Spivak (Calculus, 3e, p. 39) writes:
Undoubtedly the most important concept in all of mathematics is that of a function---in almost every branch of modern mathematics functions turn out to be the central objects of investigation.
My question is: Would most mathematicians agree with this claim? (I'd like to be able to confidently quote this to high-school students learning about functions and calculus.)
Historically speaking, things really took off in analysis in the 17th century when the concept of change received a mathematical form with the development of infinitesimal calculus by the likes of Fermat, Barrow, Leibniz, and Newton. So possibly the concept of change is even more important historically than that of function which did not take center stage until the middle of the 18th century, and in its modern form until the middle of the 19th century.