Every other field of study has more artsiness than Mathematics.
However, Mathematics also still has a lot of artsiness to it.
And remember what David Hilbert has told about one of his students who decided to go into arts instead of keep learning Math with him. He told "he did not have enough imagination to become a mathematician".
https://en.wikipedia.org/wiki/Experimental_mathematics
Worth googling too, a wide range of things come up:
We had mathematics long before we had physics.
So it is pretty obvious that physic is founded upon a liberal art - mathematics.
I disagree. People haven't had a Mathematics before Pythagoras. All Mathematics people had at that moment was that 1 golden coin + 1 golden coin = 2 golden coins or one copper knife. But trading is not mathematics if not talking about modern things like HFT with broad using of probability theory (and we obviously are talking about ancient times).
Physics is understandable even with way more simple (and way more ancient) species then humans. For example, an ape can take a stick and use more heavy end to make a more powerful hit. Birds seems to understand physics quite well - starting from setting wings while flying and ending to general intelligence of crows.
And BTW why are you concerned that in the pyramid of knowledge (Biology is a science > Chemistry is a science > Physics is a science > Mathematics is a language) there are three sciences and one a non-science?
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?
[Upon hearing that one of his students had dropped out to study poetry]
- David Hilbert
