The Quarterly is indebted toSciences, Paris, which originally published this paper under the title,Les Mathématiques et la pénsee créatrice,” inSciences, numéro 34, for permission to print an English-language version of Professor Zeeman's paper, and is indebted to Professor Zeeman himself for the English version itself. To keep as closely to the original as possible, the use of the first person instead of the third is followed, but the reference list has been rearranged inThe Quarterly's usual style.