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.

翻译：Davies等人(2021年)最近发表的一篇论文(2021年)描述了如何利用深层次的学习(DL)技术找到可信的假设,这些假设导致了两个最初的数学结果:一个是结结结理论,一个是表述理论。我在此指出,DL技术应用于数学的意义和新颖性在所审查的论文中被大大夸大,并且在大众科学出版社的一些账户中被大肆夸大。在结结结论结果中,DL的作用很小,传统的统计分析可能已经足够。在表述理论结果中,DL的作用大得多;然而,它与数十年来在实验数学方面所做的工作没有多大的差别。此外,使DL技术在数学方面的应用变得有用的DL的显著特点是否适用于广泛的数学问题还不清楚。最后,我认为这里的DL“指导人类直觉”是没有帮助和误导性的;DL的主要作用是将许多可能的推测标记为虚假的,其他几个可能值得研究的。当然,这个表述结果代表DL对数学研究的原始和有意义的应用,但其意义更大。