Actually there has been a lot of research in this area. It's called automatic theorem proving. There have been some successes but not close to replacing mathema

Actually there has been a lot of research in this area. It's called automatic theorem proving. There have been some successes but not close to replacing mathematicians. If you compare it to chess then the computer programs are still at the beginner level. First year math students will be able to prove things that the computer cannot, yet. It's an intriguing area. Computer programs can perfectly well check whether a proof is correct, so in principle all you have to do is enumerate all "proofs" and pick out the valid ones. In practice the research is focused on doing this search more efficiently and intelligently.