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science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence ...
and
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
that have been solved and ''closed'' by researchers in the late twentieth century are Fermat's Last Theorem and the four-color theorem.K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", ''Illinois J. Math'' 21: 429–490. K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", ''Illinois J. Math'' 21: 491–567. An important open mathematics problem solved in the early 21st century is the
Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured ...
. Open problems exist in all scientific fields. For example, one of the most important open problems in biochemistry is the protein structure prediction problem – how to predict a
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
's structure from its sequence.


See also

* Lists of unsolved problems (by major field) * Hilbert's problems * Millennium Prize Problems


References


External links

* *{{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=free
Open Problem Garden
The collection of open problems in mathematics build on the principle of user editable ("wiki") site