Thurston (1994) describes mathematics as being recursively defined. Mathematical advancements help refine our thinking, and more sophisticated thinking leads to new mathematical concepts and structures. In other words, the content of mathematics contains what we can conceive of as “mathematics” at any given time: “The subject matter of mathematics changes to reflect how we think.”
Polanyi (1958), Personal Knowledge.
Mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting.
Related: Self-reference