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I always recommend anybody wanting to learn a language should just start using it. Find a project and learn the language and libraries as you need them.

What's the equivalent for learning mathematics? A lot of mathematics seems only useful for learning more advanced mathematics.

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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?

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.

Write an optimizer or route finder.

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