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Or maybe we should not let pure mathematicians decide which problems are interesting, but reward the practical applications instead.

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This is wildly shortsighted view of mathematics. Historically many of the subfields of math which are presently most valuable were considered useless for decades or centuries. Number theory, non-Euclidean geometry, group theory, and Boolean algebra, to name a few.

This is false dichotomy. Many mathematical achievements were produced while looking at practical problems: Fourier is a good one. For every mathematician that accidentally made a practical contribution, there are many more that produced nothing of value, and would have with a better tuned reward function.

I guess this AI wave will divide the population more between people that think that only economic value exists, and people that dont.

Thats one of the timeless human debates.

We are now living in the perfect combo of low morality and general human automation. So i expect the next few decades dominated by people who think (and have a "proof") that doing something without an expected economic gain is useless.

If you only judge by practical applications you eliminate vast swaths of human endeavor.

Human endeavor and achievement does not make number go up for next quarter’s earnings

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