Kekulé’s dreams are often cited as the paradigm of how scientific discoveries take shape in dreams. However, the chemist’s dream accounts of 1890 have been seriously questioned by recent authors arguing that he did not have the dreams at all, that they arose out of egoistic needs and that dreams were not the primary cause of his scientific achievements. This paper tries first to relate the story of the Kekulé dream controversy in the recent chemical literature, and second, to present a detailed refutation of two positivistically-biased anti-Kekulists. In a final part the author strongly argues for the view that creative achievements are instigated by dreams or forms of dreaming as the regular case. Spontaneous forms of consciousness try out in a groping manner possible solutions and present them to waking consciousness in sudden Eurekas. Positivists hating dreams as the source of scientific discoveries adhere to an outdated ideal of science and ignore their own creative wellsprings.