What can Symbolic Computation Contribute to Mathematics?

Abstract

Symbolic Computation (Mathematics Subject Classification 2000, 68W30) is often treated as just another subject in the wide field of special topics within mathematics, on the same level as mesh generation (65L50) or quasi-Frobenius rings (16L60). Here we want to argue that actually Symbolic Computation is not so much a topic in mathematics, but a relatively novel approach to mathematical epistemology, a different and, as we believe, fruitful way of looking at mathematics and the acquisition of knowledge in mathematics.