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The medieval Latin manuscript Propositiones ad Acuendos Juvenes (English: Problems to Sharpen the Young) is one of the earliest known collections of recreational mathematics problems. [1] The oldest known copy of the manuscript dates from the late 9th century. The text is attributed to Alcuin of York (died 804.) Some editions of the text ...
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
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The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
A polynomial-time problem can be very difficult to solve in practice if the polynomial's degree or constants are large enough. In addition, information-theoretic security provides cryptographic methods that cannot be broken even with unlimited computing power. "A large-scale quantum computer would be able to efficiently solve NP-complete problems."
Problems (Greek: Προβλήματα; Latin: Problemata) is an Aristotelian or possibly pseudo-Aristotelian [1] collection of problems written in a question and answer format. The collection, gradually assembled by the peripatetic school , reached its final form anywhere between the third century BC and the 6th century AD.
An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.
The tenth problem of the Moscow Mathematical Papyrus asks for a calculation of the surface area of a hemisphere (Struve, Gillings) or possibly the area of a semi-cylinder (Peet). Below we assume that the problem refers to the area of a hemisphere. The text of problem 10 runs like this: "Example of calculating a basket.