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 (18031882)
“I think that a young state, like a young virgin, should modestly stay at home, and wait the application of suitors for an alliance with her; and not run about offering her amity to all the world; and hazarding their refusal.... Our virgin is a jolly one; and tho at present not very rich, will in time be a great fortune, and where she has a favorable predisposition, it seems to me well worth cultivating.”
—Benjamin Franklin (17061790)
“The tenth day of Christmas,
My true love sent to me
Ten pipers piping,”
—Unknown. The Twelve Days of Christmas (l. 6466)
“We have heard all of our lives how, after the Civil War was over, the South went back to straighten itself out and make a living again. It was for many years a voiceless part of the government. The balance of power moved away from itto the north and the east. The problems of the north and the east became the big problem of the country and nobody paid much attention to the economic unbalance the South had left as its only choice.”
—Lyndon Baines Johnson (19081973)