Abstract: Intuitionism school of thought helped to reconstruct the three crises lying in the basis of mathematic. The author of the article has discovered the facts of rude falsification of the genesis of the theory of incommensurable segments and modern theory of irrational numbers which are traditionally related to establishment of the multiple-theory paradigm at the end of XIX century. Based on the results of researches conducted by a Dutch mathematician Luitzen Brouwer in 1911 and a Soviet mathematician Andrey Kolmogorov in 1925, the author suggests the negative solution of David Hilbert's second problem.