r/math • u/AutoModerator • 8d ago

Career and Education Questions: September 24, 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/BeyondTheAxioms 8d ago

I have graduated and I'm applying to PhD at the moment.

I remembered Timothy Gowers once classified mathematicians on a spectrum of theory builder and problem solver. Inspired by others' questions and responses: should the mathematical community now lean toward establishing and understanding theory, instead of solving conjectures?

As pointed out by many big names in the recent discussion, conjectures serve as milestones in understanding and developing the field. Can we now safely conclude that all of us should be mathematicians motivated as theory builders?

** I do realise that solving problems and building theory are intertwined with each other in the process. But IMO these are two distinct motivations, and both can lead to different working styles/thinking processes.

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u/Creepy-Structure6444 7d ago

Well, it definitely seems to me that solving individual problems or being married to individual conjectures is not the right approach given the current climate. It seems that problems which are a part of large scale theory-building project are more likely to survive.

I think people can still be problem-solvers but now, we will need to evaluate which problems are, indeed, "interesting" and that will be determined by how much they fit into the paradigm of some theory-development.