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I'm certainly in the "love of the game" category of programmer. I honestly think that you have as many in math. And unlike computers, few people ever went into math to get rich -- so my internal estimate is even higher for the math side.
Side-topic: I think the programmers who are in it for just money are the ones that are going to get selected out. I've been at this for a long enough that when I started a programmer was a good white-collar job, but not one to get you rich. My experience, and frustration, with how the field has changed over the decades is that the quality of people has become absolutely dreadful outside of a few highly selective places. And even places like Amazon (where I spent some time) are compromised.
I get joy from many things. From tweaking things big and small. I don't think I ever really got joy from the act of writing code. It was always a means to an end. And the end doesn't have to be strictly useful. Something I've been kicking around for the past 35 years (also: crap... I'm feeling old) is an implementation of the Game of Life from John Conway who would fit in with your list perfectly. I came up with what I still think is the fastest way to play it with "normal" code in the general case. Using Claude I was able to get this implemented with a front-end that I can interact with. I get joy from the algorithm. Joy from thinking of low-level optimizations. Joy from learning more about the innards of how the processor I'm on handles cache lines.
I don't get joy from setting up a build system. No joy from setting up a front-end that runs on my Mac. Very little joy from tweaking an unrolled inner loop. Less joy from setting up unit tests.
Having AI lets me get to that joy. And it makes me incredibly happy. And it lets me paper over the parts I consider ditch digging.
My gut says that the folks in math want the same thing. Come up with an idea, and have something else handle the proof. There's joy in simply making something better or pushing the frontier a bit more.
And with AI, you can make bigger leaps. Ask bigger questions. Get more joy from discovery.
In case you're interested: https://github.com/gburgyan/vlife and a technical paper in docs that's more presentable.
There are absolutely people in math for other reasons than money, but among the countless mathematicians I've known very few have been motivated by anything that did not factor through being the first to prove/discover/define something that others care about.
That's the thing exactly. If, through using AI tools, you can be the first to prove something, isn't that a good thing? Only through discovery can we reach higher to ask bigger question. It took a lot of work as a civilization to get to the point where we had the language to construct things like the Navier–Stokes equation in the first place; they don't just get written down in a vacuum.
So we've gotten to a step change in the system. The real challenge will be to be the first the ask the question in the first place. Even if that is automated away, you're still left with the pure joy of learning and discovery which is rewarding unto itself.
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