Explore: Solutions For Society Problems

The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several

Euler's collinear solutions, these solutions form the central configurations for the three-body problem. These solutions are valid for any mass ratios,

are: The problem is not understood until after the formulation of a solution. Wicked problems have no stopping rule. Solutions to wicked problems are not

is the energy estimate for this problem. To show uniqueness of solutions, assume there are two distinct solutions to the problem, call them u {\displaystyle

yield good solutions, have been devised. These include the multi-fragment algorithm. Modern methods can find solutions for extremely large problems (millions

problems. In some cases, the lists have been associated with prizes for the discoverers of solutions. Of the original seven Millennium Prize Problems

and efficient metaheuristics for vehicle routing problems reach solutions within 0.5% or 1% of the optimum for problem instances counting hundreds or

Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from

Descartes' theorem.) However, there are no Apollonius problems with seven solutions. Alternative solutions based on the geometry of circles and spheres have