Pippa Middleton and James Matthews joyously announced the arrival of their first child last month – but his name has a deeply personal and tragic significance.

On Monday it was revealed the fitness columnist and hedge fund manager named their son, born on 15 October, Arthur Michael William Matthews.

If the Mail on Sunday’s report is correct, then the couple has most likely chosen to pay tribute to James’ late brother, Michael Matthews, with one of their son’s middle names.

On 13 May 1999, Michael Matthews – known to friends and family as Mike – disappeared while descending Mt Everest and was never seen again.  At 22, he had become, at the time, the youngest Briton to reach the top.

Although the family, including James’ other brother Spencer, have accepted Michael died that day, the fact that the exact circumstances of his death remain a mystery has haunted them ever since.

The climb

Michael, who was just 18 months younger than James, was a financial professional by day, who loved the outdoors and had become an experienced climber.

Before taking on the worlds' highest mountain, the young man had scaled the Swiss Alps, the Pyrenees between Spain and France, and Mt Kilimanjaro in Tanzania.

As remains the case, Michael paid tens of thousands of dollars to obtain the permit he needed to climb the mountain, which he did with the company, Out There Trekking.

After his death, fellow climbers described how Michael had been leading the group the entire ascent, but on the day they were reaching the peak, he was the last to reach the top.

The group spent 20 minutes at the top before making their way down. But as they did, a wild snowstorm hit. It was within the area infamously known as the Death Zone that Michael was lost.

As the heavy snow and 160km/h winds hit, Michael became separated from the lead guide. Unable to find him, the guide continued to base camp without him.

His body was never found. He was the 162nd person to die on Everest.

His family's devastation

Michael's death hit his family hard.

Spencer Matthews, 29, who appeared on the UK reality series Made in Chelsea, wrote about it in his autobiography Confessions of a Chelsea Boy.

Just a child at the time, he spoke of his own grief, but also James'.

"James took the news badly," he said.

"With just a year and a half between them, he and Mike were the closest of friends. The loss was heartbreaking for James."

Spencer, who now has a two-month-old son, Theodore Michael, who too carries his fallen uncle's name, said that his brother's death was made tougher by all the unanswered questions.

"His loss was devastating for the family and over time this became worse because the circumstances surrounding Michael’s death have never been fully explained," he wrote.

"We have not been able to say goodbye in person. We have nowhere to go to sit with him. He lives on with us in our minds only."

Still, the family have found traditions that help them cope.

"On Mike’s birthday James and I send mum and dad red roses for the age he would have been.

"I guess our family’s way of dealing with losing Mike is to believe that he goes on with us.

"It’s just that he’s in another place."

James' father David Matthews spent years trying to see the trekking company held accountable for his son's death.

"Some will suggest that we're wealthy people who want to make people suffer for the death of our son," the wealthy landowner said in 2001.

"But our boy died, we've looked into the reasons why, as most loving families would do, and we believe this is a shocking tale of deceit, desertion and a cover-up."

A 2006 private prosecution he brought against the three men working for the tour group was dismissed by a judge, who said there was no evidence the men had been grossly negligent. The family maintained their belief that faulty oxygen systems may have played a role in Michael's death, though this was never proven.

Paying tribute to Mike

In the wake of Michael's death, his family decided to put their grief towards something positive and launched the Michael Matthews Foundation.

James, in particular, regularly carries out gruelling physical challenges, including the six-day 245.3km Marathon des Sables in 2008, to raise money for the foundation.

That money is then used on aid projects in developing nations, including building infrastructure and digital resources in schools as well as providing safe accommodation for girls.

Both he and Spencer have also paid tribute to their brother by giving their sons Arthur and Theodore the middle name 'Michael'.