Constructive Mathematics Day

Introduction

This all day meeting will take place on Friday December 9th in room G15 of the Newman Building of the School of Mathematics.

Follow the link for the Programme of the meeting

The meeting will consist of some invited lectures in the general area of constructive mathematics and its foundations. The meeting has been arranged at rather short notice and was sparked by the fact that both Nicola Gambino will be visiting Manchester from Montreal (with MIMS funding) and Peter Schuster will be on a visit from Munich (as a PhD external examiner). In addition I am very glad that Michael Rathjen (Leeds), Giovanni Sambin (Padua) and Steve Vickers (Birmingham) have also agreed to give talks.

Brands of constructive mathematics provide alternative approaches to the mainstream classical approaches to mathematics. Perhaps their most distinctive feature is the use of Intuitionistic Logic rather than the mainstream Classical Logic which takes for granted such principles as the law of excluded middle (A or not A) and the method of argument by contradiction (prove A by deriving a contradiction from assuming not A).
Brouwer's Intuitionism has been the most distinctive and controversial brand of Constructive Mathematics, having classically false theorems such as `Every total function from reals to reals is continuous'. Errett Bishop's approach to Constructive Analysis has been the most successful and straightforward, and moreover is compatible with classical mathematics. There are other brands of mathematics that use Intuitionistic Logic, two others being Russian Recursive Mathematics and Topos Mathematics.
Several settings have been put forward for presenting the foundations and development of one or other of the brands of constructive mathematics, three of them being the set theoretical, the type theoretical and the category theoretical. In the last few years it has become more and more apparent that these different settings can be understood to be just alternative views of the same subject and that the various brands of constructive mathematics along with classical mathematics can be understood as possible extensions of a significant common core.

The Constructive Mathematics day brings together researchers from varied backgrounds who share a common interest in the foundations and development of constructive mathematics.
There will be an introductory tutorial on Friday morning at 10.00, also in room Newman room G15, before the start of the meeting, on some of the topics that will be discussed during the meeting. This will be mainly aimed at interested students taking the course MT4171/5161. But others are very welcome to attend.

Peter Aczel (petera@cs.man.ac.uk)

Sponsors

This meeting was made possible by the support of MIMS and the School of Computer Science, The University of Manchester.