Open problem
Encyclopedia
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
and the four color map theorem. An important mathematics 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 – how to predict a protein
's structure from its sequence.
It is common in graduate school
s to point out open problems to students. Graduate students as well as faculty members often engage in research to solve such problems.
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
that have been solved and closed by researchers in the late twentieth century are Fermat's Last Theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
and the four color map theorem. An important mathematics open problem solved in early 21st century is the Poincare Conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
.
Important open problems exist in many fields, such as Physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, Chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, Biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
, Computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, and Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. For example, one of the most important open problems in biochemistry is the protein structure prediction
Protein structure prediction
Protein structure prediction is the prediction of the three-dimensional structure of a protein from its amino acid sequence — that is, the prediction of its secondary, tertiary, and quaternary structure from its primary structure. Structure prediction is fundamentally different from the inverse...
problem – how to predict a protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
's structure from its sequence.
It is common in graduate school
Graduate school
A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree...
s to point out open problems to students. Graduate students as well as faculty members often engage in research to solve such problems.
See also
- List of unsolved problems (by major field)
- Hilbert's problemsHilbert's problemsHilbert's problems form a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics...
- Millennium Prize ProblemsMillennium Prize ProblemsThe Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of September 2011, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize being awarded by the institute...
External links
- Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ("wiki") site