What evidence would convince you that mathematics is empirical?
If your argument was a tautology then what’s the point?
Would you consider interactive theorem proving to be empirical or not? The sort of experiment you perform is you try to see if the computer accepts your proof or not.
He is trying to erase the distinction when talking about mathematics specifically because it leads you to question your own biases.
Mathematics is neither liberal arts nor natural science.
Mathematics is a liberal art.
Mathematics is a natural science.
Mathematics is both liberal arts and natural science.
Which is the “correct” classification of Mathematics is the sort of pointless quarrel that happens at universities.
There is no right answer - the purpose is to argue and understand all biases/positions. The purpose is respectful human interaction around unresolvable differences.
Defining is what humans do.
To ask for a better definition of “defining” seems like a dead end question.
Perhaps asking why humans do what they do yields better answers?