Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows:
Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.
A Diophantine equation is an equation of the form
where p is a polynomial with integer coefficients. It took many years for the problem to be solved with a negative answer. Today, it is known that no such algorithm exists in the general case. This result is the combined work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson.
Read more about Hilbert's Tenth Problem: Formulation, Diophantine Sets, History, Applications, Further Results, Extensions of Hilbert's Tenth Problem
Famous quotes containing the words tenth and/or problem:
“In his tenth July some instinct
taught him to arm the waiting wave,
a giant where its mouth hung open.
He rode on the lip that buoyed him there
and buckled him under.”
—Anne Sexton (1928–1974)
“What happened at Hiroshima was not only that a scientific breakthrough ... had occurred and that a great part of the population of a city had been burned to death, but that the problem of the relation of the triumphs of modern science to the human purposes of man had been explicitly defined.”
—Archibald MacLeish (1892–1982)