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Isn't this more of an age thing? Mathematicians start out as problem solvers and later become theory developers?

As you age, it becomes harder to solve difficult problems but easier to develop theories due to greater experience.

I don't think so, based on historical evidence. At least it doesn't seem to be like before- and after-45 or other midlife age. From all great theory builders, we rather see like this age being closer to late twenties. They start out by solving some minor problems, often ambitiously taking the labourous technical ones, and then boom, out of nowhere new stage-setting theory, not necessarily much related to previous work. These frameworks open new hard problems which then are becoming mainstream, while frameworks that emerge by accretion of facts and experience hardly make such impact. I give Alain Connes as an example; man steadily, for most of his academic life i.e. last 30 years, outlines theories at a rate of one per two or three years.

Erdos was always a problem solver.

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