Comment by adrian_b

Technological progress is bottlenecked by the fact that there are many mathematical problems for which currently there are no known practical methods of solution.

Because even with supercomputers the equations that describe many physical systems cannot be solved, research and development is still based on a lot of empirical methods, i.e. things must be physically built and measured, because mathematical computations cannot predict their properties with sufficient accuracy.

So if some miraculous algorithms would be discovered for the approximate solution of the systems of equations that are insoluble for now, that could accelerate technological progress a lot in certain domains, especially for the discovery of new materials or chemical substances with desirable properties.