Diophantine Set - Application To Hilbert's Tenth Problem

Application To Hilbert's Tenth Problem

Hilbert's tenth problem asks for a general algorithm deciding the solvability of Diophantine equations. The conjunction of Matiyasevich's theorem with earlier results known collectively as the MRDP theorem implies that a solution to Hilbert's tenth problem is impossible.

Read more about this topic:  Diophantine Set

Famous quotes containing the words application to, application, tenth and/or problem:

    It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.
    René Descartes (1596–1650)

    The best political economy is the care and culture of men; for, in these crises, all are ruined except such as are proper individuals, capable of thought, and of new choice and the application of their talent to new labor.
    Ralph Waldo Emerson (1803–1882)

    Coming out, all the way out, is offered more and more as the political solution to our oppression. The argument goes that, if people could see just how many of us there are, some in very important places, the negative stereotype would vanish overnight. ...It is far more realistic to suppose that, if the tenth of the population that is gay became visible tomorrow, the panic of the majority of people would inspire repressive legislation of a sort that would shock even the pessimists among us.
    Jane Rule (b. 1931)

    If we parents accept that problems are an essential part of life’s challenges, rather than reacting to every problem as if something has gone wrong with universe that’s supposed to be perfect, we can demonstrate serenity and confidence in problem solving for our kids....By telling them that we know they have a problem and we know they can solve it, we can pass on a realistic attitude as well as empower our children with self-confidence and a sense of their own worth.
    Barbara Coloroso (20th century)