TITLE: What advantage humans have over computers in mathematics?
QUESTION [56 upvotes]: Now that AlphaGo has just beaten Lee Sedol in Go and Deep Blue has beaten Garry Kasparov in chess in 1997, I wonder what advantage humans have over computers in mathematics?
More specifically, are there any fundamental reasons why a machine learning algorithm trained on a large database of formal proofs couldn't reach a level of skill that is comparable to humans?
What this question is not about
We know that automated theorem proving is in general impossible (finding proofs is semi-decidable). However, humans are still reasonably good at this task. I'm not asking for a general procedure for finding proofs but merely for an algorithm that could mimic human capability at this task.
Another caveat is that most written mathematics at the moment is in a form that is not comprehensible to computers. There do exist databases of formal proofs (such as Metamath, Mizar, AFP) and, even though they are quite small at the moment, it is conceivable that in future we could have a reasonably sized database. I'm not asking whether you believe that a substantial amount of mathematics will be formalized one day -- I'm willing to make this assumption.
Finally, there is the issue of the sheer machine power required to run this. Again, I'm willing to assume that we have a large enough computer to train an AlphaGo-style algorithm and then use reinforcement learning for "practice runs".

REPLY [2 votes]: What advantage humans have over computers in mathematics?

There is an active research in machine learning world, more specifically in NLP (natural language processing) that tries to answer contrary, and even more general question:

What computers can do, that we previously thought that only humans can do?

In my opinion the most interesting approach is an ongoing collaborative benchmark for NLP models called BIG-bench; it is just a bunch of tasks which you can test your model on, or test yourself (or your friends, family or foes)! What is important, you can also add your own tasks.
Regarding the OP question, you can browse the tasks by the keywords here. For example you can test if your model is capable to "understand" Mathematical Induction. You may ask it if the following is true:

1 is an odd integer. Adding 4 to any odd integer creates another odd integer. Therefore, 9 is an odd integer.

You can even "check" if you model is self-aware. Moreover, regarding @logicute answer, you can "measure" your models creativity in various of tasks.
So, can computers do math already or not?... It hasn't been tested carefully yet, but not yet perhaps. Will they?... To answer this question I believe we should keep track of the projects like BIG-bench.