1016/j.sbi.2007.06.001, PMID 17572080 

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