She soon bought her own bicycle, a black one with orange wheels (Princeton colors), and they began taking long rides around the city. “What really struck me about Sage was her ability to describe the world, not only her thoughts but our activities together,” he said. “I think that comes from describing things to her father. She allows me to see things differently and amplifies everything we do.”

Without exactly discussing it, they began living together. “It wasn’t a conscious decision to move in together or live together,” he said. “We wanted to be together so much that to not live together would be weird.”

She moved into his tiny studio on the Lower East Side, which at that time had three pieces of furniture: a large desk with a glass top, an uncomfortable modern chair and an uncomfortable bed. Yet she was perfectly comfortable there. “He has the most amazing, joyful way of going through life,” she said. “He sings and dances and laughs and runs the shower too long before he gets in.”

They even write together at the desk, which becomes the dinner table when they cook for friends, which is often. “They managed to live in this tiny room and create a marvelous social life together,” said Katrina Cary, an aunt of Ms. Mehta. “Sage would come back and say, ‘Oh, we just had this huge gang of friends over.’ ”

One of those friends, Eliza Gray, an assistant editor at The New Republic magazine, said: “You can always count on them to talk about something interesting, whether it’s yoga or an artist or something in history or a place or a song or even politics. They’re never dull. They’re both unique.”

Months after they moved in together, they went swimming in Maine. She sat on the dock deliberating and stalling, as is her way, while he dived right in.