The small island is in the eastern Aegean Sea and lies around four miles off the coast of Turkey.
Mosley, 67, is well-known for co-authoring the 2013 book “The Fast Diet.” The plan, later known as the 5:2 diet, involved drastically reducing calories for two days a week while eating healthily on other days.
He later wrote another weight loss book, “The Fast 800.”
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An appeal for information about Mosley, together with a photo of him wearing a blue polo shirt and baseball cap, was posted on a local Facebook group Wednesday evening, saying that he had set off to walk back from a local beach at about 1:30 p.m. and “failed to make it home.”
Further updates on the post the following day said that a search and rescue team was sent from Athens “with drones and other more sophisticated equipment to extend the search.”
A police spokesman said that Mosley’s phone was found at his accommodation, according to the BBC.
Mosley’s disappearance also made headlines on Greek news outlets Friday, with one newspaper noting that the island had faced severe heat Wednesday. The BBC reported that temperatures on Symi had exceeded 40 degrees Celsius (104 Fahrenheit) that day.
According to his personal website, Mosley studied at the University of Oxford and worked as an investment banker before turning to medicine. He later joined the BBC as a trainee, and went on to work on science and history documentaries.
In 2002, he was nominated for an Emmy award for his work as an executive producer on the documentary series “The Human Face,” presented by Monty Python star John Cleese.
In recent years, he has continued to appear regularly on British television.
He and his wife, Clare Bailey Mosley, a doctor who created recipes for his Fast 800 plan, have four children.