Infeasibility of solving finite mathematical problems - Brown, Adam (ProQuest Dissertations & Theses, 2010)
We prove that the decision problem for finite mathematical statements, though recursive, is infeasible in seemingly any realistic model of computation. In particular, we construct of a set of finite mathematical statements which can only be feasibly solved by programs long enough to explicitly encode a decision for each statement. This result was published in Hungarian, in 1973, by Michael Makkai and appears here for the first time in English. In this paper we: (1) elucidate Makkai’s proof as an adaptation of Gödel’s first incompleteness proof, (2) strengthen his 1973 result and (3) reflect on this result from the perspectives of computational complexity and algorithmic information theory (Kolmogorov complexity).