We are getting all of these new mathematical solutions generated with the assistance of AI. They get published on blogs, on X, and so forth. Many “serious” mathematicians are aghast. “They should publish in (human) peer-reviewed journals, so we know what is true and what is false.” The current peer-review model, I should remind you, is a recent invention from the second half of the twentieth century. We had the whole Scientific Revolution and the incredible first half of the twentieth century without it. How did you find out, in 1880 or 1920, that something “was true”? Same as always.
1.Youcheck it yourself. If you are capable of rerunning the experiments, you do. If it is mathematics, you read over the arguments critically. 2.Typically that is too expensive, so you rely on people you trust. Maybe a couple of famous mathematicians went over a proof and declared it correct. So you accept it as correct. Isn’t our peer-review model just step 2, but better organized? No. It is qualitatively different. Step 2 is inherently part of a marketplace. It is open. It is dynamic. So it is possible, for example, for a teenager to become known as an obsessive proof-checker even though that teenager has no formal credentials. And a highly credentialed individual who makes wrong decisions can eventually stop being a reference for many. Our peer-review model is not like that; it is closed. Notice what you do not see, typically, when you grab a “peer-reviewed” article: the list of people who vouched for it to be formally published. There are two mistakes that someone reviewing work can make. They can say it is great work when it isn’t. I cover this part. But a more important mistake is to reject work that is great. When Einstein published several breakthrough papers in 1905 he was a nobody, a clerk with no doctorate. Had he gone through our system, he would have needed to convince the old guard of his ideas. How would it have turned out? We don’t know. But it is entirely possible that the dissemination of his ideas could have been blocked for a time. And then there is the very nature of “good.” The current peer-review model is a dichotomy: it is either in or out. But there are no absolutes on this Earth. And it can sometimes take a long time for work to be understood as good or bad. The famous AI paper “Attention Is All You Need” is now viewed quite differently from when it appeared online. I am not sure most people reading it at the time understood what they had on their screen. Going back to the AI math breakthroughs: should they go through the established peer-review mechanism? You would hope that they would get a fair and fast review. You can pretty much forget about fast: it would take months or years. As for fair… here is the famous mathematician Doron Zeilberger: « Their “ideology” is not that nice. Human Mathematics got splintered into about 100 almost-mutually-exclusive fiefdoms, but with a clear pecking order, and with a highly dysfunctional system of peer-reviewed journals, some of them more “prestigious” than others. The more “prestigious” specialties and journals look down on the less prestigious ones. In sum, many mathematicians are “intellectual snobs,” dismissive of areas more concrete or applied than theirs. (…) In short, (many) mathematicians are not as “nice” as they seem from the outside, and their elitist-snotty-pretentious “ideology” would hopefully disappear with them. Let’s hope that computers will be both wiser and kinder practitioners of math. » Here is what I hope we will soon see. Math was never meant to be so divorced from reality. It just became difficult for the average engineer to pursued more advanced mathematical considerations. I believe that this might soon change. The excellent engineer might be able to break the state-of-the-art by building new math. That wouldbe exciting.Peer review is only as good as the peers. Since peer review determines who gets to join the peers, review communities tend to decline in the absence of additional oversight. Wikipedia and some social sciences come to mind