Mathematical Culture and Thought

Mathematical Culture and Thought

On the Nature of Mathematical Entities

Document Type : Translation

Authors
Z. Naghizadeh
A. Hashemi Borzabadi
Department of Mathematics, Faculty of Sciences, University of Science and Technology of Mazandaran, Iran
10.30504/mct.2025.1554.2091
Abstract
In this article, Reuben Hersh concisely formulates his view on the nature and mode of existence of mathematical entities. According to this view, mathematical entities can be considered from three interconnected aspects: social, mental, and neural. On the one hand, mathematics is a social and historical institution that is perpetuated through education, interaction, and mathematical texts; on the other hand, mathematical entities are the objects of individuals' thought and mental representation, and these mental activities are accompanied by neural processes in the brain. Hersh does not regard any of these three aspects as independent of the other two, and in conclusion, he relates this multifaceted and interdisciplinary conception to a phenomenological attitude.
Keywords
mathematical entities
humanistic philosophy
methodology
the body of established mathematics
phenomenology
Subjects

Hersh, R., On the nature of mathematical entities, in Humanizing Mathematics and its Philosophy, B.
Sriraman, ed., Birkhäuser, Cham, 2017, 361-363.

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  • Receive Date 21 April 2025
  • Accept Date 27 April 2025
  • Publish Date 22 May 2026