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:

    Preaching is the expression of the moral sentiment in application to the duties of life.
    Ralph Waldo Emerson (1803–1882)

    It is known that Whistler when asked how long it took him to paint one of his “nocturnes” answered: “All of my life.” With the same rigor he could have said that all of the centuries that preceded the moment when he painted were necessary. From that correct application of the law of causality it follows that the slightest event presupposes the inconceivable universe and, conversely, that the universe needs even the slightest of events.
    Jorge Luis Borges (1899–1986)

    You boast of spending a tenth part of your income in charity; maybe you should spend the nine tenths so, and done with it.
    Henry David Thoreau (1817–1862)

    I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.
    Jean Giraudoux (1882–1944)