Anyway, this morning I happened to stumble across fionwe's post below, and the discussion about the old Aes Sedai who hadn't reached her full potential. Thought I'd post some thoughts on why/how that could happen.

Given how AS hierarchy is based on strength, the only logical reason I can think of for why any particular AS would not be motivated to reach her full potential is if she is already the strongest AS. Pretty much anyone lower in the strength hierarchy would have the motivation. Even if the person had no interest in being a leader in the WT, what they were permitted to do, and how effectively they could do it, would still be based on how high up in the hierarchy they were. So, they'd be motivated to reach full potential no matter what they wanted to do. Unless they were already the strongest known channeler.

As for why such a channeler wouldn't be pushed by teachers (as Accepted) or her Ajah Head (as AS) to reach full potential ... well, consider what might happen when someone comes to the WT with the potential to be stronger (and therefore, in their minds, greater) than any AS in recent history (within their lifetimes, say). The Tower isn't used to training such individuals - they don't have the experience to know how hard to push them. So they're cautious - they train slowly, to make sure they don't make any irreversible mistakes.

Eventually, the channeler (still not having reached full potential) passes the test for AS, and chooses an Ajah. At this point there's not much motivation for the Ajah Head to push for full potential, either. Partly for selfish reasons - why speed up the process of getting supplanted by someone greater than you? And if the channeler (already as strong as, or stronger than, anyone in the WT) has no political ambitions, and would prefer to go off adventuring on her own ... well, she's already the best-equipped AS to handle any threats to her well-being. And, being the strongest, she's also in a position to say "I don't care what you want me to do, I'm doing what I want to do".

And if such a channeler has angreal and ter'angreal at her disposal to use at crunch time ... well, again, there's not much motivation for her to reach full potential - she's plenty capable as-is.

The parallel to Elayne is clear, then. Elayne was said to have had the greatest potential of any AS in 1000 years, when she went to the Tower.

So in my mind, the most probable answer re who the mystery AS is ... should be glaringly obvious to anyone having read this post.