Soft Question: Do most mathematicians agree that the function is "the most important concept in all of mathematics"? 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.)
 A: 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.
A: I remember that I was awe-struck the first time I saw the geometric definition of an ellipse turned into the equation $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2}=1$ after making a few "trivial" restrictions. In all of the years that I have spent teaching and tutoring, no one else has ever expressed to me that same elation. I think that you can demonstrate a concept, but not the importance of a concept. That is a function of time, experience, and hand-built paradigms.
A: A function has a precise meaning when working in a given mathematical framework.
But if you are working in Category Theory, you might prefer to never (directly) use the word function, highlighting instead the concepts of arrows and morphisms.
So, why go out on a limb and say that any concept in mathematics is the 'most important'?
If anything mathematics has evolved into a process that obtains results. Defining a function as part of that process is just a result of taking the journey. The thing that has become quite evident now is that this process is all about abstraction.
Many centuries passed without a precise definition of a function, and yet they were 'understood' in the minds of scientists and engineers and great advances were made in understanding physics and chemistry.
Today cosmologists use math to study black holes and the decade that is now passing into the history books is being recognized as the ‘golden’ decade for the study of these, um, concrete objects; see the PBS article
3 major moments from the ‘golden’ decade of black holes
Science Dec 27, 2019 4:33 PM EST
One can only ponder the momentous changes to mathematics as it 'assimilates' these discoveries and finds an abstract way of unifying the quantum mechanics/gravity realities of the universe.
