Deep Learning and Mathematical Intuition: A Review of (Davies et al. 2021)

Abstract

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.