It depends on what you mean by fully formed. For example the idea of vectors and quaternions, which seem so natural, is quite new (~250 years old) [1] When max

It depends on what you mean by fully formed. For example the idea of vectors and quaternions, which seem so natural, is quite new (~250 years old) [1] When maxwell derived and unified electromagnetic theory, he didn't use constructs like the gradient and divergence of vector fields (those concepts didn't exist), instead performing those operations 'just' partial derivatives [2]. Sure, the math is explicitly identical, but the modern concepts of operators on vector fields that is so powerful just didn't exist which, to me, is rather telling about the evolution mathematical thinking: we are all doing the same thing (and have been for a long time) but way we think about it evolves with our notation. And notation that we are used to is actually quite new [1] https://www.math.ucdavis.edu/~temple/MAT21D/SUPPLEMENTARY-ARTICLES/Crowe_History-of-Vectors.pdf https://www.math.ucdavis.edu/~temple/MAT21D/SUPPLEMENTARY-AR... [2] http://rstl.royalsocietypublishing.org/content/155/459.full.pdf http://rstl.royalsocietypublishing.org/content/155/459.full....