His body was discovered at Giant Gate Falls on Wednesday, March 30, after an extensive search of the area.
Friend Tom Hanson, of Maryland in the US, formerly of Rangiora, said the news of Attenborough's death came as an "awful shock".
He described his friend as a really nice guy who was quiet but eager to learn about many different things.
The two of them attended a summer school together in Bulgaria to study maths, where Attenborough published a paper.
"I was really excited to see what he was going to achieve in his life. He seemed so full of potential," Hanson said.
Former University of Canterbury mathematics lecturer Liz Ackerley said Attenborough had excelled in the university papers he had taken while still enrolled in his last year at Wakatipu High School.
Attenborough was Wakatipu High's Dux in 2017 when he delivered "a wonderful valedictory speech", principal Steve Hall said.
"Hamish was an exceptional student, particularly in mathematics," said Hall.
"As well as Dux, Hamish was the Year 11 Top Scholar, and achieved scholarships in physics and chemistry and an Outstanding Scholarship in mathematics."
He also won the school's Crombie-Lockwood Trophy for knowledge, wisdom and perception, and achieved his Duke of Edinburgh silver award.
"Hamish will be fondly remembered at WHS - not only for his intellect and achievements, but as a person. Softly-spoken, kind and humble, one of his teachers described him as a 'top young man'," Hall said.
"Hamish's passing is very sad, and our thoughts are with his family and friends."
