As we know, Arthur Winfree passed away a relatively short time ago. His memory motived us to investigate his great influence in the biomathematical development of one of the most important branches of Biological Sciences, i.e. the Chronobiology. In this paper we present the \textquotedblleft giants\textquotedblright, paraphrasing Newton, on whose shoulders Winfree stood up seeing farther about biological rhythms, as well as some of his contemporaries. We can appreciate Winfree's influence in the field observing that when he decided change his interest towards other fields, there appeared a certain fading in the number of people working in circadian rhythms from a mathematical point of view. However, the solid basements built by the founders of this branch of Science have allowed that nowadays not only high quality papers of biomathematical contents continue to appear in important journals, but also papers of pure mathematical problems inspired by circadian rhythms. In fact, the building of the interface of Biology and Mathematics has been reinforced in such a manner that both disciplines have mutually benefited. Finally, we present a section in which it is possible to appreciate a few articles that have appeared after Winfree.