Volume 34, 1998
Philosophy of Mathematics
The Issue of Experiment in Mathematics
The issue of the status of mathematical knowledge a priori or a posteriori has been repeatedly considered by the philosophy of mathematics. At present, the development of computer technology and their enhancement of the everyday work of mathematicians have set a new light on the problem. It seems that a computer performs two main functions in mathematics: it carries out numerical calculations and it presents new areas of research. Thanks to cooperation with the computer, a mathematician can gather different data and facts concerning the issue of interest. Moreover, he or she can carry out different "tests" with the aid of a computer. For instance, one can study strange attractors, chaotic dynamics, and fractal sets. By this we may talk about a specific experimentation in mathematics. The use of this kind of testing in mathematical research results in describing it as an experimental science. The goal of the paper is to attempt to answer the questions: does mathematics really transform into experimental or quasi-experimental science and does mathematics vary from axiomatic-deductive science into empirical science?