Our intuitions strongly reflect the fact that the former problems in such pairs seem more difficult than the latter. But beyond collapsing distinctions currently appear almost self-evident, the coincidence of \(\textbf{P}\) and \(\textbf{NP}\) would also have a more radical effect on the situation which we currently face in mathematics. For suppose that \(\mathsf{T}\) is a recursively axiomatic theory which is sufficiently strong to formalize our current mathematical theorizing – e.g. Zermelo Fraenkel set theory with the Axiom of Choice [\(\mathsf{ZFC}\)], supplemented as needed with large cardinal hypotheses. Observe that regardless of the proof theoretic strength of \(\mathsf{T}\), the following question about derivability in this theory will still presumably be decidable in polynomial time: