Such statements are generally believed unlikely to be independent of strong theories like PA.

1 On the significance of \(\textbf{P} \neq \textbf{NP}\)? The appreciation of complexity theory outside of theoretical computer science is largely due to the notoriety of open questions such as 1–4. \) – has attracted the greatest attention. e. the Millennium Problems (Cook 2006). g. (Sipser 1992), (Fortnow 2009), and (Fortnow 2013). \) will prove to have far reaching practical and theoretical consequences outside of computer science. Perhaps the most significant of these revolves around the pos