Contents
Next: INTRODUCTION.
Up: No Title
Previous: No Title
Over the last quarter Century and especially
during the last decade, a dramatic `re- experimentalization' of Mathematics has
begun to take place. In this process, fueled by advances in hardware, software and
theory, the computer plays a laboratory role for pure and applied
mathematicians; a role which in the eighteenth and nineteenth centuries the
physical sciences played much more fully than in our century.
Operations previously viewed as non-algorithmic, such as indefinite
integration, may now be performed within powerful symbolic manipulation
packages like Maple, Mathematica, Macsyma, Scratchpad to name a few.
Similarly, calculations previously viewed as ``practically'' non-algorithmic
or certainly not worth the effort, such as large symbolic Taylor
expansions are computable with very little programming effort.
New subjects such as computational geometry, fractal geometry, turbulence,
and chaotic dynamical systems have sprung up. Indeed many second-order
phenomena only become apparent after considerable computational
experimentation. Classical subjects like number theory, group theory and
logic have received new infusions. The boundaries between mathematical
physics, knot theory, topology and other pure mathematical disciplines are
more blurred than in many generations. Computer assisted proofs of ``big''
theorems are more and more common: witness the 1976 proof of the Four
Colour theorem and the more recent 1989 proof of the non-existence of a
projective plane of order ten (by C. Lam et al at Concordia).
There is also a cascading profusion of sophisticated computational and
graphical tools. Many mathematicians use them but there are still many who
do not. More importantly, expertise is highly focused: researchers in
partial differential equations may be at home with numerical finite element
packages, or with the NAG or IMSL Software Libraries, but may have little
experience with symbolic or graphic languages. Similarly, optimizers may
be at home with non-linear programming packages or with Matlab. The
learning curve for many of these tools is very steep and researchers and
students tend to stay with outdated but familiar resources long after these
have been superceded by newer software. Also, there is very little
methodology for the use of the computer as a general adjunct to research
rather than as a means of solving highly particular problems.
We are currently structuring ``The Simon Fraser Centre for Experimental and
Constructive Mathematics'' to provide a focal point for Mathematical
research on such questions as
``How does one use the computer
- to build intuition?
- to generate hypotheses?
- to validate conjectures or prove theorems?
- to discover nontrivial examples and counter-examples?''
(Since we will be offering a number of graduate student, post-doctoral and
visiting fellowhips we are keen to hear from interested people.)
Contents
Next: INTRODUCTION.
Up: No Title
Previous: No Title