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Projects in pure math are basically just research. I would say just follow your curiosity and try to figure things out. You might not be scratching novel work for awhile, but its still enjoyable.

I don't know exactly what you like to work on, but perhaps theres some related mathematical area youre curious to know more about?

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To me, projects in math usually meant trying to apply it to model something or understand something/answer some question by finding a solution.

But that may be because my education always put the pure math and applications in close proximity.

Yeah I think that's basically the idea. Just solve whatever problems you find interesting via whatever means you can.

Eg Galois theory kind of looks like this: Applying an abstract model of symmetry to a model of polynomials to answer a question about solvability.

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