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I believe that building systems that can do mathematics is one of the most exciting frontiers in AI today.
There are a few reasons:
1 - Mathematics is entirely computational. That is, mathematics is a domain that can be explored without limit by purely computational means. The same can not be said about other domains of science. As a task for AI mathematics confers some of the same advantages that game playing provide. In particular, the possibility of producing infinite training data through exploration, analogous to self-play in adversarial games.
2 - If we think of mathematics as a game, it’s notable that the size and scope of it dwarfs even complex computer games. In some sense mathematics may is an infinite game. That is, there is no limit to the range of assertions in the various interconnected sub fields of mathematics that may be relevant to make progress on a given problem.
3 - Mathematics touches the real-world. Much of science and engineering is built on a foundation of mathematics. Building a system that could augment human mathematicians could accelerate intellectual progress in many fields, including AI itself.
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