Matiyasevich'stheorem has since been used to prove that many problems from calculus and differential equations are unsolvable.
Matiyasevich'stheorem, proven in 1970 by Yuri Matiyasevich[?], implies that Hilbert's tenth problem is unsolvable.
Matiyasevich'stheorem itself is somewhat more general than the unsolvability of the Tenth Problem; it can be stated as "Every recursively enumerable set is Diophantine ".
----------------------------------------------- Simultaneous Rigid $E$-Unification is not so Simple Anatoli Degtyarev Yuri Matiyasevich Andrei Voronkov Simultaneous rigid $E$-unification has been introduced in the area of theorem proving with equality.
– Dy The Importance was that its solution is the main step in solution of general quadratic Diophantine equations in two variables and useful for Matiyasevichtheorem on non-existence of the general algorithm for solving Diophantine equations.
Yuri Matiyasevich and the 10-th Problem of Hilbert
Then in 1970 Yuri Matiyasevich solved the 10-th Problem of Hilbert showing that such an algorithm that can solve any Diophantine equation does not exist !
There's a famous theorem, due to Yuri Matiyasevich, which proves that there's no computational way of answering this question in general.
That is, do the equations have integer solutions?" That question — yes or no, for any particular example — is not one a computer could answer in any finite amount of time.
In particular cases, you might be able to give an answer by means of some algorithmic procedure.
