"The field of mathematics" is something that humans engage in, chiefly to advance human understanding in about the most abstract way possible. It's not some self-sufficient, sentient being that exists for its own sake. Also, contrary to what's often repeated by AI maximalists, it's not a major source of innovation in other disciplines; most of the math the world actually runs on is hundreds of years old.

We do math mostly for fun.

>It's not some self-sufficient, sentient being that exists for its own sake

If humans didn't exist do you think a^2 + b^2 = c^2 would cease to be a thing? Math is built on top of logic and it is something that exists independent from the physical realm.