What are mathematics? Why has philosophy maintained privileged relationships with them since their beginnings in ancient Greece? The enigma of this relationship has never ceased to occupy philosophers and mathematicians throughout the centuries. Badiou attempts here to decipher it in a remarkably understandable way, combining pedagogical clarity and simple but enlightening examples. Avoiding equations and technical terms, he focuses on the purely conceptual dimension of mathematics and their involvement in the construction of philosophical discourse as an uninterrupted condition. He highlights that thanks to the rational concept of "proof," mathematics were the first form of thought to break free from the authority of religious transcendence, the dogmas of tradition, the enchantment of mythological narratives, and the revelation of truth - something that was absolutely necessary for the emergence of philosophy. From this perspective, he comments on the status of mathematics in the thinking of all the great philosophers from Parmenides to Wittgenstein.

For Badiou, mathematics are not a language of formalistic constructions but a form of thought. Mathematics are ontology itself, that is, the exploration and representation of all forms of multiplicity, "because everything that exists is a form of multiplicity," regardless of its material substrate. That is why the structures that describe mathematics are found in the most heterogeneous domains of nature and human experience. Weaving the praise of mathematics and philosophy, Badiou emphasizes the urgent need to heal the rift that modernity has brought to their mutual relationship.