"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.
There are plenty of very difficult math problems with practical application. Just because they don't interest some subset of academic mathematicians does not mean they don't exist. And you don't have to literally invent a field of mathematics to do valuable work applying it (and applying it may be difficult).
>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.
We do math mostly for fun.