ARTIFICIAL INTELLIGENCE AND THE PRODUCTION OF KNOWLEDGE

This article investigates the entry of artificial intelligence into the production of mathematical knowledge and examines the epistemological, methodological, and philosophical transformations that may arise from the participation of non-human intelligence in mathematical investigation. The analysis begins with the distinction between computational discovery, formalization, verification, and scientific recognition. It examines whether an artificial intelligence system can be considered merely a technological tool or whether, under certain conditions, it can participate in different stages of mathematical investigation, including the formulation of conjectures, exploration of mathematical structures, production of proofs, and identification of new questions. The article subsequently develops a distinction between technological utility and the expansion of human capability. Drawing on philosophical perspectives associated with Aristotle, John Dewey, Amartya Sen, and the capability approach, it examines the difference between technologies that primarily replace human activities and technologies that expand the possibilities available to human beings. The central conceptual distinction is expressed through the relationship: TECHNOLOGICAL POWER ↓ HUMAN CAPABILITY ↓ AUTONOMY ↓ LEARNING ↓ KNOWLEDGE ↓ ACTION ↓ ACHIEVEMENT Within this framework, artificial intelligence is examined not only according to what it can perform in place of a human being, but also according to what it makes possible for the human being to investigate, understand, create, learn, decide, and accomplish. The article proposes that the evaluation of artificial intelligence should therefore consider two distinct technological architectures: replacement and expansion. Replacement reduces human participation in a given operation, whereas expansion increases the space of possibilities available for human investigation and action. The same artificial intelligence system may contain both dimensions, depending on how it is incorporated into the investigative process. Mathematics provides the principal field of analysis because mathematical knowledge allows a clear distinction between computational production and mathematical validation. An AI system may generate calculations, explore conjectures, compare structures, identify relationships, assist in formalization, and produce candidate proofs. These operations, however, are distinguished from formal verification, interpretation, reproduction, and scientific recognition. The article proposes an investigative architecture in which the interaction between human and artificial intelligence can be represented as: HUMAN ↓ QUESTION ↓ AI ↓ EXPLORATION ↓ DISCOVERY ↓ VERIFICATION ↓ UNDERSTANDING ↓ EXPANDED CAPABILITY ↓ NEW QUESTION Under this model, the production of a result by artificial intelligence does not necessarily represent the end of mathematical investigation. A verified result may return to the human researcher, generate new understanding, expand investigative capability, and produce new questions. Knowledge production can therefore become a cyclical process in which artificial intelligence expands the mathematical space accessible to human investigation. The article also introduces the distinction between computational power and human potential. Greater computational power does not automatically imply greater human capability. The relevant question is whether the relationship between the computational system and the human being produces an effective conversion of technological resources into human capabilities. The central question developed throughout the article is therefore: When a non-human intelligence increases the space of possibilities of a human intelligence, should the relationship be understood as substitution of the intellect or as an expansion of its potential? The investigation concludes by proposing that the value of artificial intelligence should not be evaluated exclusively according to its immediate utility, its computational power, or the number of human tasks it can replace. It should also be examined according to its contribution to human understanding, autonomy, learning, investigation, creation, and knowledge production. In this sense, the article places the emergence of artificial intelligence in mathematics within a broader philosophical question concerning the future architecture of knowledge: whether artificial intelligence will primarily substitute human intellectual operations or contribute to the expansion of the space in which human beings can investigate, understand, and produce knowledge.