On humanization of mathematics: aesthetic mathematics

TL;DR

The paper asks how mathematics can be re-envisioned through human-centered, aesthetic lenses. It proposes a three-era framework (white, blue, green) to organize evolving ideas and introduces modal mathematics and modal monadology as tools to encode humanized perspectives, alongside a strategy for addressing the Riemann Hypothesis via model theory. A key claim is that traditional mathematics already embodies humanized elements, and that connecting logic, category-like ideas, and epistemic frameworks can enrich mathematical practice. The work emphasizes interdisciplinary relevance, including AI ethics and humanities-inspired perspectives, and outlines future directions for foundational research and cross-domain collaboration.

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.