Learn English – the word for “victim” but with a positive connotation

In this context, maybe a phrase, such as well-studied would be good. It implies that the mathematical objects have been known for a while, but does not have any negative connotations (to me), nor implies great antiquity. I think it depends a lot on the context. Had you asked for a similar word to describe cheese, I'd have suggested aged or well aged, but I don't think that applies at all in this case. ;)

I re-wrote one of your sentences to not use the word "old". In the other two contexts, I honestly don't see anything wrong with it.

The Foo sequence is named after John Foo, but it is actually the same sequence as earlier discovered by Amy Bar in 1945.

Mentor or Motivator would work as alternative terms. (I like catalyst too)

Enabler picked up its negative connotation from psychologists. In relation to behavioral psychology it refers to someone who assists a person with self-destructive behavior - not just drug use, but addictions or negative behavior patterns of any kind. (Making excuses, assisting in covering it up, obtaining materials, etc). It's not technically a specifically negative term but at least in the US it's almost never used outside of the context of enabling addictions or other negative life patterns.