Truth and the beautiful

The article examines the problem of identifying truth and beauty in meaningful axiomatic theories, and the formation of these values in the process of teaching certain sections of a mathematics course of a general education school with the characteristic features of meaningful axiomatic theories.. Certain groups of criteria of scientific or mathematical beauty are considered as a factor in the formation and identification of truth and beauty.Such criteria were introduced by the Scottish philosopher Hutcheson in the 18th century, and his many followers in subsequent centuries. This work examines the formative, unifying and logical groups of objective criteria of scientific beauty. It shows that: a) formative criteria: symmetry, comparison, harmony, rhythm, applicability are more prone to the formation and identification of the beauty of objects of a meaningful axiomatic theory than the truth in it; b) unifying criteria - unity of diversity, generality, mathematical recording of scientific laws are aimed at revealing the truth in a meaningful axiomatic theory. And the beauty of objects here is determined by the connection of criteria with truth, c) logical criteria - logical rigor, clarity, simplicity, reduction of the complex to the simple are aimed at the formation and identification in a meaningful axiomatic theory of both truth and the formation and identification of the beauty of objects.