Which came first, the chicken (mathematics) or the egg (science)? Did science spawn mathematics, or was it the other way around

Scientists sometimes needed to create new mathematics to solve some of their problems. At other times, the mathematics was already there just waiting to be used, although the use often had not been foreseen by anyone, until scientists noticed its relevance and applied it. The chicken/egg analogy is used to illustrate how it is often difficult to determine which came first. This is done by presenting several examples from the history of mathematics and the history of science from both points of view. Sometimes it does not matter that the mathematics we study has no immediate practical use. There may be, as history teaches us, unforeseen real world applications arising in the future, and this often must be left for others to discover at a later time.