Towards Open mathematics: the Transformation of the Practice of Mathematical Proof from Individual to Socio-Digital (in Russian, 2019) / На пути к открытой математике: трансформация практики математического доказательства от индивидуальной к социоцифровой (original) (raw)

In digital culture, mathematical practice undergo substantial and far-reaching changes. In this paper, an attempt is made to scrutinize the changes in the mathematicians’ conception of the nature and purpose of mathematical proof. The theme is further narrowed by choosing only one trend within the framework just mentioned. This trend consists in intensified interest in social and communicative aspects of mathematical proof. Mathematical proof is understood as a socio-digital event that supports mutual understanding and co-creativity within the community maintains the conveyance of methodology and contributes to the collective ways to guarantee the historical stability of mathematical knowledge. When facing “the problem of complexity” (E.B. Davies) contemporary mathematicians crave for reaching a new level of integration by adaptation and further development of brand-new digital technologies. The program can be identified as “open mathematics” (Felix Breuer). In this connection, I propose an account of the computer as a device for effective integration of multiple human actions to imitate an appearance of being produced by one actor. This account allows us to dispense with contrasting the computer with the human being(s) and thereby with the contrasting computer proofs with human proofs within the mathematical practice. Keywords: philosophy of mathematics, mathematical practice, communication, digital culture, computer.