I think Gödel's Incompleteness Theorem puts the lid on finding out all of mathematics (there are infinitely many theorems). But we already have theorem-provers doing some pretty amazing things. You can pay to have a theorem named after you, for crying out loud. I believe Mathematica can do things people can't do, even given enough time....which leads me to the question "Can we construct an algorithm that, given the rules of math, teaches itself math and consequently arrives at solutions for problems currently unattainable for humans". Maybe not in this era but I certainly don't know that.
I am working on deep learning as well but as part of the Masters program. For those interested to see some battles between stockfish and AlphaZero watch this with some commentaryI work with machine learning on a daily basis in my day job, so I've really become interested in these types of projects. Neural networks have become absolutely amazing with regards to the types of problems they can solve. Stockfish has been the gold standard of chess for years now and AlphaZero actually calculated less potential moves than Stockfish on average. Instead it will search for patterns that lead to optimal outcomes.