More than a quarter of a century after a gifted young mathematician was found dead at the bottom of a cliff in Sydney, his family hope their suspicions of a gay hate murder may finally be confirmed.

The NSW Coroner has ordered a rare third inquest into the death of Scott Johnson, a 27-year-old American student, whose naked body was discovered at the base of Manly's North Head in December 1988.

The first inquest, in 1989, ruled his death a suicide. But Johnson's family rejected that conclusion, and a private investigation which they funded in the mid-2000s uncovered evidence of gay hate gangs operating in Sydney in the late 1980s.

Their campaign led to a second inquest in 2012, which returned an open finding. The Coroner referred the matter to NSW Police's Unsolved Homicide Team.

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The family hope the latest inquest, expected to be held next year, will conclude that Johnson was murdered - and even identify his killers. "The perpetrators are probably still alive and local," said Johnson's brother, Steve, after a hearing at Glebe's Coroner's Court.

"I think this lights a fire under the people who committed this crime and thought they got away with it," he told Fairfax Media.

The NSW Coroner, Michael Barnes, said new evidence had come to light since the 2012 inquest, and it "could well lead to a different finding were it accepted".

The evidence is believed to relate to police interviews with former gang members who have admitted to carrying out violent attacks against gay men in the 1980s.

Johnson, who had moved to Australia from the United States to be with his partner and study mathematics, died on the day he was due to celebrate finishing his doctoral thesis. John Agius, SC, representing the family at this week's hearing, said there was "not a skerrick of evidence that would support the notion of suicide".

Agius also said a private investigation funded by the family had identified up to 50 possible suspects and five anti-gay "gangs or loose groups" operating in the Manly area at the time of Johnson's death.

NSW police have welcomed a third inquest. However, Unsolved Homicide Squad detectives said they did not expect it to reach a different conclusion from 2012.

Johnson's brother appealed for help. "I would call for anyone who knows anything about how the [gay] beats worked, how the violence worked, the gangs that roamed the northern beaches ... If you heard any of these stories, please come forward," he said.

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