On Feb. 1, he drove to Boston to meet her. Both were extremely nervous. “Here’s this tall, beautiful girl that I’ve been talking to for weeks and 5 percent of her vocabulary I have to Google, so I’m kind of intimidated,” he said.

She said: “I had a crush on him and I hadn’t even met him. It made no sense.”

The two talked for nearly five hours. Remembering that date, she still sounds giddy, amazed to have actually experienced not just chemistry but love at first sight. “I was really attracted to him,” she said. “He looks like an actor. He’s 6-1 and very into physical fitness. He walks with confidence. He has these gorgeous dark eyes.”

In a way, their experience was not so different from that of an arranged marriage: After only a few meetings, both knew (but did not say) that they had found their spouses.

Even so, they continued to be formal and chaste in each other’s company. “Whenever we were ending our dates, she would almost put out her hand to shake mine,” he said. “One time, I just ignored it and opened up my arms and she hugged me.”

Dr. Shaikh introduced mischief and pranks into her very serious, organized life. Whenever they took walks around Boston, he would purposely lead her astray, for fun. “She has no sense of direction,” he said, laughing. “She’s oblivious to street signs. Even when she turns on the GPS on her phone, it causes more confusion.”

Ms. Naeem’s sister said, “Everything in her life has been very structured, and Rayhan is the one who disturbs that structure, in a good way.”