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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent ...
The word problem is a well-known example of an undecidable problem. If A {\displaystyle A} is a finite set of generators for G {\displaystyle G} , then the word problem is the membership problem for the formal language of all words in A {\displaystyle A} and a formal set of inverses that map to the identity under the natural map from the free ...