AIs haven't so far re-invented math because machine learning algorithms have no way to do symbolic manipulation directly - their results emerge statistically from the very large data set of human-generated inputs.

But you can't do math by clever guessing. You have to actually manipulate the symbols. Some of the hardest to help math students I ever tutored had this issue - they would just jump to an answer intuitively without showing their numbers, and they were right... maybe half the time. But they would not participate in the boring step-by-step grind the crank symbolic process it takes to get math calculations right every time.

Do I think this is instrinsically impossible for AI forever? Heck no! There's no reason that brand-new techniques won't be invented, or conceivably a breakthrough in statistical machine learning that somehow gets past this.

However, the techniques we have haven't gotten us anywhere close, and I don't believe they ever will.