I don't think any mathematician will agree with you on that (I'm a phd student in math). Examples (i.e. data) is foundational to a mathematical intuition which is a foundation of writing proofs. Drawing a line between the two would be ridiculous.
Data for mathematicians rarely looks like tables of numbers. More often it looks like a list of simple manifolds where we can do computations by hand, or topological spaces that don't have the usual properties, or fields of characteristic different from what you're most comfortable with, or continuous functions whose derivative is zero almost everywhere but are not constant. The first thing my advisor asks me when I say "I might be able to prove X" is whether it's true in the simplest examples.
Data for mathematicians rarely looks like tables of numbers. More often it looks like a list of simple manifolds where we can do computations by hand, or topological spaces that don't have the usual properties, or fields of characteristic different from what you're most comfortable with, or continuous functions whose derivative is zero almost everywhere but are not constant. The first thing my advisor asks me when I say "I might be able to prove X" is whether it's true in the simplest examples.