A number of journals appear to have frothed themselves into a moral panic over AI. There is certainly a lot of AI-generated crap appearing in multiple places, and the arXiv moderators are no doubt playing whack-a-mole trying to keep it down. On the other hand, other aspects of the profession continue on, unchanged.
I submitted a paper in January 2025 to TAMS. A number of my papers are long and technical, and I am not surprised that they take a long time to review. This paper, however, is both short and elementary. So it was somewhat surprising to me that it took over 16 months to receive a referee report. Out of curiosity, I also asked ChatGPT to produce a referee report. That took 30 minutes, and produced a far more substantial report than the one I had received. In addition to all of the more or less cosmetic issues addressed by the (presumably) human referee, ChatGPT also found non-trivial mathematical points that required addressing.
The most interesting correction, in my mind, was the following. At one point, we considered a lattice \(\Phi\) of rank \(d\) and chose successive minimal vectors \(\mathbf{v}_1, \ldots, \mathbf{v}_d\); that is, \(\mathbf{v}_1\) is a nonzero vector of shortest length, \(\mathbf{v}_2\) is a vector of shortest length not in the span of \(\mathbf{v}_1\), and so on. Then something happened in the paper which could be taken straight out of Serre’s talk on how “not to do mathematics”. Specifically, at some point it was assumed that these vectors generated the lattice \(\Phi\), but this was never stated. Instead; a claim was subsequently made that depended on this fact implicitly. The great thing about never mentioning something that you use is that you don’t have to prove it either, and in this case, when you are forced to actually think about it, it is easy to see that it is false! For example, \(\Phi\) could be the lattice \(\mathbf{Z}^n\) together with the vector \((1/2,1/2,\ldots,1/2)\). Such arguments are exactly a good way to slip something past a reviewer. To compound the issue, this was part of a section giving an alternate argument and was not used elsewhere in the paper. So the referee completely missed it, but ChatGPT did not.
As far as I understand the policy of TAMS, it would have been against the rules for the reviewer even to ask ChatGPT to look at the paper, let alone ask it to generate the report. But at least in this case — and I do stress this particular case — it would have been not only more time efficient by a factor of over 20,000, but also much more accurate and precise. I believe that literally the only comment made by the referee that was not made by ChatGPT was the recommendation to use the construction: Let \(k\) be an integer satisfying \((k,n)=1\) over the alternate Let \((k,n)=1\) be an integer.
There are many things in our profession which work quite well, and which AI threatens to make, if it hasn’t already, significantly worse. But there are many things in mathematics that are clearly broken as well. We should at the very least take the changes that will be forced on our profession by AI as a chance to finally address some of these lingering issues, many of which relate to what we publish and how we publish it, head on.