A mature player might be reflexively defined as one who is individuated, who has "come to terms" with himself/herself in regard to music. Of course that state of mind is purely internal and might not be communicated to other people. Indeed, a happily "mature" player in this sense might seem three shingles short of a roof to other musicians. You might think of a few names but of course I couldn't possibly comment.
Thanks for your response, Ted. I suppose maturity in playing is linked to maturity in person (though I wonder if they actually go hand-in-hand ? ). I certainly don't mean to single out performers for the sake of singling them out, I just thought I could learn from examples of what people find to be mature or not.
If I were to try to define it, I suppose I would think of maturity in playing as being a mix of "musical maturity" as well as personal maturity. Now, musical maturity is an odd thing (not that personal maturity is not), I think, and something that can seem (or actually be) very subjective. I would say though, that it is linked to a basic knowledge about music and the personal ability to use that knowledge in a way that the performer decides.
For me, I think my own musical maturity is linked to knowing those things about music that I think are important to my goals as a musician. My goal as a musician is perhaps more holistic than the idea of standing on stage just to perform, and I suppose that's a good reason I can't seem to separate myself from both singing and piano (composition and teaching, too), when many people seem to think that only one should be seriously pursued. I think that musical maturity is linked to a holistic sense of music as well as the ability to express that sense in a personally satisfying way. I don't think that really says anything in particular though.
Not everybody feels the need to know the names of chords, for example, yet I wouldn't necessarily rule out a performance as immature, where the
function of chords is coherent (even if the names of them are not known). And then again, I think "function" can be a limiting concept, too !