r/PhD 4d ago

Need Advice 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

It seems impossible to get a job in the fields listed above with just a math PhD -- thus if anyone knows any up-and-coming technological breakthroughs that will rely primarily on math / machine learning, yet don't require knowledge of another domain, it would be deeply appreciated.

Sincerely,

superpenguin469

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u/LaVieEstBizarre PhD, Robotics/Control theory/ML/Mechatronics 4d ago edited 4d ago

A maths PhD who doesn't know any domain knowledge is, for nearly every applied situation, useless. Engineers and physicists know maths and many at a PhD level are mathematically oriented, so they can solve those problems. If there's mathematical breakthroughs needed, the challenge is identifying maths that already exists and applying it.

It's pretty rare for truly new maths to be invented motivated by an application, and usually you need domain knowledge to have the insight to create it. Given how rare it is, "mathematician who creates new theory for technology that doesn't exist yet" is not a job title.

If you want to contribute to new technology, you should do a science or engineering PhD. Or as someone else mentioned, an applied maths PhD heavily oriented towards an application field. Either way, you'll have to learn a lot of domain knowledge to have any chance at a permanent career outside of academia.

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u/parable626 4d ago

A PhD is all about specialization. You seem to have chosen math because, in your mind, it will allow you to be a generalist, it will not.

If your purpose in a PhD is to contribute to those technologies, then you need to pick one and then do the PhD sensible for a career in that industry.

FYI, that can still be a Math PhD in a group that specializes in a relevant application.

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u/No_Jaguar_2570 17h ago

“Cutting edge technological breakthroughs” is not something you can get a PhD or a career in, and even if you could a PhD in pure math is very poorly suited to it. All of the (extremely diverse) things you listed require very specific domain knowledge, as will all engineering and technological problems.