Cops are investigating whether Martha Corey-Ochoa, who was valedictorian at her Dobbs Ferry high school, jumped to her death or accidently fell from John Jay Hall at 511 W. 114th St. and Amsterdam Avenue at 11 p.m.
She was pronounced dead at the scene, police said.
"Martha was passionate about mathematics and literature, and recognized as a very talented writer," Columbia Dean Kevin Shollenberger wrote in an email to students, the Columbia Spectator reported.
The email from school administrators informing students of the death offered grief counseling.
"The Columbia community mourns the loss of Martha Corey-Ochoa, a first-year student at Columbia College, and extends our very deepest condolences to her family and friends," said Columbia spokesman Brian Connolly.
During an orientation event Tuesday morning, students had a moment of silence for Corey-Ochoa.
"Everyone was just in shock," said Vivian Valiente, a 20-year-old junior at Columbia helping with orientation. "It's so early in the year."
Corey-Ochoa died on her second day at Columbia University.
"She was very excited" about starting school, Angela Singh, 18, a New Jersey resident said of Corey-Ochoa. "I saw the email. I felt really upset. She was the first person I met here.
"She was really happy to be here," she added.
Corey-Ochoa fell to her death from the 14th floor, where her room was located, authorities said.
Ryan Rodrigues, an 18-year-old from California, said he spotted the body while walking with four other members of his track team. Rodrigues said he ran across the street to St. Luke's Hospital in hopes of flagging a doctor or emergency worker.
"He performed CPR for five minutes straight," Rodrigues said of the man who aided Corey-Ochoa.
Students who had moved into the freshman dorm Monday said the residence hall was on lockdown before students were told to stay in a courtyard on campus.
Corey-Ochoa was valedictorian at Dobbs Ferry High School in Westchester. She told a local publication she planned to double major in English and math.
“I’m looking to get a Ph.D. and teach at a university,” she told The Rivertowns Daily Voice in June. “I’ll probably end up teaching mathematics, but I’d like to continue working in the English language and possibly publish some books of poetry."
Lisa Brady, superintendent of the Dobbs Ferry school district, praised Corey-Ochoa as a promising student who took advanced classes in her senior year and played violin in her school's orchestra.
"We are terribly saddened to tell you of the untimely death of one of our Class of 2012 graduates, Martha Corey-Ochoa," Brady wrote in a letter to the community. "A brilliant student and last year’s valedictorian, Martha had just begun her freshman year at Columbia University."