finding articles that I liked

Sadly, I don’t think it’s possible. The like button is just to upvote what you think it is a useful question. It isn’t a way to bookmark a question for later.

If you want to keep up to date with new replies, the best way is to subscribe to the question. If you just want to find it later, then a normal browser bookmark is probably the best solution.

Looking at the API, there isn’t really a great way to retrieve someone’s list of likes. We’d have to query every question in turn and check if you had liked it or not.

We could do something like send an email when you hit the like button, to give you a record that way. The other way would be to list everyone’s likes in our own database, which isn’t an appealing idea to me. I’ll add it to my list of things to look into and see if we can do anything.

Mark