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<title>Open problem</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Open problem</span></span>

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<p>In <a href="Science" title="Science">science</a> and <a href="Mathematics" title="Mathematics">mathematics</a>, an <b>open problem</b> or an <b>open question</b> 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).

</p><p>In the <a href="History_of_science" title="History of science">history of science</a>, 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.

</p><p>Two notable examples in <a href="Mathematics" title="Mathematics">mathematics</a> that have been solved and <i>closed</i> by researchers in the late twentieth century are <a href="Fermat's_Last_Theorem" title="Fermat's Last Theorem">Fermat's Last Theorem</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and the <a href="Four-color_theorem" class="mw-redirect" title="Four-color theorem">four-color theorem</a>.<sup id="cite_ref-Appel1977a_2-0" class="reference"><a href="#cite_note-Appel1977a-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Appel1977b_3-0" class="reference"><a href="#cite_note-Appel1977b-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> An important open mathematics problem solved in the early 21st century is the <a href="Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a>.

</p><p>Open problems exist in all scientific fields.

For example, one of the most important open problems in biochemistry is the <a href="Protein_structure_prediction" title="Protein structure prediction">protein structure prediction</a> problem<sup id="cite_ref-Vendruscolo1999_4-0" class="reference"><a href="#cite_note-Vendruscolo1999-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Dill2007_5-0" class="reference"><a href="#cite_note-Dill2007-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> – how to predict a <a href="Protein" title="Protein">protein</a>'s structure from its sequence. In 2024, <a href="David_Baker_(biochemist)" title="David Baker (biochemist)">David Baker</a> and <a href="Demis_Hassabis" title="Demis Hassabis">Demis Hassabis</a> were awarded the <a href="Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> for their contributions to protein structure prediction.

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<ul><li><a href="Lists_of_unsolved_problems" title="Lists of unsolved problems">Lists of unsolved problems</a> (by major field)</li>

<li><a href="Hilbert's_problems" title="Hilbert's problems">Hilbert's problems</a></li>

<li><a href="Millennium_Prize_Problems" title="Millennium Prize Problems">Millennium Prize Problems</a></li>

<li><a href="Conjecture" title="Conjecture">Conjecture</a></li>

<li><a href="Wikenigma" title="Wikenigma">Wikenigma</a>, wiki for open problems</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFFaltings1995" class="citation cs2">Faltings, Gerd (July 1995), <a rel="nofollow" class="external text" href="https://www.ams.org/notices/199507/faltings.pdf">"The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles"</a> <span class="cs1-format">(PDF)</span>, <i>Notices of the AMS</i>, <b>42</b> (7): <span class="nowrap">743–</span>746, <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9920">0002-9920</a></cite></span>

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<li id="cite_note-Appel1977a-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Appel1977a_2-0">^</a></b></span> <span class="reference-text">K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", <i>Illinois J. Math</i> <b>21</b>: 429–490. <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0543795">0543795</a></span>

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<li id="cite_note-Appel1977b-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Appel1977b_3-0">^</a></b></span> <span class="reference-text">K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", <i>Illinois J. Math</i> <b>21</b>: 491–567. <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0543795">0543795</a></span>

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<li id="cite_note-Vendruscolo1999-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Vendruscolo1999_4-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFVendruscoloNajmanovichDomany1999" class="citation cs2">Vendruscolo, M.; Najmanovich, R.; Domany, E. (1999), "Protein Folding in Contact Map Space", <i>Physical Review Letters</i>, <b>82</b> (3): <span class="nowrap">656–</span>659, <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/9901215">cond-mat/9901215</a></span>, <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999PhRvL..82..656V">1999PhRvL..82..656V</a>, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.82.656">10.1103/PhysRevLett.82.656</a>, <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6686420">6686420</a></cite></span>

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<li id="cite_note-Dill2007-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dill2007_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFDillOzkanWeiklChodera2007" class="citation cs2">Dill, K.A.; Ozkan, S.B.; Weikl, T.R.; Chodera, J.D.; Voelz, V.A. (2007), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110720080804/http://laplace.compbio.ucsf.edu/~jchodera/pubs/pdf/protein-folding-problem.pdf">"The protein folding problem: when will it be solved?"</a> <span class="cs1-format">(PDF)</span>, <i>Current Opinion in Structural Biology</i>, <b>17</b> (3): <span class="nowrap">342–</span>346, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.sbi.2007.06.001">10.1016/j.sbi.2007.06.001</a>, <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17572080">17572080</a>, archived from <a rel="nofollow" class="external text" href="http://laplace.compbio.ucsf.edu/~jchodera/pubs/pdf/protein-folding-problem.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2011-07-20</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nobelprize.org/prizes/chemistry/2024/summary/?utm_source=chatgpt.com">"Nobel Prize in Chemistry 2024"</a>. <i>NobelPrize.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2025-02-03</span></span>.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><cite id="CITEREFKennedyNorman2005" class="citation cs2">Kennedy, Donald; Norman, Colin (2005), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="http://www.sciencesignaling.org/cgi/content/summary/sci;309/5731/75">"What Don't We Know?"</a></span>, <i>Science</i>, <b>309</b> (5731): 75, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.309.5731.75">10.1126/science.309.5731.75</a></span>, <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15994521">15994521</a></cite></li>

<li><cite class="citation cs2">"So much more to know", <i>Science</i>, <b>309</b> (5731): <span class="nowrap">78–</span>102, July 2005, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.309.5731.78b">10.1126/science.309.5731.78b</a>, <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15994524">15994524</a></cite></li>

<li><a rel="nofollow" class="external text" href="http://openproblemgarden.org">Open Problem Garden</a> The collection of open problems in mathematics build on the principle of user editable ("wiki") site</li></ul></div><div><div class="zim-footer">

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