ROUND TABLE: The phenomenon of mathematical intuition: are there “shortest paths” in cognition?

Abstract

Intuitive insights are the result of unconscious processes, the deep mechanism of which is hidden from consciousness. At the level of consciousness, only the finished result is given. In this context, alternative interpretations of the phenomenon of mathematical intuition are analyzed. Mathematical geniuses sometimes say they knew the theorem was true before they found the proof. Either 1) In this case, there are only illusions of self-observation, which does not have access to unconscious processes of information processing. At the level of the unconscious, a large amount of information is processed according to the same algorithms of Discrete Units (sort of like a “super-speed processor” on an unconscious level). Or 2) The creatively gifted subjects at the unconscious level open up The short way a solution that is radically different from the known algorithms for sequential execution of mathematical operations. In that case, the phenomenon of genius is akin to a certain ability to “pave short paths”. Argument is in favor of version 1 of D.Hofstadter, who refers to Theorem A.Church. According to this theorem, in no formal system is there a universal method for distinguishing theorems from non-theorems. The argument for version 2 is the phenomenon of Savants, which can easily find answers to some of the most complex mathematical questions, although they are poorly versed in conventional algorithms. Similar to the generative grammar of H.Chomsky, the hypothesis of “innate”, natural for the brain of mathematics is considered.

Speaker

Yuliya M. Duplinskya
Saratov National Research State University Professor of Department of Theoretical and Social Philosophy
Russia

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