The term was introduced by Mark Burgin, whose book Super-recursive algorithms develops their theory and presents several mathematical models.
The Church–Turing thesis in recursion theory relies on a particular definition of the term algorithm.
Based on his personal definitions that are more general than the one commonly used in recursion theory, Burgin argues that super-recursive algorithms disprove the Church–Turing thesis.
Burgin's interpretation of super-recursive algorithms has encountered opposition in the mathematical community.
One critic is logician Martin Davis, who argues that Burgin's claims have been well understood "for decades".