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:
“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)
“Only in the problem play is there any real drama, because drama is no mere setting up of the camera to nature: it is the presentation in parable of the conflict between Man’s will and his environment: in a word, of problem.”
—George Bernard Shaw (1856–1950)