The girl who never came back: New York socialite who vanished in 1910 is America's oldest missing persons case - here are the top theories about her disappearance

Dorothy Arnold was 25 when she disappeared from her Upper East Side mansion with today's equivalent of $1,000 on an icy Monday morning in December 1910. 

The eldest daughter of perfume importer Francis R Arnold left her jewelry and passport at home and strolled towards Central Park, never to be seen again, according to The Charley Project which tracks missing persons cases. 

Her disappearance has stumped detectives for more than 100 years, making her case the oldest recorded missing persons case in American history and what the Times has called 'one of New York's greatest mysteries'. 

'A hundred years later, I don't expect any kind of resolution,' Jane Vollmer, Dorothy's great-niece told the National Geographic last month. 

Full name Dorothy Harriet Camille Arnold, the socialite's last words to her mother were 'I'll telephone you' as she stepped out of their Manhattan mansion on East 79th Street. 

Arnold gave different accounts of her plans for the day to different people - telling one friend she was shopping with her mother, and her mother that she wanted to go by herself. 

She set off toward Fifth Avenue and stopped at the Park and Tilford's candy store where she paid for some chocolates using her father's credit card at 1.45pm. The clerk told investigators at the time that she had appeared to be in high spirits. 

Arnold went on to purchase a book at Brentano's on 27th and Fifth, before bumping into a friend who she chatted with for a few minutes, telling them she was headed for Central Park. 

Her mother waited to meet her for lunch at the Waldorf-Astoria hotel that day, but she never turned up. 

When she didn't return home that night, the family grew concerned. Fearing bad publicity from contacting the police, they hired a private investigator.   

Nonetheless, the case later prompted a flurry of media attention across America and Europe, along with a mammoth search mission involving the NYPD, private detectives and even the Pinkerton Agency. 

But no conclusive evidence ever emerged. Theories abound, ranging from abduction to voluntary disappearance, yet none provide a definitive answer to the question that has haunted generations.

One prevailing theory suggests that Dorothy may have met with foul play. As a young woman of privilege, she undoubtedly attracted attention from admirers, some of whom may have harbored less than honorable intentions. 

Investigators did uncover one piece of information - that Arnold had been secretly dating George C Griscom Jr., a Pittsburgh, Pennsylvania engineer in his forties at the time of her disappearance. 

He too heralded from a wealthy family. Police found that Arnold had spent a week with him several months prior to her disappearance. At the time, she told her family she was staying with college friends. 

On the way home from her secret visit, she also pawned $500 worth of jewelry for $60. 

Griscom is not a suspect because he was in Florence, Italy, in December 1910. 

He also joined the search party for her in Manhattan and said that he would propose to her once she was found. 

Another theory authorities looked into was that Arnold had faked her disappearance, but this was largely discredited over time. 

'Some people believed that Arnold took her own life; others theorized she had been pregnant and died in a botched abortion,' according to The Charley Project. 

But area hospitals were checked and Arnold was never found. Though the case has been closed for almost a hundred years, mystery continues to shroud the life of Dorothy Arnold.