# 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.