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Problem

A problem is an exercise whose solution is desired. Mathematical "problems" may therefore range from simple puzzles to examination and contest problems to propositions whose proofs require insightful analysis.

Although not absolutely standard, The Greeks distinguished between "problems" (roughly, the construction of various figures) and "theorems" (establishing the properties of said figures; Heath 1956, pp. 252, 262, and 264).

There are many unsolved problems in mathematics. Two famous problems which have recently been solved include Fermat's last theorem (by Andrew Wiles) and the Kepler conjecture (by T. C. Hales). Among the most prominent of remaining unsolved problems are the Goldbach conjecture, Riemann hypothesis, the conjecture that there are an infinite number of twin primes, as well as many more. K.S. Brown, D. Eppstein, S. Finch, and C. Kimberling maintain extensive pages of unsolved problems in mathematics.

See also

Axiom, Corollary, Porism, Lemma, Postulate, Principle, Proof, Proposition, Tautology, Theorem, Unsolved Problems Explore this topic in the MathWorld classroom

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References

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Problem

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Weisstein, Eric W. "Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Problem.html

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