Profundidad, estética y la actual filosofía de las matemáticas: un caso de estudio del teorema de Picard-Lindelöf

The aim of this manuscript is to offer the reader a general introduction to the concept of depth in mathematics, which has been largely absent from the philosophical literature in the Spanish language, and subsequently to propose an original formulation of depth grounded in the idea of bands of truth. The work is divided into three parts. After a general introduction to the topic of the article, an approach to the notion of depth is presented from the perspective of the mathematical state of the art, showing its existence and relevance, and reviewing the main problems and attempted solutions proposed by authors who have addressed this issue. Subsequently, a case study is developed in which the characteristics of depth are illustrated through the Picard–Lindelöf theorem. Finally, the article examines how this concept and the research surrounding it give rise to new indications concerning depth, in particular its understanding as an interdisciplinary relation, which may prove useful, interesting, and fruitful for contemporary philosophy of mathematics.