 Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.The essence of Penrose's argument is that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Gödel-type results are provable by human mathematicians.He takes this disparity to mean that human mathematicians are not describable as formal proof systems and are not running an algorithm, so that the computational theory of mind is false, and computational approaches to artificial general intelligence are unfounded.