  Nobel laureate Philip Anderson and Elihu Abrahams once stated that, "even if
machines did contribute to normal science, we see no mechanism by which they
could create a Kuhnian revolution and thereby establish a new physical law." In
this Perspective, we draw upon insights from the philosophies of science and
artificial intelligence (AI) to propose necessary conditions of precisely such
a mechanism for generating revolutionary mathematical theories. Recent
advancements in AI suggest that satisfying the proposed necessary conditions by
machines may be plausible; thus, our proposed necessary conditions also define
a moonshot challenge. We also propose a heuristic definition of the
intelligibility of mathematical theories to accelerate the development of
machine theorists.
