Will computers do mathematics?

Computers can now beat humans at chess and at go. Surely one day they will beat us at proving theorems. But when will it happen, how will it happen, and what should humans be doing in order to make it happen? Furthermore -- do we actually want it to happen? Will they generate incomprehensible proofs, which teach us nothing? Will they find mistakes in the human literature?

I will talk about how I am training undergraduates at Imperial College London to do their problem sheets in a formal proof verification system, and how this gamifies mathematics. I will talk about mistakes in the modern pure mathematics literature, and ask what the point of modern pure mathematics is.