There's a single answer to that question: yes, math very much has an impact without humans in the loop.
Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.
t. low information voter.
If you tell someone they can't use a matrix multiplication with better asymptotic performance than n^2.3755 from 1990 they're going to shrug and not care.
You give your AI the problem, like 'make this computer program faster and more reliable', and it'll go off and do the math necessary to make it so.
For all we know, P vs NP will never be resolved neither by human nor AI, and the world will just keep turning.
I am saying that applications supplied and supply an inexhaustible amount of good problems and questions to consider. Purely theoretical concerns also supply some questions, but even if that well dries up for some reason, applications persist.
As the US has offshored manufacturing, the number of patents issued for those processes has fallen. Innovation occurs where the foundational understanding is applied; they arise from a desire to do the required work more efficiently.
Similarly in math, attempting to solve a problem leads to new questions. IF you actually do the work.
You need to have done enough of the work to know what the correct next question are, or you need to rely on AI for everything.