THE UNITING SIGNS OF SCIENTIFIC BEAUTY IN THE PROCESS OF TEACHING MATHEMATICS

In works [1–3] we presented the logical and forming groups of objective attributes of the scientific beauty in the learning process of mathematics. The last group of objective features of the scientific beauty are the unifying signs. The unification of things, phenomena, people, societies, etc., arrives the generality of certain properties and can have both a positive and a negative meaning. However, in mathematics (and science in general) only the positive side of this process is seen and, consequently, the manifestations of unity here are considered beautiful. In this paper we will consider the following unifying signs of the scientific beautiful: unity in diversity and universality, applicability, a mathematical record of scientific regularity. Unity in diversity is the first criterion proposed by Hutcheson as a general aesthetic principle for evaluating beauty both in nature and in science. This criteria is realizing in general theorem of mathematics. However, the application of any theorem for any particular case or the derivation from it of any consequence Hutcheson considers perfect, and this is the second sign of the beautiful Hutcheson – a sign of universality. These signs of the scientific beauty, characterizing Hutcheson, are widely manifested in the applications of mathematics in the very diverse branches of science and technology. These applications of mathematics express by themselves, the unity of various phenomena of science and technology, which also affirm the universality of mathematical theorems. According M. V. Volkenstein, any clear and harmonious formulation of scientific truth in the language of mathematics brings an aesthetic impression, and such a record is the principle of aesthetics of mathematics [7]. This principle is widely manifested in the interdisciplinary connections of mathematics in the teaching mathematics.