Noether

Canon
Noelle and Aether are friends. Although they have not met outside of Noelle's Hangout Event as Noelle makes no appearance in any archon quests. In the current timeline, both of them haven't met. Only in the Hangouts Event. Although from Noelle's Hangout Event, Noelle does acknowledge Aether's existence and admires him.

Whisper of the Paper Rose
Aether agrees to Noelle's request, and asks where she wants to start. Noelle excitingly says she would like to get Aether's opinion on something, stating her daily routine. Aether says Noelle needs rest, however she says she still has work to do, though Aether says a true knight needs rest, finally convincing her. The two then head to Good Hunter, however Noelle is once again interrupted by someone. Noelle asks Aether for help, and he agrees to help. Noelle suggests they go to Majorie's store for items, and once they arrive, the two choose a gift.

Finally, after Noelle and Aether are done giving the gift to the person and recommending a location, Noelle wonders if Windrise isn’t popular anymore. However, Aether asks if she wants to go there with him. Which she is surprised by but agrees. Once they're there, Noelle gives Aether a rose, and he asks if she knows the meaning of a rose. She says she does, however is unknowingly wrong.

Quotes
"Whenever you need me, I'll be there."

- Noelle's voiceline "Chat: Being Reliable" "Please get some rest, you must be tired from today's adventure. I should head back to the Knights of F— Sorry? you want me to watch over you until you fall asleep? I—I... I mean, of course, it's no problem. But, um... You're not just teasing me, are you?"

- Noelle's voiceline "Good Night: "Since you're always so busy adventuring, there must be so many little things you never get round to, surely? Well, you need not worry about them adding up, because today, I am all yours — your exclusive maid for the entire day! Just leave it all to me! ...Also, I'd like to take this opportunity to wish you a very happy birthday!"

- Noelle's voiceline "Birthday"

Noelle's Birthday Mail
"I was in the middle of my chivalric training today when I received a bouquet of fresh flowers from the citizens of Mondstadt. Master Jean said that it was a token of gratitude from everyone and wished me a happy birthday. I don't expect anyone to repay me for my help, but I am moved that they remembered me because of that. I feel like I've improved a little compared to last year... But I'm still far from becoming your reliable shield. This is one of my dreams. I need to try harder for your sake! I can't wait to show you the fruits of my determination! Just wait until my next birthday!"

- Noelle's birthday mail "I haven't let up a moment in the past year. Whether as a maid helping those around me or in my daily training, I strive to be the best I can be. Still, there are times when I do feel like I can't go on anymore... At times like these, I look to the stars. The thought of you, far more brilliant than me, persevering somewhere under the night sky makes me feel like my fatigue is not worth mentioning. The day has finally come and it feels a little earlier than expected. I admit that I feel slightly nervous but not as much as I am excited. Now, I can finally show you the fruits of my labor. I hope you'll be here to see it!"

- Noelle's second birthday mail

Fanon
The ship Noether is not very popular among genshin fans, Noemine, the ship between Lumine and Noelle is much more popular. The ship began when some of the endings of Noelle's Hangout Event were leaked in the 1.4 update. When the Hangout Event released, many fans considered the Hangout Event as romantic, calling it stuff like "Noelle's Romantic Route" or a date. Noether rivals with Xiaother, Aether's most popular ship, and Barbelle, Noelle's most popular ship. On Ao3, they have only 34 works currently.

Fandom
ART