Colóquio 

29/05/2001, 17:00 — 18:00 — Anfiteatro Qa2, Torre Sul, IST
John L. Bell, University of Western Ontario, London

The Rehabilitation of Infinitesimals in Mathematics and Physics

One of the most remarkable recent developments in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played a central role in the early development of the calculus and mathematical analysis. One of the most useful concepts of infinitesimal to have thus acquired rigorous status is that of a quantity so small (but not actually zero) that its square and all its higher powers can be set to zero. In my talk I will describe how infinitesimals of this kind can be used to develop the differential calculus and basic differential geometry. Time permitting, I will also describe the form that spacetime metrics assume in this approach.