Grense vir die wiskundige denke?

Inaugural--Department of Mathematics, Rand Afrikaans University, 22 October 1970@@In the evolution of Mathematics at least two mutations can be discerned: during the Greek era mathematics, which started out as a practical art, became a deductively organised science; during the second half of the nineteenth century a second revolution took place: mathematics became "abstract". In this latter development mathematics is seen transcending limits imposed on it during the previous two and a half millennia, notably the limits of linkage to physical reality, of rigid interpretability, and of truth. Drawing the consequences of this trend, the following conclusions are sketched: there exist no specifically mathematical entities or relations; mathematical thought should not be limited to results obtainable in some existing formal system or by some known constructive method; one should not try to cast final "foundations" for mathematical thought.