This work introduces the notion of naysayer proofs. We observe that in numerous (zero-knowledge) proof systems, it is significantly more efficient for the verifier to be convinced by a so-called naysayer that a false proof is invalid than it is to check that a genuine proof is valid. We show that every NP language has logarithmic size and constant-time naysayer proofs. We also show practical constructions for several example proof systems, including FRI polynomial commitments, post-quantum secure digital signatures, and verifiable shuffles. Naysayer proofs enable an interesting new optimistic verification mode potentially suitable for resource-constrained verifiers, such as smart contracts.