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Turing's proof is a proof by Alan Turing, first published in November 1936 [1] with the title "On Computable Numbers, with an Application to the Entscheidungsproblem".It was the second proof (after Church's theorem) of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture that some purely mathematical yes–no questions can never be answered by computation; more technically ...
Problem solving is the process of ... and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution
A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert's eighth problem, and is still considered an important open problem a century later. The problem has been well-known ever since it was originally posed by Bernhard Riemann in 1860.
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 [1] laid the foundations of graph theory and prefigured the idea of topology.
A proof that P = NP could have stunning practical consequences if the proof leads to efficient methods for solving some of the important problems in NP. The potential consequences, both positive and negative, arise since various NP-complete problems are fundamental in many fields.
George Pólya's work on problem solving, [198] the construction of mathematical proofs, and heuristic [199] [200] show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2] Since the problem had withstood the attacks of ...
Abel–Ruffini theorem. In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.