Thus on the basis of the previous argument, Penrose concludes that because mathematicians are able to ascertain whether a given computation (see previous examples) halts they are using a computationally irreducible process.
``Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth''
Roger Penrose in Shadows of the Mind, 1994.
``The cognitive capabilities of human beings are not based on any knowably sound algorithm or algorithms and thus the essential features of the human mind will never be explained computationally''