Of course a mathematician improves when gaining nowledge and understanding. The question is how fast that happens and how easily that can be applied in different contexts or how hard it is to even recognize when which fact might be relevant for solving a problem. Knowing something like conformal geometry algebra is useless if possible use cases don't become obvious unless you're just following some form of instructions by someone who does.

I wouldn't say this is a hard rule though as a fresh, unbiased mind can also lead one down an overlooked path with surprising results.

Well, there is the work of learning patterns, and then there’s the skill of matching patterns. In the mental model I have, the former yields improvements over time, while the latter probably declines with age. Of course, there’s also collaborations, strategizing (what to work on, when to call it quits, etc) that likely improves with time.

They improve at knowing mathematics, not raw pattern recognition ability.