The relevance can be seen from the second link above (the review of the book) which highlights the essential points viz. the importance of Intrinsic vs. Extrinsic Motivation. It is short enough that you can easily go through it. Then apply it to understand why mathematicians are angry.
I don't understand why you can't just articulate the point yourself. It took me a while to guess what you were getting at. Could it be the quote:
Our egos are powerful things. They want to believe that we’re each better than we are, and we want to believe that we’ve mastered our chosen areas – that we’re the best. Whether that’s objectively verifiable or just wishful thinking isn’t the point. If we want to motivate people, we’ll give them ways to become masters or, at the very least, allow them to feel competent in what they’re doing.
In which case, yes, there is a loss of that source of motivation. And that's coming for us all - or rather it's coming for some of us in most professions. Most people are perfectly average in their chosen areas and never got the satisfaction of being at the top of their profession. Yet we still go to work. I imagine it will take some getting use to for Fields Medalists, but I think the average grad student that happened to just love mathematics and never aspired to be a medalist will still like doing math. Magnus Carlsen still became the best chess player ever even though AI's have been better than humans for decades now.
Most sources of intrinsic motivation are unaffected by these developments in AI. It may be the case that extrinsic motivations may be harmed by all of this if there's less money for mathematicians in the math community. The letter lists a lot of reasons to like how the math community does math, and I don't see any real reason they can't just keep doing math that way.
Honestly, I still don't understand the point you're trying to make. Or the realization you're hoping I'll have.
