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The problem of determining if a given set of Wang tiles can tile the plane. The problem of determining the Kolmogorov complexity of a string. Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers.
Vacuum World, a shortest path problem in which the goal is to vacuum up all the pieces of dirt. In scientific disciplines, a toy problem [1] [2] or a puzzlelike problem [3] is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a ...
The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. 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 ...
The Kissing Number Problem. A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to ...
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.
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
[1] Scarcity is the limited availability of a commodity, which may be in demand in the market or by the commons. Scarcity also includes an individual's lack of resources to buy commodities. [2] The opposite of scarcity is abundance. Scarcity plays a key role in economic theory, and it is essential for a "proper definition of economics itself". [3]
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 .