On humanization of mathematics: aesthetic mathematics

TL;DR

This paper explores the concept of humanizing mathematics through aesthetic and philosophical approaches, proposing new directions and interpretations that emphasize the subjective and human aspects of mathematical understanding.

Contribution

It introduces the idea of humanized mathematics, including traditional and novel forms, and discusses a logical approach to the Riemann Hypothesis within this framework.

Findings

Mathematics can be interpreted as a humanized discipline.

Aesthetic and philosophical elements enrich mathematical understanding.

A logical approach to the Riemann Hypothesis is proposed.

Abstract

This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective dimensions of mathematics. These approaches aim to make mathematics humanize. It proposes novel directions in mathematics, stressing that the ideas presented here are provisional. Furthermore, it argues that mathematics can take multiple humanized forms. Even traditional mathematics can be interpreted as a form of humanized mathematics. To support this perspective, several mathematical observations are provided. Additionally, a general approach to addressing the Riemann Hypothesis, focusing on proof by contradiction and mathematical logic, particularly model theory, is outlined. The paper also briefly reflects on my prior research through this idea on humanization and concludes with general remarks and future directions.