  A recent paper by Davies et al (2021) describes how deep learning (DL)
technology was used to find plausible hypotheses that have led to two original
mathematical results: one in knot theory, one in representation theory. I argue
here that the significance and novelty of this application of DL technology to
mathematics is significantly overstated in the paper under review and has been
wildly overstated in some of the accounts in the popular science press. In the
knot theory result, the role of DL was small, and a conventional statistical
analysis would probably have sufficed. In the representation theory result, the
role of DL is much larger; however, it is not very different in kind from what
has been done in experimental mathematics for decades. Moreover, it is not
clear whether the distinctive features of DL that make it useful here will
apply across a wide range of mathematical problems. Finally, I argue that the
DL here "guides human intuition" is unhelpful and misleading; what the DL does
primarily does is to mark many possible conjectures as false and a few others
as possibly worthy of study.
  Certainly the representation theory result represents an original and
interesting application of DL to mathematical research, but its larger
significance is uncertain.
