A Multidisciplinary Educational Path on the Concept of Infinity: The Traditional Way and the Contribution of AI
A Multidisciplinary Educational Path on the Concept of Infinity: The Traditional Way and the Contribution of AI

Summary/Abstract: Aim. This paper deals with an educational path on the concept of infinity, a fundamen- tal concept in mathematics and in every field of human theoretical and applied knowledge. The aspects of a traditional way are considered and compared to the possible contribution of AI. Methods. A possible traditional multidisciplinary path is presented and compared with the results obtainable through the use of ChatGPT and MathGPT. It starts from the definition of this basic concept, passing through the difference between potential and actual infinity, the concept of infinitesimal, and some paradoxes of the infinity. The analy- sis is then extended to physics, philosophy and art. Results. The traditional approach appears to be adequate and well-structured, with the possibility of interesting and fruitful additions; the approach through AI does not seem to add further positive elements, and brings with it inevitable underlying problems, relating to transparency, responsibility and privacy. Conclusions. The non-technical but rigorous treatment allows the use of this work as an interesting educational introduction to one of the most important concepts that the human being has always dealt with. At the same time, it reveals the unavoidable limitations of AI.

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