Pattern recognition and the ability to construct, destruct and handle abstract structures in your mind IS the essence of IQ. Just have a look at the usual tests.

What people don't like, or even question, about this concept is the correlation between IQ and "intelligence" (whatever this is).

IQ seems to be mostly a genetic trait. Test results kind of normalize in grown up humans. Childhood experience gets less and less significant with age, which points to a strong genetic influence. (According to Wikipedia).

I think a lot of people actually don't like the implication arising here, as it points in the direction that you need to be born "smart" to be "smart" — and that you can't change mostly anything about that significantly no matter what you do.

Nevertheless there seems to be a difference how fast, or even if, one can reach "full potential".

IQ is just a trait, and without the right stimulus it won't develop quickly. This seems no different to other genetic traits after all.

I'm of course not going into the question whether IQ is a good, or even adequate, measure of "intelligence" (whatever this is), as this is a can of worms… At least it's quite sure not the full picture. One can for example excel at arts or sports without a high IQ.

> It’s not at all evident to me that pattern recognition is trainable to a high degree.

Wouldn't that mean that mathematicians do not actually improve during their careers outside of things like management and publishing?

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.