[lubujackson]

Worth noting that mathematicians also argue over the art vs. science approach to math itself. Ask one what makes a formula "elegant", for example, can lead to some hand-waving that boils down to "you know it when you see it."

My take: the art is always about the human communication through the medium. As soon as programming is abstracted beyond the 1s and 0s, every choice represents a mental model for communicating intent from a human to a computer and by extension, from a human to a human. Writing "elegant code" is all about communicating intent to other programmers.

You can say the same about math - so much of the human-ness of math is backed into the symbols we use to represent things and relationships. Just think of the human impact of doing multiplication in Arabic numerals vs. Roman numerals and you can understand how math is totally a human construct.

But underneath it, the logic of multiplication is non-human and those that focus on that are the "science-minded" ones. But so much of our human understanding comes from the "art-minded" ones, for obvious reasons.

[Tainnor]

Mathematicians love arguing about which proof is the most elegant or most insightful, and which definitions are the ones that most captivate the essence of a concept (ask three mathematicians from different fields to define Euler's constant e, for example).

So yeah, there is very clearly a human and subjective element in mathematics, even when the results themselves are objective (modulo axioms and inference rules).