In
science
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
and
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, 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
The history of science covers the development of science from ancient history, ancient times to the present. It encompasses all three major branches of science: natural science, natural, social science, social, and formal science, formal. Pr ...
, 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 a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
that have been solved and ''closed'' by researchers in the late twentieth century are
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...
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.
Open problems exist in all scientific fields.
For example, one of the most important open problems in biochemistry is the
protein structure prediction
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its Protein secondary structure, secondary and Protein tertiary structure, tertiary structure ...
problem
– how to predict a
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metab ...
's structure from its sequence.
See also
*
Lists of unsolved problems (by major field)
*
Hilbert's problems
*
Millennium Prize Problems
The Millennium Prize Problems are seven well-known complex mathematics, mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem ...
*
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...
*
Wikenigma, wiki for open 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=
Open Problem GardenThe collection of open problems in mathematics build on the principle of user editable ("wiki") site