> In the past, the path to a math Ph.D. cultivated resilience, resourcefulness, critical thinking, and a healthy skepticism (…) but suddenly you can produce a passable Ph.D. thesis with the push of a button

But actually nothing changed. Or maybe a path to "resilience, resourcefulness and critical thinking". Because human brains still needs to be shaped by years of training on some quality "literature", of some form.

We still must/want to human-[re]check important results, right ? And that require years of students time dedicated to memoizing facts and doing exercises in discovering already discovered results - learning and weights tuning, in the brains.

Yes, demotivator factor is very high or maybe just more visible then usual. Especially for brain paths forming - an that process is not quite stated in university and other education...

I think that when LLMs finish words and sentences shuffling and finds most of low hanging fruits in cutting edge of research ;) then only humans can move things forward, via abstractions, syntesis or old good paradigm abandoning. Hard to imagine LLM on their own "discover" something and then drops all that "literature" it was trained on as obsolote :) In next prompt it will happily return you old texts without any influence of just discovered paradigm shift.

In XIX century we got quite stagnation in science - it was belived that everything was already discovered, explained, just some few experiments are needed because some numbers do not adds up... And that proliferated to philophy and culture via some "proofs" for atheists. But in 1905 a paper was published... Too bad politicans do not get implications of that and still was pushing communism decades later...

So we realy want humans with brain pathways shaped mostly "old way" - the only one way available for human beings - by that training called "education". As always there is resistance and pain and attempts to find a shortcuts by cheating. Maybe this is time to clearly state that brain workings training is big part of education ? Just like in gym you are repeating to trying to lift weights up to your limit and even little above, with supervisor oversight.