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What exactly does a mathematician do after PhD

I'm interested in pursuing this career because of my interest in Math. I know that this is usually a research position, but I was curious if there was anyone in this field that could give me more detail
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Great question! A PhD in math (in any subject really) consists of new and substantial contributions to the subject. A PhD student works with their advisor to find, solve, and communicate new ideas or solutions in the field. For the most part, one works toward a PhD to continue working in their chosen field - both via research, and teaching. This often means finding a job at a university where you will teach math courses to undergraduate students, be expected to continue publishing new research in your field, and engage in general departmental duties (hiring, committees, advising, etc). Depending on the university, there may be more of an emphasis on the teaching side or on the research side.

Many new math PhD students apply for what are known as "postdocs" - which are short positions (2-3 years) at another university where they teach fewer courses than a full professor, are able to work with new researchers in their field to continue research that stemmed from their dissertation, and to find new research problems to work on. With more publications to their name, the postdoc will be more attractive to universities looking for long term faculty compared to students who have just finished their PhD.

It's also possible for PhD students to find jobs in industry, outside of universities. Some fields of study can lead more naturally to industry jobs than others (statistics, financial math, applied math in general), but even students who have specialized in theoretical fields can find jobs like these. A math PhD can serve as proof that you are a logical thinker, able to quickly learn complicated ideas, and contribute in novel ways to a body of knowledge built up by like-minded and technical practitioners. When it's phrased like that, many companies could be willing to give a person like that a chance to think about their problems, even if they don't have industry-specific experience! The most popular places that come to mind are in the financial industry (banks, hedge funds), in government/research centers (see, e.g., and in software/tech companies (the most well-known are IBM or Microsoft research labs, but there are also opportunities which don't involve pure research at many companies).

For PhD students who find jobs inside of academia, their day-to-day likely looks a lot like their how they spent their days as PhD students (though likely with more teaching duties, and working more independently). For PhD students who find jobs in industry, their days really depend on the company/group they're in - and can range from pure research (similar to academia) or thinking about very specialized problems.

I hope that helps give you sense of the opportunities available to PhD students! I'm happy to answer any follow-up questions.

Source: I got a PhD in Math at Columbia, was an assistant professor in Math for 3 years, and then joined a couple of tech companies. I also regularly evaluate PhDs for jobs that we're hiring for.
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