People thought, back in the 17 century, that imaginary were useless (except as a trick for some calculations). Turns out the research into these numbers back then is amazingly useful today, 300 years later, in electronics and such.
Publicly funded maths research should continue, even if some taxpayers feel it's a waste of money.
However, with AI it actually may become so cheap that the scattergun random approach becomes more viable rather than less. It’s when human time and resources are scarce that you need to optimise. The hobbyist approach may therefore ironically continue, but without the hobbyists.
Thats great! So in other words it should be perfectly fine for AI to solve all of the supposedly useless math problems so that it might possibly be useful later. No need to worry about the mathematicians hobbies here.
of course not.
Hobbies can still be done even if AI gets it done more quickly. Just like today, where knives are made much faster/cheaper in presses and CNC machines, vs a blacksmith hammering. But still, there are hobby blacksmiths.
Note, I think the debate is mainly over what research should be funded, not whether any research should be funded.
In fact, the taxpayer should be funding fundamental research because it's so hard to justify profit from it - but that funding would benefit all in the long future.
So leaving the applied research that have commercial value be funded by private, commercial interests, would make more sense.