A theorem prover is software that helps construct and verify mathematical proofs under strict logical rules. In practice, it can check whether each step in a proof follows from the last one, making the result machine-checkable rather than just persuasive. Some tools assist a user interactively, while others automate large parts of the reasoning.
In cyber security, theorem provers matter because they can prove properties that are hard to trust by inspection alone: protocol correctness, access-control logic, cryptographic assumptions, and safety of critical code. Defenders use them to model systems and verify that a design cannot reach an unsafe state or violate a policy. Attackers can also benefit indirectly, because the same formal methods can help find edge cases, inconsistent assumptions, or flawed protocol logic. The key value is precision: a verified claim is stronger than a test result, especially for high-assurance systems.