  Recent years have seen the dramatic rise of the usage of AI algorithms in
pure mathematics and fundamental sciences such as theoretical physics. This is
perhaps counter-intuitive since mathematical sciences require the rigorous
definitions, derivations, and proofs, in contrast to the experimental sciences
which rely on the modelling of data with error-bars. In this Perspective, we
categorize the approaches to mathematical discovery as "top-down", "bottom-up"
and "meta-mathematics", as inspired by historical examples. We review some of
the progress over the last few years, comparing and contrasting both the
advances and the short-comings in each approach. We argue that while the
theorist is in no way in danger of being replaced by AI in the near future, the
hybrid of human expertise and AI algorithms will become an integral part of
theoretical discovery.
