Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be interested no matter how you did it.
But this isn't all of what they do, probably not even most of what they do. Like in software engineering, it's not always obvious which question would be the most useful one to ask. A lot of mathematical work also goes into what we call "theory-building", where you could say that primary work goes into coming up with definitions rather than theorems. Mathematicians also care a great deal about how something is proved; a lot of them are some of the most aesthetically picky people I've ever met. Words like "ugly", "beautiful", "creative", and "boring" are used to describe both definitions and proofs all the time.
From the outside, it can look like all they're doing is pumping out proofs at any cost. But I promise you that when I talk to mathematicians who don't have any experience building software, they have a similarly narrow view of that field as well! Both fields, from the inside, look a lot more human than you might expect.
Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled.
Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems.
To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon
But "what mathematicians care about" is much, much broader than what gets you published in a fancy journal. Mathematics as a human activity is millennia old, much older than the concept of journals or even universities, and that activity is, to me, very beautiful, worth preserving, and more of an art than a game. The incentive structure of academia for the past few decades has done a pretty bad job at preserving that art form, but that doesn't mean mathematicians as actual human beings don't care about it --- if they didn't, they probably would have chosen a different career.
Now, that still doesn’t help an LLM distinguish between good and bad correct proofs. But it still really helps a lot. On top of that, taste in proofs is a lot more uniform than taste in coding. That helps LLMs be better at judging the quality of a proof, because there’s less disagreement in the wider world.
(Although in general, there's no true difference between "I answered the question correctly, but the question was mapped to this thing we call 'reality' wrong", and "I answered the question incorrectly", because you can (try) adding the constraints that you really wanted targeted in case A, to case B, and boom, suddenly a question/answer pair that was "Answered correctly, but question doesn't map to reality" now becomes, "You answered this question wrong". However, individuals generally tend to have some breakpoint to differentiate between the two).
For example, create a DFA for a regex, not too bad just use Thompson's algorithm and then NFA->DFA. But now we have to care about efficiency, user API, maintainability of definitions etc.
Coding is more of a human problem than math
AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.