Partial triumph or total failure?

Conclusion

These examples show that no conclusions can be drawn about the significance of a false proof even when it comes from the work of first class mathematicians.

Admittedly, Euler had the advantage that his work was studied by Gauss who, like Rumplestiltskin, could turn straw into gold and Stieltjes lived at the beginning of a period when interest in the Riemann zeta functions and the distribution of primes was high. Perhaps in the final analysis, the significance of an idea depends on the imagination and creativity of those dealing with it.