Date & Time: Thursday, August 14, 2008, 15:00-16:00.
Venue: Ramanujan Hall
Title: Smooth Infinitesimal Analysis (SIA) - A Journalistic Report
Speaker: K. V. S. Prasad, Chalmers University
Abstract: The Continuous has challenged people at least as long as language has been around (how much as opposed to how many). Infinitesimals have been used as a way to analyse it since the beginning of Greek mathematics. As a practical tool for the Calculus, they were used by Newton, Leibniz, the Bernoullis and others, to derive correct results - see Thompson's "Calculus made easy". Yet, because they couldn't be accounted for in a logical way, they were driven underground - still used by physicists but not by mathematicians, for whom the nineteenth century limit method of analysis became orthodoxy.
But many modern mathematicians dislike lines made of points. Robinson's non-standard analysis and SIA are two formalisations of infinitesimal analysis, yielding calculus results by simple algebra.
This talk by an outsider merely alerts you to the existence of these fields, and to the pluralism that has been lost to orthodoxy. The main purpose of the meeting is to start a discussion.