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{{redirect|Open question|information on open-ended questions|closed-ended question}}
{{redirect|Open question|information on open-ended questions|closed-ended question}}


In [[science]] and [[mathematics]], an '''open problem''' or an '''open question''' is a known problem that can be accurately stated, and has not yet been solved (no solution for it is known). Some questions remain unanswered for centuries before solutions are found. Two notable examples in [[mathematics]] that have been solved and ''closed'' by researchers in the late twentieth century are [[Fermat's Last Theorem]]<ref>{{Citation |last=Faltings|first=Gerd|year=1995|month=July|url=http://www.ams.org/notices/199507/faltings.pdf|format=PDF|title=The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles|journal=Notices of the AMS|volume=42|issue=7|pages=743&ndash;746|issn=0002-9920}}</ref> and the [[four color map theorem]].<ref name=Appel1977a>K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", ''Illinois J. Math'' '''21''': 429&ndash;490. MR 58:27598d</ref><ref name=Appel1977b>K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", ''Illinois J. Math'' '''21''': 491&ndash;567. MR 58:27598d</ref>. An important open problem solved in early 21st century is the [[Poincare Conjecture]].
In [[science]] and [[mathematics]], an '''open problem''' or an '''open question''' is a known problem that can be accurately stated, and has not yet been solved (no solution for it is known). Some questions remain unanswered for centuries before solutions are found. Two notable examples in [[mathematics]] that have been solved and ''closed'' by researchers in the late twentieth century are [[Fermat's Last Theorem]]<ref>{{Citation |last=Faltings|first=Gerd|year=1995|month=July|url=http://www.ams.org/notices/199507/faltings.pdf|format=PDF|title=The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles|journal=Notices of the AMS|volume=42|issue=7|pages=743&ndash;746|issn=0002-9920}}</ref> and the [[four color map theorem]]<ref name=Appel1977a>K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", ''Illinois J. Math'' '''21''': 429&ndash;490. MR 58:27598d</ref><ref name=Appel1977b>K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", ''Illinois J. Math'' '''21''': 491&ndash;567. MR 58:27598d</ref>. An important open problem solved in early 21st century is the [[Poincare Conjecture]].


Important open problems exist in many fields, such as [[Physics]], [[Chemistry]], [[Biology]], [[Computer science]], and [[Mathematics]]. For example, one of the most important open problems in biochemistry is the [[protein structure prediction]] problem<ref name=Vendruscolo1999>{{citation
Important open problems exist in many fields, such as [[Physics]], [[Chemistry]], [[Biology]], [[Computer science]], and [[Mathematics]]. For example, one of the most important open problems in biochemistry is the [[protein structure prediction]] problem<ref name=Vendruscolo1999>{{citation

Revision as of 04:41, 13 September 2011

"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 that can be accurately stated, and has not yet been solved (no solution for it is known). Some questions remain unanswered for centuries before solutions are found. 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 open problem solved in early 21st century is the Poincare Conjecture.

Important open problems exist in many fields, such as Physics, Chemistry, Biology, Computer science, and Mathematics. 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.

It is common in graduate schools to point out open problems to students. Graduate students as well as faculty members often engage in research to solve such problems.

See also

References

  1. ^ Faltings, Gerd (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 {{citation}}: Unknown parameter |month= ignored (help)
  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, 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?" (PDF), Current Opinion in Structural Biology, 17 (3): 342–346, doi:10.1016/j.sbi.2007.06.001, PMID 17572080


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