Geese are highly socially intelligent and have incredible memory but they lack complex problem solving skills like most parrots. They will learn names for things, to come when called, to go inside their shed/kennel/ barn for bedtime, the meaning of “NO,” and some simple tricks.
I had a gander “Pear” who learned to flap on command, and I’ve seen others teach their geese to turn around on command, beyond that other things get more complicated with how they figure out ways to do things. Two of my ganders “Paranip and his son Roxby” know how to open doors. They didn’t exactly work out how to do this all on their own, they don’t have complex problem solving brains like cockatoos, but they both spent time inside due to health reasons and they learned it by watching me do it over and over “memory.” The only thing that prevents them from actually doing it and coming inside whenever they please is that the door handle is a bit to high for them to have proper leverage to pull the lever down while pulling towards them, though it doesn’t stop them from trying.
They can also be stubborn though. They do things if they’re willing or there’s a good enough incentive. All goslings will automatically follow or come to you on command, that’s a survival instinct. Older geese still instinctively want to be with their flock members “goose or human” for survival reasons but it isn’t as urgent as goslings, and if they don’t want to do something they won’t. My goose Apricot is pretty good at coming to me when called, unless she has something she knows she shouldn’t and then she’s not only not going to come to me, she’s going to start running as soon as she knows I’ve spotted her “social intelligence + memory.”
Geese and other birds are amazing with social intelligence in that they can recognize their inability to do something and recognize that you as a human can do something that they themselves cannot, which is a trait not many creatures have besides us and dogs. Wild canids like wolves or coyotes can’t even do that. For example my geese will “ask” me for something. It’s hard to notice if you aren’t used to goose behavior but they’ll do it to the best of their abilities by walking or looking/pointing with their bill at a treat on a table or at the door they know their treats lie behind, then look at me, then back at the object of their desire, they’ll do this repeatedly.
Another example is if one of them needs help, is sick or trapped, sometimes the others will seek you out and scream until you appear, then lead you to where the other is. I’ve also seen ducks sometimes do this. “Social intelligence.”