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{{Short description|In science and mathematics, not yet solved problem}}
{{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 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 [[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 mathematics open problem solved in early 21st century is the [[Poincare Conjecture]].
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]]<ref>{{Citation |last=Faltings|first=Gerd|date=July 1995|url=https://www.ams.org/notices/199507/faltings.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 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|543795}}</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|543795}}</ref> An important open mathematics problem solved in the early 21st century is the [[Poincaré conjecture]].
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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

Open problems exist in all scientific fields.
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For example, one of the most important open problems in biochemistry is the [[protein structure prediction]] problem<ref name=Vendruscolo1999>{{citation
| last1 = Vendruscolo | first1 = M.
| last1 = Vendruscolo | first1 = M.
| last2 = Najmanovich | first2 = R.
| last2 = Najmanovich | first2 = R.
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| doi = 10.1103/PhysRevLett.82.656
| doi = 10.1103/PhysRevLett.82.656
| bibcode=1999PhRvL..82..656V
| bibcode=1999PhRvL..82..656V
|arxiv = cond-mat/9901215 | s2cid = 6686420
}}</ref><ref name=Dill2007>{{citation
}}</ref><ref name=Dill2007>{{citation
| last1 = Dill | first1 = K.A.
| last2 = Ozkan | first2 = S.B.
|last1 = Dill
| last3 = Weikl | first3 = T.R.
|first1 = K.A.
| last4 = Chodera | first4 = J.D.
|last2 = Ozkan
| last5 = Voelz | first5 = V.A.
|first2 = S.B.
| year = 2007
|last3 = Weikl
|first3 = T.R.
| title = The protein folding problem: when will it be solved?
|last4 = Chodera
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| journal = Current Opinion in Structural Biology
| volume = 17
|first4 = J.D.
| issue = 3
|last5 = Voelz
|first5 = V.A.
⚫
| pages = 342–346
| doi = 10.1016/j.sbi.2007.06.001
|year = 2007
| url = http://laplace.compbio.ucsf.edu/~jchodera/pubs/pdf/protein-folding-problem.pdf
|title = The protein folding problem: when will it be solved?
⚫
|journal = Current Opinion in Structural Biology
⚫
| pmid = 17572080
|volume = 17
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}}</ref> &ndash; how to predict a [[protein]]'s structure from its sequence.
|issue = 3

⚫
|pages = 342–346
It is common in [[graduate school]]s to point out open problems to students. Graduate students as well as [[Faculty (teaching staff)|faculty]] members often engage in research to solve such problems.
|doi = 10.1016/j.sbi.2007.06.001

|url = http://laplace.compbio.ucsf.edu/~jchodera/pubs/pdf/protein-folding-problem.pdf
⚫
== See also ==
⚫
|pmid = 17572080
|url-status = dead
|archive-url = https://web.archive.org/web/20110720080804/http://laplace.compbio.ucsf.edu/~jchodera/pubs/pdf/protein-folding-problem.pdf
|archive-date = 2011-07-20
⚫
}}</ref> &ndash; how to predict a [[protein]]'s structure from its sequence.


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==See also==
* [[List of unsolved problems]] (by major field)
* [[Lists of unsolved problems]] (by major field)
* [[Hilbert's problems]]
* [[Hilbert's problems]]
* [[Millennium Prize Problems]]
* [[Millennium Prize Problems]]
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==External links==
==External links==
*{{citation | last1 = Kennedy | first1 = Donald | last2 = Norman | first2 = Colin | year = 2005 | title = What Don't We Know? | journal = Science | volume = 309 | issue = 5731 | pages = 75–75 | doi = 10.1126/science.309.5731.75 | url = http://www.sciencesignaling.org/cgi/content/summary/sci;309/5731/75 | pmid = 15994521}}
*{{citation | last1 = Kennedy | first1 = Donald | last2 = Norman | first2 = Colin | year = 2005 | title = What Don't We Know? | journal = Science | volume = 309 | issue = 5731 | pages = 75 | doi = 10.1126/science.309.5731.75 | url = http://www.sciencesignaling.org/cgi/content/summary/sci;309/5731/75 | pmid = 15994521| doi-access = free }}
*{{Citation |author= |title=So much more to know |journal=Science |volume=309 |issue=5731 |pages=78–102 |year=2005 |month=July |pmid=15994524 |doi=10.1126/science.309.5731.78b}}
*{{Citation |title=So much more to know |journal=Science |volume=309 |issue=5731 |pages=78–102 |date=July 2005 |pmid=15994524 |doi=10.1126/science.309.5731.78b|doi-access= }}
* [http://garden.irmacs.sfu.ca Open Problem Garden] The collection of open problems in mathematics build on the principle of user editable ("wiki") site
* [http://openproblemgarden.org Open Problem Garden] The collection of open problems in mathematics build on the principle of user editable ("wiki") site


[[Category:Open problems| ]]
[[Category:Open problems| ]]


{{Math-stub}}

[[es:Problema no resuelto]]
[[fr:Problème ouvert]]
[[ko:미해결 문제]]
[[id:Masalah terbuka]]
[[it:Problema aperto]]
[[pl:Problem otwarty]]
[[pt:Anexo:Lista de problemas em aberto]]
[[sl:Seznam nerešenih problemov]]

Latest revision as of 15:01, 12 September 2023

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.

See also

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References

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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. MR543795
  3. ^ K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", Illinois J. Math 21: 491–567. MR543795
  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
  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
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