The nature of properly human mathematics

TL;DR

This paper explores the nature of human mathematics, emphasizing its dependence on axioms, its evolving yet universal features, and its structural organization influenced by cognitive constraints.

Contribution

It introduces a perspective that human mathematics is shaped by cognitive biases and structural organization, highlighting universal features despite its evolution over time.

Findings

Human mathematics is limited by cognitive and linguistic factors.

Mathematical knowledge is organized structurally due to brain functions.

Universal features of human mathematics persist despite its historical evolution.

Abstract

We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning of the human brain privileges concept naming and short formulations. This leads to organizing mathematical knowledge structurally. We consider briefly the problem of non-mathematical sciences.