What do mathematicians teach us about the World ? An anthropological perspective

Abstract

The activity of mathematicians is examined here in an anthropological perspective. The task effectively performed reveals that, independently of their own representation, mathematicians produce in actuality a « virtual physics ». The principles of demonstrative proof as described and assessed by Aristotle, are first introduced, displaying a latitude in the demonstrative methodology open to mathematicians, with modes of proof ranging from the compelling to the plausible only. Even such leeway in the matter of proof has been felt at times by mathematicians as an intolerable constraint. The proof by reductio ad absurdum is shown to be by-passable and effectively by-passed by mathematicians. The calculus is examined which Morris Kline characterized both as « the most original and most fruitful concept in all of mathematics » and being plagued by a lack of mathematical rigor. The reason for this is that the world in its very build forced the calculus to be what it became, at times in contradiction with the mathematical code of practice. The mathematician enters the world of mathematics armed with his intuition of how the world at large operates. This he imports within mathematics and designs mathematical objects with an in-built « virtually physical » plausibility. The culture around him is impatient with mathematics which do not find their way to providing models. A double system of constraints, both inner and outer, contribute at making mathematics a « virtual physics ».