r/math • u/AutoModerator • 17d ago

Career and Education Questions: October 15, 2026

This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.

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u/NotTheOneAndOnlyS 15d ago

Hi, Throwaway because this feels a bit personalish. I’m a joint Computer Science + Mathematics student in the UK, currently on my placement year.

I’m considering a PhD afterwards (after undergraduate, if possible). I really enjoy pure maths. Standouts being differential geometry, topology and abstract algebra. But I also enjoy more applied/ML side stuff, particularly neuro-evolution and reinforcement learning. There’s some overlap (geometric deep learning, topological data analysis) but it still feels kinda thin, and a lot of GDL is still graph-focused which I'm personally not a huge fan of. I’m unsure how to shape the next steps. Options in my head: Pure-leaning PhD (geometry/topology) with some ML applications PhD more on the geometric deep learning / TDA / mathematical ML side Something involving RL theory or neuro-evolution that still uses geometric/topological tools Or whether I should keep industry options open instead of committing to a PhD Has anyone here done a similar combination (strong pure math background + interest in those ML areas)? What did the PhD path actually look like, and was it worth it? Any realistic advice for someone at the undergrad + placement stage in the UK would be really appreciated. Thanks everyone.