This talk explores some surprising aspects, which perhaps may be called emergent behaviour, of the use of apparently simple-to-build software tools for mathematics. In particular, we look at some new insights which can be gained into old subjects when viewed through a computational lens. Depending on time and interest of the audience, the talk may cover elementary Riemann surfaces, linear algebra and analysis, and/or a new/old function now known as the Lambert W function. The talk will end with speculations on the effects of MathML and OpenMath, reasoning by analogy with what we have seen in the past decade for other subjects.