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But the major reason is to understand how to cope with full history dependence in a (deceptively easy-looking) problem. On the Ester's Book International Conference in Israel (2006) Robbins' problem was accordingly named one of the four most important problems in the field of optimal stopping and sequential analysis.
When the research is complete and the researcher knows the (probable) answer to the research question, writing up can begin (as distinct from writing notes, which is a process that goes on through a research project). In term papers, the answer to the question is normally given in summary in the introduction in the form of a thesis statement.
[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.
Establishing whether a constraint satisfaction problem on a finite domain has solutions is an NP-complete problem in general. This is an easy consequence of a number of other NP-complete problems being expressible as constraint satisfaction problems. Such other problems include propositional satisfiability and three-colorability.
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The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution.
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If the stable roommates problem instance has a stable matching, then there is a stable matching contained in any one of the stable tables. Any stable subtable of a stable table, and in particular any stable subtable that specifies a stable matching as in 2, can be obtained by a sequence of rotation eliminations on the stable table.