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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry.In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped ...
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, 21, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [ a ] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
[9] [10] Finding the capacity of an information-stable finite state machine channel. [11] In network coding, determining whether a network is solvable. [12] [13] Determining whether a player has a winning strategy in a game of Magic: The Gathering. [14] Planning in a partially observable Markov decision process.
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics.This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski.It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics.
Apple co-founder Steve Jobs’ net worth was around $10.2 billion when he died in 2011. Some analysts estimate he’d be worth around $7 billion today. That’s a hefty chunk of change, but it’s ...
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.