Basing on mathematical concept of algorithm, gnoseological aspects of solvability of science problems are observed. It is shown that 1) “insolvability” of many problems is relative (they are solved in a sense that the falsity of the premises is shown); 2) the existence of “insolvable” problems is by no means an index of limits and capabilities of human intellect, it only testifies to “Man’s having discovered so deep regularities with regard to which the premises earlier advanced disclose their groundlessness”.
