A video game for teaching the concept of a mathematical proof

Two students in my game development course would like, as a final project, to develop a video game for teaching mathematics. In contrast to the many other games for teaching maths, which focus mainly on problem solving, they want to focus on the concept of a mathematical proof, in particular: proofs of classic theorems in number theory, such as Euclid's theorem or the fundamental theorem of arithmetics. Students often find such proofs hard to learn due to their "infinite" nature: while any finite number of examples is not sufficient, there is a finitely-written proof that covers all infinitely-many cases. The difficulty is both in understanding the proofs and in writing their own proofs.

As an example in-game idea that might be used to illustrate these abstract concepts, we thought of a hero that must defeat a monster. The hero can shoot at the monster some special cases of the theorem (e.g. prime numbers), but this only slows the monster down temporarily. In order to defeat it completely, the hero must build an "induction machine" that can construct cases endlessly. There are many other proof concepts that should be considered.

My questions are:

• Are there video games that aim to teach the concepts of mathematical proofs (rather than just problem solving)?
• What are some research papers regarding the difficulties encountered by students in learning mathematical proofs?