The Mathematics of the Minor versus the Mathematics of the Major: A Deleuzian Reading of the Ontological Shift in Geometry

Ghanatir, Shahāb Ad-Dīn

doi:10.30465/os.2026.53392.2080

The Mathematics of the Minor versus the Mathematics of the Major: A Deleuzian Reading of the Ontological Shift in Geometry

Document Type : Research Paper

Author

Shahāb ad-Dīn Ghanatir

The Student of PhD in visual arts, Faculty of Visual Arts, art university

10.30465/os.2026.53392.2080

Abstract

Introduction:
This article offers a Deleuzian reading of the shift from Euclidean to non-Euclidean geometry in order to show that this transition is not merely a technical modification within mathematics, but a profound philosophical transformation in the ontology of space. Traditionally, Euclidean geometry presents space as fixed, homogeneous, and governed by universal and stable coordinates. By contrast, non-Euclidean geometry—especially in its Riemannian form—introduces a conception of space that is variable, differential, and relational. From a Deleuzian perspective, this shift can be understood as a movement from an axiomatic and majority-based model of thought toward a problem-based and minority-oriented one. In this framework, mathematics is not simply a formal system of measurement; it becomes a mode of thinking that reveals different ways of constituting space, identity, and relation. The central question of the article is how Deleuze’s distinction between the mathematics of the majority and the mathematics of the minority can clarify the philosophical significance of this geometrical transformation. The article argues that the passage from Euclidean to non-Euclidean geometry should be read as a “Copernican revolution” in spatial ontology, because it replaces the idea of space as an absolute container with the idea of space as a dynamic field of singular relations. This shift also affects the concept of individuality: instead of being understood as a fixed essence, individuality emerges as a process shaped by singularities, variations, and connections.
Materials & Methods:
The article employs a descriptive-analytical method. Its approach is primarily philosophical and theoretical, combining a close reading of Deleuzian concepts with a conceptual analysis of geometrical ideas. Rather than treating geometry as a purely formal or historical discipline, the study examines how geometrical structures can be interpreted as expressions of broader ontological and epistemological assumptions. The method involves comparing Euclidean and non-Euclidean geometries through the lens of Deleuze’s philosophy. Euclidean geometry is associated with a stable, centralized, and axiomatic order, whereas non-Euclidean geometry is approached as a minoritarian and problem-centered formation that destabilizes the assumptions of classical spatial thought. Particular attention is given to concepts such as manifold, curvature, and point of view, because these notions make it possible to understand space not as a static given, but as a structured multiplicity defined by internal differences and relational dynamics. The article also extends this analysis toward contemporary physics, especially gauge theory, in order to indicate that the philosophical implications of non-Euclidean geometry continue beyond mathematics into the broader field of scientific thought.
Discussion & Result:
The discussion shows that Euclidean geometry corresponds to an ontology of space grounded in uniformity, measure, and fixed reference. In this model, space is conceived as static and universal, and objects are located within it according to stable coordinates. Such a conception aligns with what Deleuze would call an axiomatic or majority-based system: a system that regulates difference through identity, hierarchy, and centralization. Non-Euclidean geometry disrupts this model. In Riemannian geometry, space is no longer assumed to be homogeneous or globally fixed; instead, it is understood as a manifold whose structure depends on curvature and local variation. This means that spatial properties are not simply imposed from outside, but arise from differential relations internal to the space itself. As a result, the ontology of space changes from static extension to dynamic relationality. Space becomes something that is produced, differentiated, and transformed through its own internal conditions. From a Deleuzian standpoint, this is philosophically decisive. Deleuze’s mathematics of the minority is not reducible to numerical smallness; rather, it designates a mode of thinking that begins from problems, singularities, and non-totalizable relations. Non-Euclidean geometry exemplifies this mode because it does not simply replace one formula with another. It reconceptualizes the very conditions under which space is understood. The “point of view” becomes crucial here: no position is absolutely central, and spatial reality is always grasped from within a field of relations rather than from an external, universal standpoint. This shift also redefines individuality. Under Euclidean assumptions, identity tends to appear stable and self-identical. Under the non-Euclidean-Deleuzian framework, however, individuality is constituted through singularities and their connections. A singular entity is not what it is because it reflects an essence, but because it occupies a position in a network of differential relations. In this sense, the article argues that non-Euclidean geometry resonates with contemporary physics, particularly gauge theory, where relational structures and variable fields replace classical notions of fixed spatial order.
Conclusion:
The article concludes that the transition from Euclidean to non-Euclidean geometry, when interpreted through Deleuze, marks a fundamental philosophical shift in the understanding of space. This is not simply a mathematical evolution but a transformation in ontology: space is no longer conceived as a stable, universal container, but as a dynamic, relational manifold shaped by curvature, difference, and singularity. Deleuze’s distinction between the mathematics of the majority and the mathematics of the minority provides a powerful conceptual framework for explaining this transformation. Ultimately, the article shows that non-Euclidean geometry has implications that extend beyond mathematics. It challenges classical assumptions about identity, centrality, and fixed structure, and it opens the way toward a process-based ontology in which relations precede stable forms. Through this lens, geometry becomes a philosophical event: a reconfiguration of how space, individuality, and reality are thought.

Keywords

Gilles Deleuze

Mathematics of the Minor

Non-Euclidean Geometry

Ontology

Bernhard Riemann

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