Zachary Charles

I've seen this sentiment from several mathematicians, and it is understandable, but I feel it is also dangerously wrong. I say this because I think mathematicians need to adapt hard and fast, instead of wishing that the disruption from AI will somehow go away. There is a science to large language models and it predicts that with the linear scaling rate we are seeing now, capabilities will increase over the next 5 years at a similar rate as the last 5 years. To get a sense of what that means, one of the main benchmarks 5 years ago was GSM8K, whose questions you can see for yourself at huggingface.co/datasets/open…. There also seems to be a misconception that frontier labs are emphasizing math right now, and spending a lot on solving open math problems, in order to advertise the intelligence of their models. There was some truth to this 7-10 months ago, but that time has passed and most labs are now focused on coding agents. The continued improvements in math are largely a side effect. In the past, the path to a math Ph.D. cultivated resilience, resourcefulness, critical thinking, and a healthy skepticism. These qualities are still needed today, perhaps more than ever, but suddenly you can produce a passable Ph.D. thesis with the push of a button. This signals that the field needs to completely overhaul itself, starting now. My recommendation is that the future role of humans in mathematics, and similar theoretical fields, should be preserving and disseminating knowledge in oral and social forms; written papers will be the domain of AI. Over the coming months I will be involved in workshops that aim to produce more concrete proposals. But people need to come to terms ASAP with the fact that drastic change and compromise are needed to prevent the disenfranchisement of humanity from knowledge work.

I'm not so sure about the displayed isomorphism between (26) and (27), in the proof of your Theorem 7.1. The justification seems to be just a citation to Theorem 7.2.1 of arxiv.org/pdf/2306.04631, but if you go to that reference you only see a short exact sequence. GPT 5.6's confusion is understandable here, because the Theorem says "which is an isomorphism" after the exact sequence, an obvious grammatical mistake: (which map are they referring to?). But if you check the proofs, it appears to be the rightmost map to the Grothendieck--Witt group, not leftmost map \nu_{d,*}, which is an isomorphism. (For example, in the proof of the previous theorem it is explicitly stated that the map to GW is an epimorphism for j \geq d-3.) P.S. I think you should have quietly checked with experts before publicly declaring a counterexample on X. This is obviously not a venue for serious mathematics and it is highly prone to spreading misinformation, which is harmful for mathematics. P.P.S. Please nobody take this to mean that I am willing to check other AI generated solutions, or that any lack of comment from me represents failure to find an error. I just happened to be kind of interested in this one problem. I have not looked at any of the other claimed AI solutions posted on this website.