Unity and Disunity in Mathematics

TL;DR

This paper explores the contrasting notions of unity and disunity in mathematics, highlighting cultural, semantic, and philosophical differences that challenge the idea of a singular mathematical unity.

Contribution

It critically examines the ideal of mathematical unity by analyzing historical, cultural, and philosophical disunities and ambiguities within the field.

Findings

Mathematical unity is more of an aspirational ideal than a universal reality.

Disunities arise from cultural, semantic, and philosophical differences.

Certain mathematical texts are not universally accepted by practitioners.

Abstract

The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an ideal that doesn't exist. We shall point to diachronic and cross cultural disunities, to semantic, semiotic and philosophic ambiguities and to the non-acceptance of certain mathematical texts by some practitioners of the subject.