How to transition from pure math PhD to career in advancing technological breakthroughs

Hi all,

Soon-to-be PhD student who is contemplating working on cutting-edge technological breakthroughs after their PhD. However, it seems that most technological breakthroughs require completely disjoint skillsets from math;

– Nuclear fusion, quantum computing, space colonization rely on engineering physics; most of the theoretical work has already been done

– Though it's possible to apply machine learning for drug discovery and brain-computer interfaces, it seems that extensive domain knowledge in biology / neuroscience is more important.

– Improving the infrastructure of the energy grid is a physics / software engineering challenge, more than mathematics.

– Have personal qualms against working on research or cryptography for big tech companies / government

Does anyone know any up-and-coming technological breakthroughs that will rely primarily on math / machine learning?

If so, it would be deeply appreciated.

Sincerely,

nihaomundo123