Perhaps true of the class of problems that are undecidable in, say, the Peano axioms / ZFC. However, there are many things these axioms can prove that are still useful! For example, the multiplicity of the totient function, applications of which power much of modern cryptography.

Riemann is so widely believed to be true that there are entire branches of mathematics dedicated to seeing what cool things you can learn about primes/combinatorics etc by taking Riemann to be true as an assumption.