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Abstract
The paper offers a phenomenological analysis of mathematical beauty, starting from the concrete experience of mathematicians and their actual practices rather than from external or purely aesthetic interpretations. The authors argue that mathematical beauty cannot be reduced to a formal or subjective criterion, but emerges from a plurality of features—such as clarity, surprise, unification, and conceptual fruitfulness—which appear in different ways in proofs, theorems, and the construction of theories. Drawing on reflections by mathematicians such as Gauss, Hardy, Rota, Atiyah, and Mac Lane, and through examples taken from analysis, geometry, and probability theory, the paper highlights the cognitive role of beauty as a guide to understanding and as an orienting principle in mathematical research. In dialogue with Husserlian phenomenology and with contributions from Merleau-Ponty and Richir, beauty is ultimately interpreted as the expression of a style and of an internal “harmonization” within the symbolic institutions of mathematics, rooted in their historical and cultural dimension.