> I propose the following reconceptualization of the goal of a mathematics PhD: to become a world expert on some interesting, deep topic, and to be able to convey that interest and understanding to others. Part of operationalizing this might be a thesis, but the degree would be awarded primarily on the basis of a rigorous defense, in which the student explains the topic to their examiners until they are satisfied.

I think this is a refreshingly forward looking idea and I agree with it 100%, especially the the "rigorous defense" part. That is a good measure of how well the topic has been researched and understood by the researcher. This is where the humans can be "in the loop".

> How different would this look from current PhDs? I think students would still meet with an advisor, who might suggest a topic. That topic could be explored with AI assistance, or not, but the student would be responsible for understanding it; it might be much more open-ended and larger than the typical PhD is currently.

Interesting point about "more open-ended" and "...larger than the typical PhD". I think the author has a point. Earlier, the bottleneck was the candidate's/researcher's understanding and knowledge. Now with AI tools, it is so much easier to zero in to relevant knowledge, get your questions answered quickly which might lead to understanding more quickly.

For e.g., before the advent of public libraries and printing press, the knowledge was inaccessible and guarded. So that was the bottleneck.

Then books became ubiquitous and the bottleneck to knowledge and understanding was people's motivation AND knowledge of WHAT books and topics to research.

Then came the internet and free PDFs of books and research articles. Now, the bottleneck was still people's motivation and a mild version of what books and topics to research. I say "mild" because one can lookup articles and newsletters, and book reviews and come up with a list of reading.

Now comes AI and it looks like the only bottleneck is people's motivation.

I believe there was also a silent, yet potent, bottleneck all along which is also removed by AI: personal tutor/coach/teacher/professor etc. Let's say if I am reading a textbook on manifolds or some research paper and I have a question about a specific theorem or even a mathematical operator being used. Before AI my only way to get my questions answered was to read more books (PDFs or print), or ask on math exchange or math overflow and wait for someone to answer, or to ask a professor. This could take up to a week.

Now all of that has been cut down to 1 hour or less with an interactive chatting session.

!!!!!

So....the only bottleneck is people's motivation! QED

Exciting time!