In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim or that a particular set of problems cannot be solved in general. Such cases are also known as negative proof, proof of an impossibility theorem, or negative result.

Proof of space (PoS) is a type of consensus algorithm achieved by demonstrating one's legitimate interest in a service (such as sending an email) by allocating a non-trivial amount of memory or disk space to solve a challenge presented by the service provider. The concept was formulated in 2013 by Dziembowski et al.

Proof of concept (POC or PoC), also known as proof of principle, is a realization of a certain method or idea in order to demonstrate its feasibility, or a demonstration in principle with the aim of verifying that some concept or theory has practical potential. A proof of concept is usually small and may or may not be complete.