Mathematical problem

A question or task in mathematics whose solution requires reasoning, calculation, or proof. It may ask for a value, a construction, an explanation, or a proof of a claim.

Mathematical statement: A declarative sentence in mathematics that can be evaluated as true or false. A problem often asks whether a mathematical statement is true or requests its proof.
Problem-solving: The process of finding and justifying a way to resolve a question or task. Mathematical problem-solving organizes the search for a solution and its verification.
P versus NP problem: The open question of whether every problem whose solution is efficiently checkable is also efficiently solvable. It is a prominent example of a problem whose difficulty concerns entire classes of tasks.
Decision problem: A computational problem whose answer for each input is yes or no. Some mathematical problems ask only whether a specified condition can be met.
Mathematical definition: A precise specification of the meaning of a mathematical term or object. Definitions determine which objects and properties a problem concerns.
Mathematical reasoning: The use of logical and quantitative arguments to draw conclusions about mathematical objects. Reasoning connects a problem's assumptions to a valid answer or proof.
Riemann hypothesis: The conjecture that every nontrivial zero of the Riemann zeta function has real part one-half. Its unresolved proof problem links a precise statement to deep consequences for prime numbers.
Optimization problem: A problem that seeks the best feasible value of an objective under specified constraints. Optimization asks for a best solution, rather than merely any solution.
Mathematical conjecture: A mathematical claim proposed as true but not yet established by proof. Proving or refuting a conjecture is a central kind of mathematical problem.
Algorithm: A finite, specified sequence of steps for performing a computation or solving a class of tasks. Algorithmic problems seek procedures that reliably produce answers across inputs.

Linked from 2 pages