It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.
It would be great if all mathematics had obvious utility, but that's demanding perfection. It doesn't mean mathematics would be worth doing if it had no utility. In fact, we often try to do mathematics in a way that guarantees some amount of utility; that's why we use proof-based methods in leu of wishful thinking.
Should I write a mathematics paper concluding "true = false" and argue that mathematics is not about utility? No. Such a thing is utterly useless, and it would be ridiculous to propose that I'm doing mathematics without taking the necessary care to ensure my work is useful.