Oh, but I have to add something to my own rambling above. I said "I play the piano because I like it, not because I want praise from anyone else". That is very true, but I have also been in the situation that there is a piano, maybe someone here can play a little? And I blush and say no, because I suck at memorizing and besides I cannot master ANY of my "project pieces" to such an extent that they are fun to listen at.
So there is the piano, and I feel that it would have been nice with a little tune here, yeah. Just to cheer people up, you know.
I discussed this with my teacher some days ago, when I proudly announced that I FINALLY have learned how to memorize pieces. She said something very clever: "you know, when people want to hear you play, they don't want to hear anything long and complicated. They want a short, easy-going little piece, why don't you learn a few of them?"
Indeed that was true. When they ask you to play, they don't really ask for the Hammerklavier Sonata. So she gave me two lovely little pieces, one page each, one by Mozart and one by Chopin. I will memorize them over Christmas and then have them "up my sleeve".
I realize it could have seemed depressing, what I wrote - it will take you a decade before you can study the real hard pieces. (And a lifetime to master them ...) But meanwhile, if you want to play not just for your own sake but also to be able to entertain people at the party etcetera, you can gain a little repertoire in a few months, maybe a year or so.
So let's not underestimate the short, easy pieces. It is good when you are "almost there" with Fantasie Improptu etcetera, but you may still find yourself in situations when people just want to hear you play Happy Birthday and Auld Lang Syne. If you can play them well, and on demand, people will definitely say you are good!