This fact is closely related to the algorithmic unsolvability of the Halting problem.
From the en.wikipedia.org
The lambda calculus emerged in his famous 1936 paper showing the unsolvability of the Entscheidungsproblem.
From the en.wikipedia.org
For example, the conventional proof of the unsolvability of the halting problem is essentially a diagonal argument.
From the en.wikipedia.org
Ruffini was the first to controversially assert the unsolvability by radicals of algebraic equations higher than quartics.
From the en.wikipedia.org
Wouldn't it be nice if computer students knew all about unsolvability, Turing tests, the theory of languages.
From the scienceblogs.com
As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
From the en.wikipedia.org
Because there exists a recursively enumerable set that is not computable, the unsolvability of Hilbert's tenth problem is an immediate consequence.
From the en.wikipedia.org
Their proofs demonstrate a connection between the unsolvability of the decision problem for first-order logic and the unsolvability of the halting problem.
From the en.wikipedia.org
The first results about unsolvability, obtained independently by Church and Turing in 1936, showed that the Entscheidungsproblem is algorithmically unsolvable.
From the en.wikipedia.org
More examples
The property (of a problem or difficulty) that makes it impossible to solve
(unsolvable) insolvable: not easily solved; "an apparantly insolvable problem"; "public finance...had long presented problems unsolvable or at least unsolved"- C.L.Jones