> I want my AI to use all the advantages it has to reinvent the landscape of mathematics

The interesting thing about math, or science, and art in general, comparing it to games like chess or go is that science gives you the freedom to continue to excel as a human while in games we have lost the game and/or the league.

Science and art are infinite and no AI can produce infinity.

Sure but note that's not "your AI". It's a closed-source, proprietary system by DeepMind who typically publish a result to reap the hype and then bury the system forever (see AlphaGo).