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:

    If you would be a favourite of your king, address yourself to his weaknesses. An application to his reason will seldom prove very successful.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    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)

    They say all lovers swear more performance than they are able, and yet reserve an ability that they never perform; vowing more than the perfection of ten, and discharging less than the tenth part of one.
    William Shakespeare (1564–1616)

    Like the effects of industrial pollution ... the AIDS crisis is evidence of a world in which nothing important is regional, local, limited; in which everything that can circulate does, and every problem is, or is destined to become, worldwide.
    Susan Sontag (b. 1933)